Organized by: Yu Jin, Daniel Gomez, King Yeung (Adrian) Lam
Note: this minisymposia has multiple sessions. The other session is MS02-ECOP-1.

• Nancy Rodriguez University of Colorado Boulder (Applied Mathematics)
  "Animal movement"
A successful wildlife management plan relies on two key factors: (1) the understanding of driving factors influencing the movement of social animals and (2) the understanding of what movement strategies are optimal depending on the environment. In this talk, I will first discuss results from work focused on determining how some social animals, such as Meerkats, move. We present a non-local reaction-advection-diffusion model along with an efficient numerical scheme that enables the incorporation of data. The second part of the talk will focus on how directed movement can help species overcome the strong Allee effect on both bounded and unbounded domains. I will also discuss the connection to optimal movement strategies in the context of the strong Allee effect.
• Andreas Buttenschön University of Massachusetts Amherst (Department of Mathematics and Statistics)
  "Spatio-Temporal Heterogeneities in a Mechano-Chemical Model of Collective Cell Migration"
Small GTPases, such as Rac and Rho, are well known central regulators of cell morphology and motility, whose dynamics also play a role in coordinating collective cell migration. Experiments have shown GTPase dynamics to be affected by both chemical and mechanical cues, but also to be spatially and temporally heterogeneous. This heterogeneity is found both within a single cell, and between cells in a tissue. For example, sometimes the leader and follower cells display an inverted GTPase configuration. While progress on understanding GTPase dynamics in single cells has been made, a major remaining challenge is to understand the role of GTPase heterogeneity in collective cell migration. Motivated by recent one-dimensional experiments (e.g. micro-channels) we introduce a one-dimensional modelling framework allowing us to integrate cell bio-mechanics, changes in cell size, and detailed intra-cellular signalling circuits (reaction-diffusion equations). Using this framework, we build cell migration models of both loose (mesenchymal) and cohering (epithelial) tissues. We use numerical simulations, and analysis tools, such as local perturbation analysis, to provide insights into the regulatory mechanisms coordinating collective cell migration. We show how feedback from mechanical tension to GTPase activation lead to a variety of dynamics, resembling both normal and pathological behavior.
• Daniel Gomez University of Pennsylvania (Mathematics)
  "Multi-Spike Solutions in the Fractional Gierer-Meinhardt System"
The singularly perturbed Gierer-Meinhardt (GM) system is a model reaction-diffusion system used to study the pattern forming effects of short-range activation and long-range inhibition in biological systems. The singularly perturbed limit in which the activator has an asymptotically small diffusivity leads to the formation of multi-spike solutions in which the activator is strongly localized at discrete points. Using formal asymptotic methods we can obtain detailed descriptions of both the structure and linear stability of these multi-spike solutions. In this talk we will discuss recent work on the formal asymptotic analysis of multi-spike solutions to the one-dimensional fractional GM system in which both the activator and inhibitor exhibit Lévy flights. We will highlight how the singular behaviour of the corresponding fractional Green's function plays a crucial role in the asymptotic analysis of spike solutions and how, depending on the fractional order, this leads to direct analogies with spike solutions to the classical GM system in one-, two-, and three-dimensional domains.
• Yixiang Wu Middle Tennessee State University (Department of Mathematical Sciences)
  "Concentration phenomenon in a reaction-diffusion epidemic model with nonlinear incidence mechanism"
I will talk about our recent work on a reaction-diffusion epidemic model with nonlinear incidence mechanism. I will discuss about the global boundedness and existence of solutions of the model. I will show that the infected people may concentrate on certain hot spots when the movement rates of infected people are limited. The hot spots will be characterized by the coefficients of the model, and if the hot spots consist with a single point then the infected people concentrate as a Dirac Delta measure. Numerical simulations will be performed to illustrate the results.

Organized by: Yu Jin, Daniel Gomez, King Yeung (Adrian) Lam
Note: this minisymposia has multiple sessions. The other session is MS01-ECOP-1.

• Xingfu Zou University of Western Ontario (Mathematics)
  "On a predator-prey model with fear effect, predator-taxis and degeneracy in spatially heterogeneous environmen"
I will present a diffusive predator-prey model that includes fear effect, predator-taxis, spatial heterogeneity and degeneracy on some space dependent model parameters. I will report some recent results on local and global bifurcations of steady state solutions of the model system. This is a joint work with Dr. Jingjing Wang.
• Yu Jin University of Nebraska-Lincoln (Mathematics)
  "The influence of a protection zone on population dynamics"
Protecting native species or endangered species has been an important issue in ecology. Differential equations have been applied to incorporate protection zones in the habitat of species to investigate the influence of protection zones on long-term population dynamics. We derive a reaction-diffusion model for a population in a one-dimensional bounded habitat, where the population is subjected to a strong Allee effect in its natural domain but obeys a logistic growth in a protection zone. We establish threshold conditions for population persistence and extinction via the principal eigenvalue of an associated eigenvalue problem, and then propose strategies for designing the optimal location of the protection zone under different boundary conditions in order for the population to persist in a long run.
• Arwa Abdulla Baabdulla University of Alberta (Department of Mathematical and Statistical Sciences)
  "Mathematical Modelling of Reovirus in Cancer Cell Cultures"
Reovirus is a nonpathogenic virus that inhabits the enteric tract of mammals. It is a double-stranded RNA virus that showed the ability to naturally infect and lyse tumors under in vitro and in vivo conditions. Unmodified reovirus (T3wt) is currently being evaluated as an anti-cancer therapy in more than 30 clinical trials in different types of cancer such as metastatic breast cancer, prostate cancer, and colorectal cancer. Dr. Maya Shmulevitz from Li-Ka Shing Institute of Virology, University of Alberta and her PhD student Francisca Cristi focus in their laboratory to improve reovirus as a cancer therapy. In collaboration with them, we are trying to answer the following questions via mathematical modelling: How far does the virus spread depending on the binding rate? How does the viral invasion speed depend on the binding rate? How does reducing the binding rate affect the plaque size?
• Domènec Ruiz-Balet Imperial College London (Mathematics)
  "The tragedy of the commons via traveling waves in mean-field games"
The main topic of the talk is to observe mathematically the tragedy of the commons in spatial models. Garret Hardin, in 1968, exposed in his seminal paper, several situations in which the uncoordinated action of selfish individuals can lead to the depletion of a common resource, the so-called tragedy of the commons. We will consider a population model that consists of the most basic reaction-diffusion equations and we will formulate a harvesting game. Making use of a mean-field game (MFG) formulation, we will observe how the MFG “reversed” travelling wave solutions in the sense that, in the absence of players the population would invade the whole domain but in the aforementioned Nash equilibria the population gets extinguished. We will also briefly discuss other population models in which this situation arises.

Organized by: Kristina Wicke, Laura Kubatko
Note: this minisymposia has multiple sessions. The other session is MS04-ECOP-1.

• Hector Banos Dalhousie University (Department of Mathematics and statistics)
  "When Are Profile Mixture Models affected by Over-parameterization?"
Phylogenetic models of protein sequence evolution not accounting for site heterogeneity are prone to long-branch attraction (LBA) artifacts, especially when reconstructing relationships on a billion-year time scale. Profile mixture models have been developed to approximate protein sequence evolution on a billion-year timescale by considering a finite mixture of stationary amino acid frequency vectors. Recently there have been questions about such models being affected by over-parameterization. Notably, people have argued that over-parameterization can negatively affect tree topology estimation if many frequency vectors are considered. We demonstrate that this is not the case based on classical statistical results, extensive simulations, and empirical examples. Moreover, our results can be applied to other types of mixture models used in phylogenetics.
• Peter Beerli Florida State University (Scientific Computing)
  "Population genetics processes impact Species Trees estimation"
We investigate the effects of DNA mutation models, population growth, and gene flow on the power to correctly infer a species tree from genomic data. These inferences are complicated by the commonly used representation of the sequence data as single nucleotide polymorphisms instead of the full DNA sequences. This data representation choice reduces the potential variability in the data and biases parameters such as the effective population size of a species downwards. Methods that may work for species with small population sizes, such as primates, will most likely fail with species that have large population sizes, such as mosquitoes.
• Lena Collienne Fred Hutch Cancer Center (Computational Biology)
  "Spaces of Discrete Time Trees"
Many algorithms for phylogenetic tree inference navigate treespace to find trees that are optimal according to some criterion. Though some software packages aim to reconstruct a distribution of trees rather than a single best tree, there is a lack of tools to analyse such distributions or samples thereof. In order to develop statistical methods for analysing distibutions over treespace, different ways of defining proximity of trees in treespace have been proposed, each of which provides a different definition of a metric space containing all possible trees. These definitions of treespace depend on the type of trees considered, for example time trees where branch lengths represent times, which we will focus on in this talk. Gaining insights into the timing of evolutionary events is important in many applications including cancer and virus evolution, which is why some software, including the popular BEAST packages, infer phylogenetic trees with timing information. In this talk we will discuss why the choice of treespace (or distance measure) should depend on the application. In particular, we consider a definition of treespace for discrete versions of time trees, which have integer-valued branch lengths. Our definition of a metric space for trees is based on tree rearrangement operations that take times of internal nodes, i.e. evolutionary events in the tree, into account. Distances in these spaces can be computed efficiently, which leads us to discussing further properties of this distance measure and how it can be used in practice.
• Tandy Warnow University of Illinois Urbana-Champaign (Computer Science)
  "New methods for very-large scale maximum likelihood tree estimation"
Maximum likelihood estimation of phylogenetic trees is one of the basic analytical steps of many biological research projects involving evolutionary questions. With increasing amounts of sequence data, the interest in estimating large phylogenies, with up to hundreds of thousands, or even millions of sequences, is increasing. Yet these estimations are challenging, since maximum likelihood is NP-hard and standard heuristics (employed in leading software, such as RAxML-ng and IQ-TREE) are not designed for these ultra-large datasets. Recent work in my lab has produced alternative strategies based on divide-and-conquer for ultra-large maximum likelihood tree estimation that show potential to enable better results on very large datasets. Among these approaches are the 'Disjoint Tree Merger' methods (originally introduced by Erin Molloy) that operate in three stages: the input sequences are divided into disjoint sets, a tree is estimated on each set, and then the trees are merged into a tree on the full set using auxiliary information computed from the input. These Disjoint Tree Merger methods have strong theoretical guarantees (e.g., statistical consistency is maintained) and surprisingly good empirical performance on large datasets. In this talk I will present our progress using this approach on large biological datasets, and discuss future directions.

