MS04 - ECOP-2
Brutus Buckeye Room (#3044) in The Ohio Union

Modeling and Analysis of Evolutionary Dynamics Across Scales and Areas of Application

Tuesday, July 18 at 04:00pm

SMB2023 Follow Tuesday during the "MS04" time block.
Room assignment: Brutus Buckeye Room (#3044) in The Ohio Union.

Note: this minisymposia has multiple sessions. The other session is MS03-ECOP-2 (click here).

Daniel Cooney, Olivia Chu

Description:

The dynamics of evolution shape the natural world across all scales, from the evolution of multicellularity to the formation of complex human and animal societies. In this session, we aim to highlight recent work on the mathematical modeling of evolutionary dynamics, bringing together researchers focused both on mathematical and biological developments in evolutionary game theory and population genetics and mathematical modelers tackling problems in biological and cultural evolution. The talks in our session will focus on applications ranging from the evolution of treatment-resistant cancers to the spatial evolution of invasive species to mutualism within and across species, while mathematical approaches will range from stochastic processes and network models for social interactions in finite populations to the derivation and analysis of ODEs and PDEs in mean-field models.

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.
Additional authors: Katy D. Heath, University of Illinois at Urbana-Champaign

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.
Additional authors: Jackson Foran; Maria Abarca; Naresh Neupane; Leslie Ries

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.
Additional authors: Alexander Bratus, Russian University of Transport, Russia; Olga S Chmereva, Lomonosov Moscow State University, Russia; Ivan Yegorov, KLA Corporation, US

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.
Additional authors: Poly H. da Silva, Columbia University, Department of Statistics

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Annual Meeting for the Society for Mathematical Biology, 2023.