Organized by: Daniel Cooney, Olivia Chu
Note: this minisymposia has multiple sessions. The other session is MS04-ECOP-2.

• Anuraag Bukkuri Moffitt Cancer Center (Integrated Mathematical Oncology)
  "Evolution of Resistance in Structured Neuroblastoma Populations"
Neuroblastoma is a pediatric brain cancer of variable clinical presentation. The causes behind the initiation, progression, and ultimate resistance of this cancer is unknown, though it is recognized that two cellular phenotypes underpin its deadliness: adrenergic (ADRN) and mesenchymal (MES). How these phenotypes influence the eco-evolutionary dynamics of neuroblastoma cell populations (especially under therapy) remains a mystery. This is due to the confu- sion surrounding whether the ADRN and MES phenotypes represent different cell types (species) or cell states (stages in the life cycle of a single species). This distinction is critical in understanding and ultimately treating neuroblas- toma. In this talk, we will introduce theoretical methods to model the eco- evolutionary dynamics in state-structured neuroblastoma populations and use these models to tease apart cell type vs. cell state hypotheses. We will then expand and generalize this framework to continuous-structured models and discuss implications for cancer and bacterial resistance more generally.
• Olivia J. Chu Dartmouth College (Mathematics)
  "An Evolutionary Game Theory Model of Altruism via Arrhenotoky"
Arrhenotoky is a unique biological mechanism in which unfertilized eggs give rise to haploid male offspring, while fertilized eggs give rise to diploid female offspring. In this work, we build a mathematical model for the arrhenotoky replicator dynamics of a beehive by adopting an evolutionary game theory framework. Using this model, we investigate the evolution of altruistic behavior in a beehive, looking particularly at hive success over a variety of parameters, controlling for altruism in workers and the queen. We find that the most reproductively successful hives have completely altruistic workers that donate all of their resources to the queen, as well as a somewhat altruistic queen that donates a small proportion of her resources to drone bees. Through these results, our model explains in part the evolutionary adoption of altruistic behavior by insects with arrhenotoky reproductive dynamics.
• Nicole Creanza Vanderbilt University (Department of Biological Sciences)
  "Modeling and analysis of cultural evolution: insights from humans and birds"
Cultural traits—behaviors that are learned from others—can change more rapidly than genes and can be inherited not only from parents but also from teachers and peers. How does this complex process of cultural evolution differ from and interact with genetic evolution? In this talk, I will discuss the dynamics of culturally transmitted behaviors on dramatically different evolutionary timescales: the learned songs of a family of songbirds and the spoken languages of modern human populations. Both of these behaviors enable communication between individuals and facilitate complex social interactions that can affect genetic evolution. My lab's work on models and analyses of these two systems demonstrate that learned behaviors, while less conserved than genetic traits, can retain evolutionary information across great distances and over long timescales.
• Wai-Tong (Louis) Fan Indiana University (Mathematics)
  "Stochastic waves on metric graphs and their genealogies"
Stochastic reaction-diffusion equations are important models in spatial population genetics and ecology. These equations arise as the scaling limit of discrete systems such as interacting particle models, and so they are robust against model perturbation. In this talk, I will discuss methods to compute the probability of extinction, the quasi-stationary distribution, the asymptotic speed and other long-time behaviors for stochastic reaction-diffusion equations of Fisher-KPP type. Importantly, we consider these equations on general metric graphs that flexibly parametrize the underlying space. This enables us to not only bypass the ill-posedness issue of these equations in higher dimensions, but also assess the impact of space and stochasticity on the coexistence and the genealogies of interacting populations.

Organized by: Kristina Wicke, Laura Kubatko
Note: this minisymposia has multiple sessions. The other session is MS03-ECOP-1.

• Nathan Kolbow University of Wisconsin-Madison (Department of Statistics)
  "Sorting gene trees by their path within a species network"
Reticulate evolution has been identified in the phylogenies of many species, and several methods have leveraged gene tree topologies to infer these species networks. Such methods are powerful for inferring reticulate phylogenies at the species level but do not provide any insights for individual genes. Here, we present a statistical method for accurately comparing subsets of gene trees based on the unknown displayed species tree they belong to within a species network. The result is an algorithm that accurately groups gene trees based on the path they follow in the species network. The displayed species tree corresponding to each group can then be inferred, deducing where individual genes did or did not follow horizontal gene transfer events in their evolutionary history.
• Brandon Legried Georgia Institute of Technology (Mathematics)
  "Inferring phylogenetic birth-death models from extant lineages through time"
Birth-death processes have been used to study population growth, with broad-ranging biological applications such as identifying speciation and extinction rates, calibrating divergence times, and studying the dynamics of pathogens in infection trees. Recent theoretical work on phylogenetic birth-death models offer differing viewpoints on whether they can be estimated from lineages through time. Recently, Louca and Pennell (2020) demonstrated that time-varying birth and death rates are not identifiable from lineage-through-time data. This was a grave result, in view of thousands of published biological and computational studies that use this data. In this talk, I explain how identifiability can be restored, while re-focusing the discussion to what actually makes inference computationally challenging. This is based on joint work with Jonathan Terhorst (University of Michigan, Ann Arbor).
• Colby Long The College of Wooster (Mathematical and Computational Sciences)
  "Phylogenomic Models from Tree Symmetries"
Models of genomic sequence evolution often include a coalescent process since different sites may evolve on different gene trees due to incomplete lineage sorting. Chifman and Kubatko initiated the study of such models, leading to the development of the SVDquartets method of species tree inference. A key observation was that symmetries in an ultrametric species tree led to symmetries in the joint distribution of bases at the taxa. In this talk, we will explore the implications of such symmetries more fully, defining new models incorporating only these symmetries, regardless of the mechanisms that might have produced them. We will also discuss phylogenetic invariants for these models and how the invariants can be used to establish identifiability of the species tree topologies.
• Julia Chifman American University (Mathematics and Statistics)
  "Cancer evolution: mathematical models and inference methods."
The advent of single-cell sequencing provides the ability to model clonal evolution of tumors within individual patients. Inference of such within-patient tumor phylogenies has the potential to advance our understanding of the variation in the process of tumor progression. The process of tumor evolution has been reviewed extensively by many authors, with strong support for the view of a tumor as an ecosystem of evolving subpopulations that compete for space and resources in their microenvironment. Phylogenetic methods have been applied in numerous ways to model tumor evolution, for both bulk tumor samples and for single-cell data. For single-cell data, the data type considered in this presentation, these methods range from the use of inferred pairwise mutation orders to reconstruct the phylogeny to specification of a mutation model and possibly also an error model, from which either a likelihood or a Bayesian inferential framework can be adopted. This presentation investigates current models and methods and compares them to our method using both simulated and empirical data. We also compare the performance of methods using data simulated over a random phylogeny versus data simulated over a phylogeny constrained by the evolving tumor.

Organized by: Daniel Cooney, Olivia Chu
Note: this minisymposia has multiple sessions. The other session is MS03-ECOP-2.

• Abdel H. Halloway University of Illinois at Urbana-Champaign (Plant Biology)
  "Maintenance of mutualistic variation within and between species"
Mutualistic interactions present shared and unique properties at different scales, such as ecological and evolutionary collapse and nestedness. One notable aspect is the presence of variation in mutualistic interactions at various ecological scales. Here, I present theoretical analysis on the maintenance of mutualism variation within and between species. Within species, I analyze how competition between plants in a mutualistic plant-microbe relationship of resource trade may promote or hinder variation in the strength of mutualistic interaction. Between species, I examine how coevolutionary niche dynamics affects variation in mutualistic association and the resulting community structure. Within a species, competition may hinder or hurt variation depending upon its mechanism. Competition may lead to more coexistence between mutualists and non-mutualists, specifically at the expense of mutualism fixation, when plants compete over some microbially obtained nutrient. However, if competition reduces the carbon used for trade, then plant abundance, and therefore competition, weakens mutualism. Between species, mutualism acts as a hinderance to within-guild diversification. Species seek to affiliate with a single mutualist leading to collapse of interspecific variation, sometimes to a single mutualistic species pair. Despite this, drift can prevent the collapse and maintain community structure. Species showed heterogeneity in niche breadth with a few generalized species and several specialized species. This heterogeneity in degree distribution also resulted in properties like nestedness. Going forward, combining within and between species processes will allow us to explore the full potential variation in mutualistic interactions.
• Judith Miller Georgetown University (Mathematics and Statistics)
  "Modeling neutrality with climate data: the spread of the cabbage white butterfly Pieris rapae in North America"
A large body of theory has identified numerous factors that can play major roles in determining the speed and ultimate extent of range expansions. Among these are dispersal patterns, traits affecting fecundity, interspecific competition and adaptation or maladaptation to local environments. Yet few empirical studies establish the reasons for the range dynamics of particular species. We develop a detailed deterministic model of the initial spread of the cabbage white butterfly Pieris rapae in North America. We parametrize the model using climate and geographic data as well as physiological and life history parameter values from numerous studies of the species. The model does not allow for adaptive evolution. We find that the model’s output is a reasonable approximation of the recorded spread of P. rapae from east to west and from points of introduction southward. By contrast, no plausible parametrization appears to replicate the observed northward spread of P. rapae into Canada. These suggestive results point the way to a full understanding of our study species and a methodology that can be applied to other species and populations.
• Artem Novozhilov North Dakota State University (Department of Mathematics)
  "On a hypercycle equation with infinitely many members"
We formulate a hypercycle equation with infinitely many types of macromolecules. This equations is studied both analytically and numerically. The resulting model is given by an integro-differential equation of the mixed type. We present sufficient conditions for the existence, uniqueness, and non-negativity of solutions. Analytical evidence is provided for the existence of non-constant steady states. Finally, numerical simulations strongly indicate the existence of a stable nonlinear wave in the form of the wave train.
• Max O. Souza Universidade Federal Fluminense (Instituto de Matemática e Estatística)
  "Continuous approximations of fixation probabilities for large populations on star graphs"
We consider a generalized version of the birth-death (BD) and death-birth (DB) processes introduced in the literature, in which two constant fitnesses, one for birth and the other for death, describe the selection mechanism of the population. Rather than constant fitnesses, in this work we consider more general frequency-dependent fitness functions (allowing any smooth functions) under the weak-selection regime. For a large population structured as a star graph, we provide approximations for the fixation probability which are solutions of certain ODEs (or systems of ODEs). For the DB case, we prove that our approximation has an error of order 1/N, where N is the size of the population. This class includes many examples of update rules used in the literature --- including the so-called BD-* and DB-* (where * can be either B or D) processes.

Organized by: Amanda Laubmeier

• Rebecca Everett Haverford College (Department of Mathematics and Statistics)
  "Nutrient driven dynamics of ecosystem diseases"
Autotrophs such as algae play an essential role in the cycling of carbon and nutrients, yet disease-ecosystem relationships are often overlooked in these dynamics. The availability of elemental nutrients like nitrogen and phosphorus impacts infectious disease in autotrophs, and disease can induce reciprocal effects on ecosystem nutrient dynamics. We use a mathematical model to illustrate the impact of disease-ecosystem feedback loops on both disease and ecosystem nutrient dynamics.
• Mohammad Mihrab Uddin Chowdhury Texas Tech University (Department of Mathematics and Statistics)
  "Understanding Bsal Transmission Dynamics to Safeguard North American Salamander Populations"
Batrachochytrium Salamandrivorans (Bsal), a deadly fungal pathogen, is a significant threat to the survival of salamander populations in North America. It has led to the extinction of some salamander species in Europe and endangered others. Bsal's ability to spread through multiple routes with approximately zero recovery and high mortality underscores the crucial need for effective control measures. We developed a system of ordinary differential equations that incorporates direct and environmental transmission pathways across two spatial scales: aquatic and terrestrial environments. Alongside different routes of transmissibility, our study takes into account the environmental zoospore load, skin spore levels, population density, and temperature fluctuations. By simulating different scenarios and analyzing the results, the study aims to offer insights into effective control measures for reducing transmission and preventing epidemic outbreaks.
• Joshua C. Macdonald Tel Aviv University (Faculty of Life Sciences)
  "Forward hysteresis and Hopf bifurcation in a NPZD model with application to harmful algal blooms"
Nutrient-Phytoplankton-Zooplankton-Detritus (NPZD) models, describing the interactions between phytoplankton, zooplankton systems and their ecosystem, are used to predict their ecological and evolutionary population dynamics. These organisms form the base two trophic levels of aquatic ecosystems. Hence understanding their population dynamics and how disturbances can affect these systems is crucial. Here, starting from a base NPZ modeling framework, we incorporate the harmful affects of phytoplankton overpopulation on zooplankton - representing a crucial next step in harmful algal bloom (HAB) modeling - and split the nutrient compartment to formulate a NPZD model. We then mathematically analyze the NPZ system upon which this new model is based, including local and global stability of equilibria, Hopf bifurcation condition and forward hysteresis, where the bi-stability occurs with multiple attractors. Finally, we extend the threshold analysis to the NPZD model, which displays forward hysteresis with bi-stability, and examine ecological implications after incorporating seasonality and ecological disturbances. Ultimately, we quantify ecosystem health in terms of the relative values of the robust persistence thresholds for phytoplankton and zooplankton and find (i) ecosystems sufficiently favoring phytoplankton, as quantified by the relative values of the plankton persistence numbers, are vulnerable to both HABs and (local) zooplankton extinction (ii) even healthy ecosystems are extremely sensitive to nutrient depletion over relatively short time scales.
• Omar Saucedo Virginia Tech (Mathematics)
  "The impact of host movement on mosquito-borne disease dynamics"
Mosquitos are known for being a source of infectious diseases and are cause of great concern within the public health community. Throughout the world, there are a variety of mosquito species that are associated with different mosquito-borne pathogens. Diseases such as malaria have surfaced in areas where they previously have not been detected, and the incidence of these diseases have been steadily increasing. A better understanding of mosquito-borne pathogens is needed as this poses a severe threat to many communities. In this talk, we will explore how epidemiological and ecological features influence mosquito-borne disease dynamics via a multi-patch compartmental model.

Organized by: Alexander Browning, Sara Hamis

• Pierre Haas Max Planck Institute for the Physics of Complex Systems (Biological Physics)
  "Impossible ecologies: interaction networks and stability of coexistence in ecological communities"
Does an ecological community allow stable coexistence? In particular, what is the interplay between stability of coexistence and the network of competitive, mutualistic, and predator-prey interactions between the species of the community? These are fundamental questions of theoretical ecology, and, since meaningful analytical progress is generally impossible for communities of more than two species, they must be addressed statistically, as pioneered by May four decades ago. In this talk, I will thus show how we addressed this interplay between stability of coexistence and the network of interaction types by sampling Lotka–Volterra model parameters randomly and computing the probability of steady-state coexistence being stable and feasible in Lotka–Volterra dynamics. Surprisingly, our analysis, covering all non-trivial networks of interaction types of N less than or equal to 5 species, revealed 'impossible ecologies', very rare non-trivial networks of interaction types that do not allow stable and feasible steady-state coexistence. I will classify these impossible ecologies, and then prove, somewhat conversely, that any non-trivial ecology that has a possible subecology is itself possible. This theorem highlights the 'irreducible ecologies' that allow stable and feasible steady-state coexistence, but do not contain a possible subecology. I will conclude by showing the classification of all irreducible ecologies of N less than or equal to 5 species which indicates that the proportion of non-trivial ecologies that are irreducible decreases exponentially with the number N of species. Our results thus suggest that interaction networks and stability of coexistence are linked crucially by the very small subset of ecologies that are irreducible.
• Aminat Yetunde Saula University of Bath (Department of Mathematical Sciences)
  "Immune cell-bacteria interactions in tuberculosis"
Tuberculosis (TB) is the second deadliest infectious disease in the world after COVID-19, with over 10 million people infected yearly. Although the causative agent - Mycobacterium tuberculosis (Mtb) has long been known, TB bacteria are still able to evade protective immune responses. Herein, as a response to TB infection, immune cells self-organise to form TB granulomas and isolate bacteria within their structures. While TB granulomas are capable of slowing or halting the growth of Mtb, it also provides a survival niche from which bacteria may disseminate. Hence, an increased understanding of the disease in the lung where the bacteria primarily attack is needed. In this work, we integrate the mechanisms involved in immune cell-bacteria interaction in tuberculosis following an established hybrid individual-based model for the development of a continuum model counterpart. The continuum model consists of a system of partial differential equations (PDEs) describing the dynamics of TB granulomas. The numerical and analytical results of the model allow the determination of different conditions under which the infection clears early, stays latent, or progresses to active disease. Our findings are compared to the results obtained using the hybrid individual-based model, where differential equations are used to track the diffusion of molecules and the individual-based model component facilitates the tracking of cellular interaction, thus, allowing the study of localised spatial effects.
• Moriah Echlin Tampere University (Medicine and Health Technology)
  "Characterizing the Impact of Communication on Cellular and Collective Behavior Using a Three-Dimensional Multiscale Cellular Model"
Communication between cells enables the coordination that drives structural and functional complexity in biological systems. In both single and multicellular organisms, systems of communication have evolved for a range of purposes, including synchronization of behavior, division of labor, and spatial organization. Synthetic systems are also increasingly being engineered to utilize cell–cell communication. While research has elucidated the form and function of cell–cell communication in many biological systems, our knowledge is still limited by confounding effects from other biological phenomena as well as the bias of evolution. In this work, our goal is to push forward the context-free understanding of what impact cell–cell communication can have on cellular behavior at the cell and population levels. We use an in silico model of 3D multiscale cellular populations, with dynamic intracellular networks interacting via diffusible signals. To explore communication, we focus on two key communication parameters: the effective distance at which cells can interact and the threshold at which the signal receptor is activated. We find that cell–cell communication can be divided into six different categories along the parameter axes, three asocial and three social. We characterize behavior at both the cellular and population level and show clear shifts in behavior between the different categories of communication. With this work, we also highlight the surprising diversity and flexibility in the responses of different cellular backgrounds to the same communication conditions. Thus, we describe some of the effects that cell-cell communication can introduce to cellular populations which can be fine-tuned for function via engineering, artificial modification, or natural selection.
• Daniel Strömbom Lafayette College (Department of Biology)
  "Facilitating the emergence of collective biological controls to combat the spotted lanternfly and similar invasive pests"
The spotted lanternfly (Lycorma delicatula) is an emerging global invasive insect pest. Due to a lack of natural enemies in regions where it is invasive human intervention is required. Standard control measures have been extensively applied but the spread and growth of the population continues, and a recent study indicates that currently used approaches may be futile and suggests that non-standard approaches are necessary. Recently the idea of bird based biological controls has re-emerged and shown to be effective in a number of studies involving native birds and native pests. However, whether birds can be effective in dealing with invasive pests is unclear. In particular, if the invaders are occasionally toxic, it may take many generations before birds or other vertebrates will start contributing to controlling it naturally, if ever. Unless, perhaps, if the birds are effective social learners and the toxicity of the invaders is rare. For example, the Great Tit (Parus major) is an exceptional social learner and have been reported to eat lanternfly that have not fed on their toxicity inducing preferred host plant (Ailanthus altissima), but avoid eating them if they have. Here we introduce a simple mathematical model for social learning in a great tit-like bird to investigate the conditions for the emergence of a collective biological control of a pest that is occasionally toxic, like the lanternfly. We find that the relationship between the social observation rate and the proportion of toxic lanternfly effectively dictate when a collective biological control will emerge, and when it will not. We also implemented the mathematical social learning model into a spatially explicit model of collective motion in bird-like animals to investigate the conditions under which lanternfly eating would emerge in the simulated flocks as a function of lanternfly toxicity. We found that the spatially explicit model reproduces key predictions of the mathematical model over a range of parameters. Our work suggests that social birds may be useful in management of the spotted lanternfly, and that to facilitate the emergence of lanternfly eating communities of social birds, removal of the toxicity inducing preferred host of the lanternfly (Ailanthus altissima) should be a priority.

Organized by: Christopher Heggerud, Tyler Meadows
Note: this minisymposia has multiple sessions. The other session is MS07-ECOP-1.

• Alan Hastings University of California - Davis (Environmental Science and Policy)
  "Transient dynamics: the key to ecological understanding"
Much of classical ecological theory is focused on the long -term behavior of ecological models yet the time scales of ecological dynamics are such that a focus on asymptotic behavior is likely misguided. Ecological conclusions change in important ways when focusing on appropriate time scales. I will begin with some of my much older work that suggests the importance of transients and some of the challenges. I will then focus on more recent work, most of which has been done with a wonderful group of colleagues from a working group that began at NIMBioS. We have given a rough classification of features that produce transients similar to approaches for understanding dynamical systems, examined implications for management, and examined transients in systems where stochasticity is important. I will also consider related issues that arise when taking into consideration changing external conditions (global change) and the implications for ecological prediction.
• Rebecca Tyson University of British Columbia, Okanogan
  "Mutualism at the leading edge: Insights into the eco-evolutionary dynamics of host-symbiont communities during range expansion"
The evolution of mutualism between hosts and symbiont communities plays and essential role in maintaining ecosystem function and thus should have a profound effect during range expansion. In particular, the presence of mutualistic symbionts at the leading edge should enhance the propagation of the host and the overall symbiont community. Here we develop a theoretical framework that captures the eco-evolutionary dynamics of resource exchange between host symbionts and their dispersal in space. We provide quantitative insights into how the evolution of resource exchange may shape community strucure during range expasion. Parasitic symbionts receive the same amount of resources from the host as mutualistic symbionts, but at lower cost. This selective advantage is strengthened with resource availability (i.e., with host density), promoting mutualism at the range edges, where host density is low, and parasitism in the core of the range, where host desnity is higher. Host growth depends on the overall benefit provided by the symbiotic community, and is maximal at the expansion edges, where symbionts are more mutualistic. The expansion of host-symbiont communities is pulled by the hosts, but pushed by the symbionts. The spatial selection also influences the speed of spread. In particular, hosts with low dependence on their symbionts, or host-symbiont communities with high symbiont density at their core (e.g., resulting from more mutualistic hosts) or at their leading edge (e.g., resulting from symbiont inoculation) enhance the speed of spread into new territories.
• Susmita Sadhu Georgia College & State University (Department of Mathematics)
  "Methods for analyzing long transient dynamics in a three-dimensional predator-prey model featuring two timescales"
The leading role of long transient dynamics in ecological timescales can be very important in explaining regime shifts. However, analytical techniques for studying long transients in relevant timescales in three or higher-dimensional ecological models is still at its infancy. In this talk, I will consider a three-dimensional predator-prey model featuring two-timescales that studies the interaction between two species of predators competing for their common prey with explicit interference competition. I will consider two different scenarios in a parameter regime near {emph{singular Hopf bifurcation}} of the coexistence equilibrium point. In one case, the system exhibits bistability between a periodic attractor and a boundary equilibrium state, with long transients characterized by rapid small-amplitude oscillations and slow variation in amplitudes, while in the other, the system exhibits chaotic {emph{mixed-mode oscillations}}, featuring concatenation of small and large-amplitude oscillations, as long transients before approaching a stable limit cycle. To analyze the transients, the system is reduced to a suitable normal form near the singular Hopf point. Exploiting the separation of timescales and the underlying geometry of the normal form, the transient dynamics are analyzed. The analyses are then used to devise methods for identifying early warning signals of a large population transition leading to an outbreak or resulting in an extinction of one of the species.
• Tyler Meadows Queen's University (Mathematics and Statistics)
  "Evolution of persister cells"
Most β-lactam antibiotics, such as penicillin, function by disrupting membrane formation during mitosis. So-called persister cells survive antibiotic treatment by entering a semi-dormant state. These cells can be used to found a new culture of microorganisms that is equally susceptible to the antibiotics as the original culture. We investigate a model for the competition between two species of bacteria with different affinities for the persister type on both the population scale and the evolutionary scale.

Organized by: Christopher Heggerud, Tyler Meadows
Note: this minisymposia has multiple sessions. The other session is MS06-ECOP-1.

• Kara Taylor University of Florida (Department of Biology)
  "Simulating microbial metacommunities within the constraints of expected mean-variance relationships"
Taylor's Power Law (TPL) is one of the few established laws in ecology, applicable to both single-species populations and communities. The relationship between species abundance means and variances calculated across mixed-species aggregates is an indicator of joint species distribution. Additionally, TPL is useful for diagnosing instances of observed unusual population distribution. One such instance is sample saturation, in which the finite capacity of a sample unit is reached, variance declines, and the mean-variance relationship takes on an inverse parabolic shape. High-diversity systems like microbiomes are excellent for exploring the properties of community TPLs; however, their complexity obfuscates analysis of generating processes. Agent-based models are a useful tool in studying complex systems. In these bottom-up models, system-level properties emerge from numerous interactions in a set environment. By altering the processes defining interactions between individuals, one can change the state of an emergent property in a quantifiable way. In this simulation study, we use an agent-based model to test ecological processes that generate abundance mean-variance relationships observed in nature. The processes under investigation are dispersal, diversification, and ecological drift, parameterized as inter-host transmission, microbial speciation rate, and microbial growth under host growth conditions, respectively. The model utilizes a finite area (simulating a host gut, for example) for microbial occupancy, and as such, we expect to observe sample saturation. We find that, of the three processes parameterized, microbial dispersal between hosts alone acts to stabilize TPL towards expectation. In the absence of dispersal, sample saturation affects the TPL of rare species but not dominant species. This effect generates aberrant mean-variance relationships across the community that we tentatively interpret as Allee effects in the closed environment. In this system, dispersal may be stabilizing because it allows poor competitors to be rescued by neighboring populations, thereby alleviating positive density dependence.
• James Powell Utah State University (Mathematics and Statistics)
  "Homogenization across scales reveals relative strengths of environmental and direct transmission of Chronic Wasting Disease in deer"
Chronic Wasting Disease is an untreatable, fatal prion disease of deer and related species, spread both directly and by indirect contact with environmental reservoirs of the pathogen. Over the last twenty years the disease has spread across North America, and prevalence is approaching 40% in some highly impacted areas. The prion, a misfolded version of a naturally occurring protein, is very stable and remains infectious for years, even when exposed to ambient cold, heat and UV. However, experiments indicate that indirect transmission depends on exceeding a critical exposure. Thus the infectious landscape is sensitive to deer aggregation (and subsequent pathogen deposition) in desirable habitats, which vary on the scale of tens of meters, while home ranges are of kilometer size and some individuals relocate home ranges over tens of kilometers. We introduce a reaction-diffusion PDE model, including terms for pathogen deposition and critical environmental hazard to exposure. The model includes spatially explicit aggregation and the potential for developing prion hot-spots via an ecological diffusion model for deer movement. The technique of homogenization reveals emergent disease behavior on large scales, and the impact of critical exposure integrated across aggregating habitats appears as an Allee effect for disease prevalence. This raises the possibility that waves of disease are `pushed’ by the accumulation of prions in pathogen reservoirs, as opposed to being `pulled’ by the movement of infected individuals into regions where R0 > 1. In fact, parameter estimates show that the critical population susceptible density is almost always too high to give R0>1 via direct transmission. We tease out the relative contribution of indirect and direct transmission pathways for CWD spread in southwestern Wisconsin, USA, the epicenter of an outbreak which has been spreading among White Tail Deer for over twenty years.
• Chris Heggerud UC Davis (Environmental Science and Policy)
  "A model free method of predicting transient dynamics."
Transient dynamics are referred to as those dynamics that happen on ecologically relevant timescales, in which classical modelling techniques often fail to capture. Due to the ever changing environments and ecosystems, increased interest has been placed on the study of transient dynamics. However, many of the advances made towards understanding transients are fundamentally mathematical and beg to be connected to ecology and ecological data. In this talk I will show how uniting the underlying theory of dynamical attractors and empirical dynamical modelling we can understand when an ecological system is in a transient state based solely on ecological time series data. We further show that several metrics can be used to predict when a transient event is coming to an end. This work connects the mathematical literature on transient dynamics to the real-world application of understanding transients and short term changes in ecological systems.
• Punit Gandhi Virginia Commonwealth University (Department of Mathematics and Applied Mathematics)
  "Conceptual modeling of dryland vegetation patterns across timescales"
Strikingly regular, large-scale patterns of vegetation growth were first documented by aerial photography in the Horn of Africa circa 1950 and are now known to exist in drylands across the globe.  The patterns often appear on very gently sloped terrain as bands of dense vegetation alternating with bare soil, and models suggest that they may be a strategy for maximizing usage of the limited water available.  A particular challenge for modeling these patterns is appropriately resolving fast processes such as surface water flow during rainstorms while still being able to capture slow dynamics such as the uphill migration of the vegetation bands, which has been observed to occur on the scale of a band width per century.  We propose a pulsed-precipitation model that treats rainstorms as an instantaneous kick to the soil water as it interacts with vegetation on the timescale of plant growth. The model allows for predictions about the influence of storm characteristics on the large-scale patterns. Analysis and simulations suggest that the distance water travels on the surface before infiltrating into the soil during a typical storm plays a key role in determining the spacing between the bands.

Organized by: Yanyu Xiao, Xingfu Zou

• Daozhou Gao Cleveland State University (Mathematics)
  "Influence of Changes in Population Movement on Total Biomass"
How animal dispersal affects the total population abundance and its distribution in a heterogeneous environment is a fundamental question in spatial ecology. In this talk, based on a multi-patch logistic model with asymmetrical migration, we study the dependence of the global and local biomass on the dispersal intensity and dispersal asymmetry. In particular, the total biomass over two patches is either constant, or strictly decreasing, or strictly increasing, or initially strictly increasing then strictly decreasing with respect to dispersal rate. On the other hand, we develop a novel population model with both migration and visitation and show that the presence of visitation can substantially change the influence of population migration on population abundance. This is a joint work with Yuan Lou and Yutong Zhang.
• Xi Huo University of Miami (Mathematics)
  "Linking mosquito trap data with models: identifiability, fitting, and applications"
Aedes aegypti is one of the most dominant mosquito species in the urban areas of Miami-Dade County, Florida, and is responsible for the local arbovirus transmissions. Since August 2016, mosquito traps have been placed throughout the county to improve surveillance and guide mosquito control and arbovirus outbreak response. In this talk, I will show how we incorporate local entomological and temperature data in an ODE model, investigate the parameter identifiability, and fit the model to mosquito trap data from 2017 to 2019. The well-calibrated model can help us compare the Ae. aegypti population, evaluate the impact of rainfall intensity in different urban built environments, and assess the effectiveness of vector control strategies in Miami-Dade County.
• Marco Tosato Western University (Applied Mathematics)
  "Impact of deer migration on tick population dynamics"
Ticks are the carriers of several vector-borne diseases worldwide. In the past few decades, they have been spreading northward across Canada and have reached areas that were originally tick-free. In this talk, we explain how the interaction between deer mobility and tick population might have played a relevant role in this. In particular, we show using a coupled system of ordinary and delay differential equations in a two-patch environment how deer migration affects tick population dynamics and may modify their suitability for specific patches.
• Tianyu Cheng Western University, Canada (Department of Mathematics)
  "Modelling the impact of society precaution on disease dynamics and its evolution"
Afraid of infection, uninfected individuals may spontaneously protect themselves against infectors in varying degrees, depending on the severity of epidemics. As a result of adopting non-pharmaceutical inventions, people almost exhibit a uniform protection level without individual differences. We introduce a mathematical model formulated by differential equations to describe the severity of epidemics and group-precaution levels relying on the severity level during the epidemics. Our model describes that the group-precaution level mainly affects the severity of epidemics by directly adjusting the number of practically susceptible; In turn, the severity change of epidemics leads to the evolution of the group-precaution level. Mathematical analysis shows that when basic reproduction number is larger than 1, the endemic equilibrium exists and is subjective to a critical parameter that combines the initial protection level and the initial number of the infectious class. Considering the time lag in responding to the severity change of epidemics, we further extend our model, which is a system of delay differential equations. We figure out the condition that Hopf bifurcations occur by theoretical and numerical techniques.

Organized by: Mihrab Uddin Chowdhury, Lale Asik, Benito Chen-Charpentier, Christina Cobbold'

• Saikanth Ratnavale University of Notre Dame (Department of Biological Sciences)
  "Optimal controls of the mosquito-borne disease, Dengue with vaccination and control measures"
Dengue is one of the most common mosquito-borne diseases in the world, and a person can get infected by one of the four serotypes of the virus named DENV-1, DENV-2, DENV-3, and DENV-4. After infection with one of these serotypes, an individual will maintain permanent immunity to that serotype, and partial immunity to the other three serotypes. Therefore, there is a risk of getting infected by this virus a maximum of four times, and the symptoms may vary from mild fever to high fever, bleeding, enlarged liver, and severe shock, and sometimes these symptoms may lead to death. It is obvious that the increase in the number of infected individuals makes a negative impact on a country’s economy. Hence, the use of different control measures such as mosquito repellents and the introduction of a vaccine against the virus is important in controlling the spread of the virus. In this study, I am presenting a methodology on how to estimate the optimal rate of vaccinations based on the QDENGA dengue vaccine and the optimal rate of control measures to reduce the number of new and severe dengue cases while minimizing the overall cost. In addition, this vaccine claims high protection against symptomatic disease and waning protection over time for some DENV serotypes. However, the extent to which protection against disease conditional on infection is unknown. I consider different scenarios subject to the possible combinations of vaccine protection and control measures to investigate the most effective parameter values to control the transmission of the virus. Disease forecasts including the number of newly infected individuals in each serotype, the optimal rate of control measure, and vaccinations for a period of ten years are performed with the help of computer software.
• Damie Pak Cornell University
  "Resource availability constrains the proliferation rate of malaria parasites"
The life cycle of the malaria-causing species involves multiple rounds of replication, with a fraction of infected red blood cells (RBCs) being committed to producing specialized stages for onward transmission to vectors. The proliferation rate is limited by the burst size or the average number of daughter cells to emerge from each infected RBC. To increase transmission, parasites would be expected to evolve to the maximal burst size that does not prematurely end the infection by killing its host. The variability in observed burst size, however, suggests that maximizing the burst size is not always the best strategy.Using a within-host model parameterized for the rodent malaria, Plasmodium chabaudi, we investigate how host mortality and resource limitation affect the optimal burst size. We focus on the acute phase which encompasses the first and typically largest wave of parasite abundance with most of the parasite’s transmission success gained disproportionately in this phase. By calculating the cumulative transmission potential at the end of the acute phase, we can then compare the transmissibility of strains with varying burst sizes.We find that greater proliferation leads to the production of more sexual forms, but there are diminishing returns in transmission success. Moreover, the benefits of faster proliferation come at the cost of significantly shortening the period of high infectivity. Therefore, the optimal burst size emerges from the trade-off between the length of the acute phase and the production of the sexual forms. By identifying resource availability as a key mechanism limiting the burst size, we are better able to understand how parasite traits can influence the varying virulence we see in malaria infections.
• Gabriella Torres Nothaft Cornell University (Department of Mathematics)
  "Impact of Disease on a Lotka-Volterra Predation Model"
Quantifying the relationship between predator and prey populations under the influence of disease provides important insight into their roles and behaviors in the ecosystem. This paper uses two models as the base for the analysis: the Lotka-Volterra predation model and the SIR disease model. Developed in the 20th century, the Lotka-Volterra predation model provides a mathematical explanation of this phenomenon and is widely recognized in both the mathematical and biological communities . Epidemiology models such as the standard susceptible-infected-susceptible (SIS) model can be used to understand the dynamics of a disease in a given population or area. There are multiple variations of this predation and infection impacting the prey population, affecting the basic model, all focused on variations on the spread of some infectious agent in the desired population. To fully understand the regulatory mechanisms that the two populations go through, we need to analyze how both predation and infection impact the prey population, which in turn affects the number of predators. In this work, we first go through the dynamics of the original Lotka-Volterra model, then perform stability and further analyses on the combined model.
• Karan Pattni University of Liverpool
  "Eco-evolutionary dynamics in finite network-structured populations with migration"
We consider the effect of network structure on the evolution of a population. Models of this kind typically consider a population of fixed size and distribution. Here we consider eco-evolutionary dynamics where population size and distribution can change through birth, death and migration, all of which are separate processes. This allows complex interaction and migration behaviours that are dependent on competition. For migration, we assume that the response of individuals to competition is governed by tolerance to their group members, such that less tolerant individuals are more likely to move away due to competition. We looked at the success of a mutant in the rare mutation limit for the complete, cycle and star networks. Unlike models with fixed population size and distribution, the distribution of the individuals per site is explicitly modelled by considering the dynamics of the population. This in turn determines the mutant appearance distribution for each network. Where a mutant appears impacts its success as it determines the competition it faces. For low and high migration rates the complete and cycle networks have similar mutant appearance distributions resulting in similar success levels for an invading mutant. A higher migration rate in the star network is detrimental for mutant success because migration results in a crowded central site where a mutant is more likely to appear.

Organized by: Rebecca Tyson, Sarah MacQueen

• Sarah MacQueen University College Dublin (School of Agriculture and Food Science)
  "Model mechanism for choice of foraging site affects predicted pollination services"
Foraging constancy, or repeated return to the same foraging location, is an important aspect of bumble bee behaviour, and should therefore be an important consideration when using modeling to predict the pollination services provided by bumble bees.  However, it is unknown exactly how bumble bees select their foraging sites, and most modelling studies do not account for this uncertainty.  We use an individual based model to explore how predicted pollination services and bee fitness change under different foraging site selection mechanisms.  We considered two different site-searching methods (random and more realistic exploration behaviour) and four different site-selection metrics (random, minimal distance, maximal wild flower density, maximal net rate of energy return) in an agricultural landscape containing wildflower, crop (in bloom), and empty (no resource) patches.  We find that site-selection metric has a greater impact on crop pollination services and bee fitness than either site-searching method or landscape characteristics.  Site-selection based on maximising the net rate of energy return leads to both the highest crop pollination services and the longest foraging trips.  We find that the percent of crop fields visited, amount of time spent foraging, number of foraging sites located in crops, and the number of flowers visited may be used to determine how real bees select their foraging sites.
• Laurence Ketchemen Tchouaga McGill University (Mathematics and statistics)
  "Spatial steady states in fragmented landscapes under monostable and bistable growth dynamics"
Many biological populations reside in increasingly fragmented landscapes, where habitat quality may change abruptly in space. A reaction-diffusion model for a single species population which propagates in a heterogeneous landscape in a one-dimensional space is presented. The landscape is composed of two homogeneous adjacent patches with different diffusivities and net growth functions (monostable and bistable). A coupling interface condition between the two patches is involved. We consider various combinations of the reaction term and establish the existence, uniqueness and—in some cases—global asymptotic stability of a positive steady state. We classify the shape of these states depending on movement behaviour and clarify the role of movement in this context. We also give an answer to the following ecological question: how can the total population abundance at a steady state exceed the total carrying capacity? The analysis of the model with a bistable net growth function on one of the two patches yields a rich and interesting structure of steady states. Under certain parameter conditions, some of these states are amenable to explicit stability calculations. These yield insights into the possible bifurcations that can occur in our system. Numerical simulations reveal fold bifurcations.
• Katie Florko  University of British Columbia ( Institute for the Oceans and Fisheries)
  "Linking movement and dive data to prey distribution models: new insights in foraging behaviour and potential pitfalls of movement analyses"
Animal movement data are regularly used to infer foraging behaviour and relationships to environmental characteristics, often to help identify critical habitat. To characterize foraging, movement models make a set of assumptions rooted in theory, for example, time spent foraging in an area increases with higher prey density. We assessed the validity of these assumptions by associating horizontal movement and diving of satellite-telemetered ringed seals (Pusa hispida)—an opportunistic predator—in Hudson Bay, Canada, to modelled prey data and environmental proxies. Modelled prey biomass data performed better than their environmental proxies (e.g., sea surface temperature) for explaining seal movement; however movement was not related to foraging effort. Counter to theory, seals appeared to forage more in areas with relatively lower prey diversity and biomass, potentially due to reduced foraging efficiency in those areas. Our study highlights the need to validate movement analyses with prey data to effectively estimate the relationship between prey availability and foraging behaviour.
• Mennatallah Gouda Utah State University (Mathematics and Statistics Department)
  "Characterization of the long-distance dispersal kernel of white-tailed deer and evaluating its impact on chronic wasting disease spread in Wisconsin"
Chronic Wasting Disease (CWD) is a fatal untreatable neurodegenerative disease that infects cervids. It is highly contagious and caused by abnormal malfunction and assembly of the normal cellular prion proteins (PrPC) into aggregation-prone prions (PrPSc). Centers for Disease Control and prevention (CDC) report that the prevalence of CWD in free-ranging deer in the US is still relatively low. However, in several states the infection rates exceed 1 deer in 10. Cervids may uptake CWD prions from direct interaction with infected individuals or from the environment. Infected individuals shed prions into the environment through feces, urine, saliva or carcass, and long-distance dispersal of infected deer poses a danger of spreading CWD to new regions. We propose an Integrodifference Model (IDE) to capture CWD dynamics and the consequences of long-distance dispersal behavior of White-Tailed Deer (WTD, Odocoileus virginianus). Currently there are no dispersal kernels available to describe the long-distance dispersal behavior of WTD juveniles. Our aim is to characterize long-distance dispersal of WTD juveniles and assess how it may affect CWD spread. We introduce a long-distance dispersal model, based on a diffusion-settling seed transport by vertebrates, accommodating a variety of hypothetical dispersal behaviors of WTD. Four kernels were obtained by solving 2D diffusion-settling Partial Differential Equation (PDE) models and approximating using Laplace’s method. We parameterized the kernels with GPS collar data collected in Wisconsin, US. Using a Maximum Likelihood Estimation (MLE) approach, we fitted the model parameters, and assessed model fits using the Bayesian Information Criterion (BIC). Sensitivity of results was determined using nonparametric bootstrapping and the impact of long-distance dispersal on CWD spread was quantified using the IDE model. A Holling type III settling rate function resulted in the most supported long-distance dispersal kernel reflecting deer preference to not settle down soon after they start dispersal. Our results will assist CWD management facilities in controlling disease spread.

• Brendon McGuinness McGill University
  "Optimization of resource consumption traits shape community structure and the strength of niche and neutral processes in competitive communities"
Resource competition theory has overlooked the feedbacks that emerge from organisms shaping their environment through resource consumption, which in turn, shape plastic changes in traits in direct response to environmental variation. Community ecology has yet to integrate this feedback to predictions of community structure that include functional diversity and relative abundance distributions. Here we study how plasticity in resource consumption traits, defined by individual energy allocation constraints, shape community structure. We adopt a model incorporating plasticity in classic consumer-resource models where consumption strategies become dynamic state variables through optimizing organism growth by gradient ascent, underpinned by investment constraints in physiological machinery for acquisition of resources. Our results predict how plasticity in resource consumption strategies results in trait dynamics that let species avoid competitors while maximizing its efficiency on available resources. Interestingly this plastic optimization in even just one species in a community allows all other non-plastic species to coexist, a case of positive facilitation with pure competitive interactions. Additionally, we build a simple model based on plasticity maximizing resource uptake while minimizing competition that is predictive of relative species abundances so long as a geometric characteristic that we define as community supply vector distance is above a certain threshold. We study two cases, one where species consumption strategies are predictive of species abundances (niche), and a second in which consumption strategies are not predictive of species abundances (neutral). In the first case, we find that initial consumption strategies are more predictive of relative abundance distributions than equilibrium consumption strategies, highlighting the importance of the consumption strategy species have when colonizing a new environment in determining community structure when these traits are dynamic. Our study suggests that plasticity constrained by individual energy allocation provides a mechanism of facilitation that promote coexistence as well determines the relative strength of niche and neutral processes as drivers of community structure.
• Farshad Shirani Georgia Institute of Technology
  "Competition, Phenotypic Adaptation, and the Evolution of a Species’ Range"
Geographic ranges of communities of species evolve in response to environmental, ecological, and evolutionary forces. Understanding the effects of these forces on species’ range dynamics is a major goal of spatial ecology. Previous mathematical models have jointly captured the dynamic changes in species’ population distributions and the selective evolution of fitness-related phenotypic traits in the presence of an environmental gradient. These models inevitably include some unrealistic assumptions, and biologically reasonable ranges of values for their parameters are not easy to specify. As a result, simulations of the seminal models of this type can lead to markedly different conclusions about the behavior of such populations, including the possibility of maladaptation setting stable range boundaries. In this talk, we present our works on harmonizing such results by developing and simulating a continuum model of range evolution in a community of species that interact competitively while diffusing over an environmental gradient. Our model extends existing models by incorporating both competition and freely changing intraspecific trait variance. We show that the spatial profile of species’ trait variance that is predicated by our model is consistent with experimental measurements available in the literature. Moreover, we show that our results reaffirm interspecific competition as an effective factor in limiting species’ ranges, even when trait variance is not artificially constrained.
• Maud El-Hachem CSIRO (Commonwealth Scientific and Industrial Research Organisation)
  "Coexistence in two-species competition with delayed maturation"
Mortality caused by competition that occurs during maturation is explicitly modelled in some alternative formulations of the Lotka-Volterra competition model. We generalise this approach by using a distributed delay for maturation time. The distributed delay separates the mature from the immature individuals, to represent a species where competition is more important for immature individuals and where maturation time is long compared to lifetime. The resulting system of delay differential equations (DDEs) is transformed into a system of ordinary differential equations (ODEs) using the linear chain approximation. We show how the survival of a species depends on the rate of maturation being able to compensate for the rate of loss due to mortality of adults and immature individuals. A species fit for survival enters into competition with another species, leading to competitive exclusion, to stable coexistence of both species, or to unstable coexistence. We determine the stability conditions using the nullclines method and local stability analysis. The introduction of a distributed delay promotes coexistence and survival of the species compared to the limiting case of a discrete delay, potentially affecting management of relevant pests and threatened species.
• Zhao (Wendy) Wang McGill University
  "Dynamics of a reduced gene regulation model with transport-driven state-dependent delay"
Time-delays arise naturally in biological systems involving transport processes. We study the dynamics of a scalar delay differential equation where the delay induced by transport depends on the state of the system, and is defined implicitly by a threshold condition. The model can be derived from an extended gene regulation model where we found that the inclusion of threshold state-dependent transcription and translation delay enriches the potential operon dynamics in contrast to models with constant delays. We systemically study the various cases when feedback and transport velocity are described by increasing or decreasing (or constant) Hill functions of the state variable. We also examine the stability and bifurcations of the steady states in a limiting case where the Hill function turns into a piecewise constant function. With constant transport velocity, the fold bifurcations always bound the stability of the steady state even in the presence of Hopf bifurcations, while the steady state when unique could lose stability in supercritical Hopf bifurcations. The dynamics with variable transport velocity is more interesting and complex due to the existence of high dimensional bifurcations of the steady states as well as periodic orbits. The steady state could undergo codimension-2 bifurcation such as fold-Hopf bifurcation and Bogdanov–Takens bifurcation that is associated with three codimension-1 bifurcations, Hopf bifurcation, fold bifurcation and homoclinic bifurcation nearby. Understanding the dynamics of the reduced scalar model may help to locate regions where interesting dynamics could occur for the full model.

• Alberto Tenore University Federico II of Naples, Italy
  "A model on phototrophic granular biofilms: microbial ecology and reactor performance"
This talk addresses the mathematical modelling of phototrophic granular biofilms, spherical, dense aggregates constituted by a relevant phototrophic component and developed in presence of light. These biofilm granules are typically cultivated within bioreactors, and represent an innovative technology in the field of wastewater treatment. Specifically, the presented model describes both the growth of phototrophic granules and the related wastewater treatment process occurring in the bioreactor. The biofilm granule has been modelled as a free boundary domain with radial symmetry, which evolves over time as a result of microbial growth, attachment and detachment processes. Hyperbolic and parabolic partial differential equations (PDEs) have been considered to model at mesoscale the transport and growth of sessile biomass and the diffusion and conversion of soluble substrates. The macroscale behaviour of the system has been modelled through first order impulsive ordinary differential equations (IDEs), which reproduce a sequencing batch reactor (SBR) configuration. Phototrophic biomass has been considered for the first time in granular biofilms, and cyanobacteria and microalgae have been accounted separately, to model their different growth and granulation abilities. To describe the key role of cyanobacteria in the photogranulation process, the attachment velocity of all suspended microbial species has been modelled as a function of the cyanobacteria concentration in suspended form. The model takes into account the main biological processes involved in photogranules-based systems: metabolic activity of cyanobacteria, microalgae, heterotrophic and nitrifying bacteria, microbial decay, EPS secrection, symbiotic and competitive interactions between different species, light-dark cycle, light attenuation across the granule and photoinhibion phenomena. The model has been integrated numerically, and the results show its consistency in describing the photogranules evolution and ecology, and highlight the advantages of the photogranules-based technology, analyzing the effects of the influent wastewater composition and light conditions on the process.
• Alejandro Anderson University of Idaho
  "Contribution of waiting times therapies on mathematical models to tackle antimicrobial-drug resistance"
Antimicrobial resistance is a global health concern that requires all possible means of control it. To avoid the onset of multidrug-resistant strains each drug is subject to a maximum time of administration and to a minimum time of administration for effectiveness, referred to as Waiting Time Constraints (WTCs) on biomedical treatments. Treatment with drug combinations and appropriated WT specifications can be modeled by a nonlinear switched system, where a mode (or subsystem) represents the specific administrated drug and the schedule of drugs is associated with an optimal control problem that aims to reduce therapeutic escape. From a dynamic perspective, WTCs significantly alter the regions of the state space of the system that can be feasibly stabilized as they prevent excessive or insufficient time spent in a given mode. Indeed, the literature lacks results on this subject except for recent outcomes for the linear case. Understanding the regions that can be feasibly stabilized is as important as control developing or system modeling; without them no well-posed control can be formulated. Nonetheless, the regions that can be feasibly stabilized by predictive controllers for a nonlinear switched system of antimicrobial resistance, where drugs are subject to WTCs, remain unknown. In this work we present and analyze a series of algorithms to compute stabilizing regions for a switched mathematical model under WTC. The results applied to antibiotic-sensitive and resistance bacteria dynamic population during the course of multi-antibiotic treatment of an infected host addresses the following problems: (i) the existence and characterization of general regions of the state space wherein controlled states trajectories under WTC can feasibly (and indefinitely) remain inside; (ii) when the conditions on WTC to avoid the emergence of resistance allows the existence of feasible and stable control strategies for the success of multiple drug treatment in suppressing the infection; and (iii) when the condition on WTC for the treatment regimen predicts the failure of the treatment due to resistance.
• Fordyce A. Davidson University of Dundee
  "Competitive outcome in biofilms: a race for space"
Bacteria can form dense communities called biofilms, where cells are embedded in a self-produced extracellular matrix. Exploiting competitive interactions between strains within the biofilm context can have potential applications in biological, medical, and industrial systems. By combining mathematical modelling with experimental assays, we reveal that spatial structure and competitive dynamics within biofilms are significantly affected by the location and density of the founder cells used to inoculate the biofilm. Using a species-independent theoretical framework describing colony biofilm formation, we show that the observed spatial structure and relative strain biomass in a mature biofilm comprising two isogenic strains can be mapped directly to the geographical distributions of founder cells. Moreover, we define a predictor of competitive outcome that accurately forecasts relative abundance of strains based solely on the founder cells potential for radial expansion - a result we confirmed experimentally. Consequently, we reveal that variability of competitive outcome in biofilms inoculated at low founder density is a natural consequence of the random positioning of founding cells in the inoculum. Extension of our study to non-isogenic strains that interact through local antagonisms, shows that even for strains with different competition strengths, a race for space remains the dominant mode of competition in low founder density biofilms. Our results, verified by experimental assays using Bacillus subtilis, highlight the importance of spatial dynamics on competitive interactions within biofilms and hence to related applications
• Jessica Renz University of Bergen
  "Learning and predicting the pathways of AMR evolution with hypercubic inference"
Understanding the evolution of antimicrobial resistance (AMR) is central for their treatment. In this talk, I want to show a possible way to address this problem from a statistical point of view, namely the hypercubic inference, which we developed and introduced during the last years at the University of Bergen. The basis of this model is a hypercubic transition graph, whose nodes represent possible resistance states and the edges between correspond to the different evolutionary steps. This new approach allows us to efficiently make predictions about the most likely evolutionary pathways leading to AMR and learn their structure and variability, even if we have incomplete datasets with uncertain states. For this we can either use Bayesian inference via Monte Carlo Markov Chain methods or a frequentist approach for the estimation of likelihoods, whereby we only need cross-sectional datasets. While we focus here on AMR, hypercubic inference can be and has been used in a very wide range of problems involving evolutionary accumulation and disease progression, including ovarian cancer, severe malaria, genome and behavioral evolution, and educational progress. The focus of the talk will be the introduction and explanation of the methods themselves, whereby I will address both the advantages and strengths of using a hypercubic structure, but also open problems and ongoing work. In addition, I will also present the results of concrete current applications to real AMR datasets from Klebsiella pneumoniae and Escherichia coli and discuss some biological insights that can be derived from them.

• Aneequa Sundus Indiana University Bloomington
  "Investigating the potential for light-mediated spatial-temporal pattern formation in cyanobacteria mixed populations using agent-based modeling"
Cyanobacteria are the largest group of photosynthetic organisms on earth. They can survive in very severe conditions (e.g., in deep oceans and near poles) due to complex mechanisms that help them adapt to the specific light spectrum of their surroundings. They are evolved to adjust their metabolism and photosynthesis optimally to their environment. One such genetic switch found in cyanobacteria is the blue-green light switch: a simple system that is likely transferrable to other bacterial species. Thus, this switch has potential use in new regulatory systems for biotechnology and optogenetics. Additionally, cyanobacteria are phototrophs and are already being used to develop more sustainable biotechnology platforms. Characterizing and optimizing a highly responsive gene regulatory system that works efficiently in individuals and populations of cyanobacteria will help to advance their usefulness in biotechnology and in the production of biofuels. We developed an agent-based model of cyanobacteria mixed populations using PhysiCell, an open source physics-based modeling software. We explored the potential of combining opto-genetic and diffusible chemical controls to guide novel spatiotemporal pattern formation. We experimented with different blue-green light spectrums along with population density and cell motility parameters to probe this system for light mediated spatial pattern formation.
• Laura Wadkin Newcastle University
  "Mathematical and statistical modelling of the spread of tree diseases and invasive pests through forest environments"
The loss of biodiversity due to the spread of destructive tree diseases and invasive pests within forests across the world is having an enormous environmental, economic, and social impact. Enhancing biosecurity is a key priority, through the control of existing diseases and pests, and by building forest resilience against new ones. Thus, we are working in collaboration with multiple forestry partners to develop mathematical models to deepen our understanding of the fundamental behaviours of key pests and pathogens, act as predictive tools for forecasting, and to explore different control strategies. Broadly, we use a combination of partial differential equations, agent-based modelling, and statistical inference techniques. This talk will present an overview of the collaborative work to date, including a case study example of the oak processionary moth infestation in London.
• Suman Chakraborty Friedrich Schiller University Jena
  "Selection pressure by specialist and generalist insect herbivores leads to optimal constitutive plant defense. A mathematical model"
Brassicaceae plants have the glucosinolate-myrosinase defense system, jointly active against herbivory. Glucosinolates (GLS) are hydrolyzed by myrosinase to produce isothiocyanates as soon as herbivory begins. Isothiocyanates exert detrimental effects on the feeding insects. However, constitutive GLS defense is observed to occur at levels that do not deter all insects from feeding. That prompts the question of why Brassicaceae plants have not evolved a high constitutive defense. The answer may lie in the contrasting relationship between plant defense and host plant preference of specialist and generalist herbivores. One of the reasons plants are in this dilemma is that they do not know what kind of herbivore will attack them in any given year, and thus have to be prepared for different possibilities. GLS content increases the susceptibility to specialist insects because these are attracted to plants with a high GLS content and are capable of coping with the toxin. In contrast, generalists are deterred by the plant GLS. Although GLS can attract the natural enemies (predators and parasitoids) of these herbivores, enemies can reduce herbivore pressure to some extent only. So, plants can be overrun by specialists if GLS content is too high, whereas generalists can invade the plants if it is too low. Therefore, an optimal constitutive plant defense can minimize the overall herbivore pressure. To explain optimal defense theoretically, we represent the contrasting host selection behavior of insect herbivores and, in addition, the emergence of their natural enemies by a non-autonomous ordinary differential equation model, where the independent variable is the plant GLS concentration. From the model, we quantify the optimal amount of GLS, which minimizes the total herbivore (specialists and generalists) pressure. That quite successfully explains the evolution of constitutive defense in plants from the perspective of optimality theory.
• Hong-Sung Jin Chonnam National University, Korea
  "Assessment of American Bullfrog spreading in Korea using cellular automata learning"
The spread of American Bullfrog, one of the 100 of the World’s Worst Invasive Alien Species, has a great impact on the surrounding ecosystem, so it will be very important to find out the possibility of spread by region. We assess whether bullfrogs will continue to spread, stop spreading and maintain populations, or become extinct 60 years after their introduction to Korea. This study is based on the results of national surveys that observed the distribution. The entire data is divided into 25 regional clusters using the Hierarchical clustering method, and the degree of spread is predicted by CNN(Convolution Neural Network) method which trains and learns the rules of ECA(elementary cellular automata) that determine evolution of the clusters. We predict the probabilities of the ECA rules for each cluster. The mean value of the population according to the predicted rules is defined as the spreading intensity and evaluated, which is multiplied by the habitat suitability to get an assessment of bullfrog spreading. Habitat suitability is obtained using Maxent.

• Anastasios Stefanou Institute for Algebra, Geometry, Topology and their Applications, University of Bremen
  "Topological Data Analysis and Phylogenetics"
In the real world, mutations of genetic sequences are often accompanied by their recombinations. Such joint phenomena are modeled by phylogenetic networks. These networks are typically generated or reconstructed from coalescent processes that may arise from optimal merging or fitting together a given set of phylogenetic trees. L. Nakkleh formulated the phylogenetic network reconstruction problem (PNRP) as follows: Given a family of phylogenetic trees over a common set of taxa, is there a unique minimal phylogenetic network whose set of spanning trees contains the family? There are different answers to PNRP, since there are different ways to define what a “minimal network” is (based on different optimization criteria). Inspired by ideas from topological data analysis (TDA) (i.e. filtered simplicial complexes), we devise a simplicial lattice-model for modeling phylogenetic networks, called the cluttergram, that generalizes the dendrogram (filtered partition) model of phylogenetic trees. We show that the collection of all cluttergrams over the same set of taxa (leaves) forms a lattice. This lattice-model allows us to solve the PNRP in a mathematically rigorous way and in a way that is free of choosing optimization criteria for the reconstruction process. The solution to the phylogenetic network reconstruction process is obtained by taking the join operation of the dendrograms on the lattice of cluttergrams (by viewing dendrograms as cluttergrams). Furthermore, we show that computing the join-cluttergram from a given set of dendrograms is polynomial in the size and the number of the input trees (dendrograms). Moreover, motivated by the tool of persistence diagram in topological data analysis, we introduce an invariant of cluttergrams, called the mergegram, by extending the corresponding construction that was defined by Elkin and Kurlin on dendrograms. Then, we show that the mergegram is a 1-Lipschitz stable invariant of cluttergrams. This new TDA-signature of phylogenetic networks enable us to utilize standard statistical pipelines (vectorization and machine learning) to study phylogenetic networks. To illustrate the utility of these new TDA-tools to Phylogenetics, in this work we provide Python implementations of the introduced concepts and also experiments with certain benchmark biological datasets. This is joint work with Pawel Dlotko and Jan Senge.
• Kristina Wicke New Jersey Institute of Technology
  "Exploring spaces of semi-directed phylogenetic networks"
Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of speciation and reticulate evolutionary events such as hybridization or horizontal gene transfer. Traditionally, two types of phylogenetic networks were considered in the literature: unrooted (undirected) ones that are often used to represent conflict in data and rooted (directed) ones that explicitly depict evolution as a directed process. Recently, however, semi-directed phylogenetic networks have emerged as a class of phylogenetic networks sitting between rooted and unrooted phylogenetic networks since they contain directed and undirected edges. For example, software such as PhyloNetworks, NANUQ, and PhyNEST reconstructs semi-directed level-1 networks from biological data. However, in contrast to rooted and unrooted phylogenetic networks, little is known about searching spaces of semi-directed phylogenetic networks to find an optimal network. In this talk, we introduce semi-directed phylogenetic networks and related concepts. We then discuss a rearrangement move, called cut edge transfer (CET), and show that the space of semi-directed level-1 networks with a fixed leaf set and number of reticulations is connected under CET. Hence, every semi-directed level-1 network in this space can be transformed into any other such network by a sequence of CETs. By introducing two additional moves that allow for the addition and deletion of reticulations, we extend our results to semi-directed (level-1) network on a fixed leaf set. As a byproduct, we also obtain connectedness results for rooted level-1 networks under a rooted version of CET.
• Sarah Bogen Utah State University
  "A trait-based modeling approach to estimate global movement potential for plant populations in a warming planet"
Understanding the spatial and temporal dynamics of plant populations has important implications for the fields of ecology and conservation. A rich body of mathematical approaches have been developed to mechanistically model population spread based on species demography and seed dispersal patterns. However, with over 390,000 plant species on Earth, it is not feasible to collect complete information on all species for the purpose of making generalized conclusions. This problem may be addressed through trait-based modeling, which seeks to represent realistic combinations of organismal traits rather than focusing on individual species. In this work, I use a Bayesian multivariate approach to synthesize sparse datasets and estimate key demographic and dispersal parameters for a population of virtual species. I then use integrodifference equations to estimate population spreading speeds for virtual species and investigate links between movement-related extinction risk and easy-to-measure plant functional traits. This work demonstrates an example of how empirical data, statistical modeling, and mathematical modeling may be synthesized to advance understanding and inform decision-making in complex fields such a spatial ecology.