Due to the coronavirus outbreak, the 2020 AMS Eastern Sectional Meeting at Tufts University has been canceled. As a replacement for the canceled in-person session, we are planning to hold an online-only version of our special session on structured population via Zoom. Our current plan is to hold the virtual meeting on the afternoon of Saturday, March 21. On each day, we tentatively plan to hold the talks from 12pm to 3pm and from 4pm to 6pm, Eastern Daylight time.
If you are interested in listening to the talks, please let us know. For convenience, please fill out the following registration form to indicate your availability. We will email everyone who fills out the form with the link to join the Zoom meeting. If you would like to join at any point during the talks on Saturday, please fill out the form and we will send you the Zoom link. We will include our schedule for planned talks on this webpage as we reconfirm our speakers for the virtual session, and the original schedule for the sectional meeting can be found on the AMS website.
Encounter rates link movement strategies to population-level interactions, and therefore translate individual movement behavior into higher-level ecological processes.
Indeed, a large body of interacting population theory rests on the law of mass action, which can be derived from assumptions of Brownian motion in an enclosed
container with exclusively local perception. These assumptions imply completely uniform space use, individual home ranges equivalent to the population range,
and encounter dependent on movement paths actually crossing. Mounting empirical evidence, however, suggests that animals use space non-uniformly, occupy home ranges substantially
smaller than the population range, and are often capable of nonlocal perception. In this presentation, I will show how these empirically supported behaviors change pairwise encounter rates.
First, I will derive analytical expressions for encounter rates under Ornstein-Uhlenbeck motion, which features non-uniform space use and allows individual home ranges to differ from the population range.
Then, I will compare OU-based encounter predictions to those of Reflected Brownian Motion, from which the law of mass action can be derived.
Reference: https://arxiv.org/pdf/1907.05902.pdf.
Co-authors: Chris H. Fleming (Smithsonian Conservational Biology Institute), Ralf Seppelt (Helmholtz Centre for Environmental Research and Martin-Luther-University Halle-Wittenberg), William F. Fagan (University of Maryland), Justin M. Calabrese (University of Maryland).
Climate change poses significant risks to smallholder farmers’ livelihoods in developing country contexts, with potential impacts on rural-urban migration.
Policymakers seeking to enhance farmers' resilience to increasing climate risk must balance this objective with other policy goals, including accelerating economic development,
reducing inequality, and maintaining food security. However, it is unclear to what extent (and in what ways) different government interventions may influence farmers' climate adaptation decisions,
and under what conditions these interventions may lead to unintended consequences. I will present initial results from a stylized agent-based model (ABM) to model smallholder farmer adaptation strategies for climate stress on crop yields.
Agents consist of farming households with heterogeneous risk preferences, wealth, and social capital; they interact by sharing information on the perceived payoffs of different strategies with other households in their networks.
The ABM models how these interactions influence the adoption of different adaptation strategies, e.g. migration and crop diversification, under increasing climate stress.
The model is calibrated using climate and socioeconomic data from South Asian subsistence farming regions. We use the model to test the effects of different risk-sharing interventions on household decision-making,
as well as to investigate how individual decision-making may differ from a socially optimal portfolio of livelihood strategies.
Coauthors: Matthias Wildemeersch (IIASA), Michael Oppenheimer (Princeton), and Simon Levin (Princeton).
We model a mobile population interacting over an underlying spatial structure using a Markov movement model. Interactions take the form of public goods games, and can feature an arbitrary group size. Individuals choose strategically to
remain at their current location or to move to a neighboring location, depending upon their exploration strategy and the
current composition of their group. This builds upon previous work where the underlying structure was a complete graph
(i.e., there was effectively no structure). Here, we consider alternative network structures and a wider variety of, mainly
larger, populations. Previously, we had found when cooperation could evolve, depending upon the values of a range of
population parameters. In our current work, we see that the complete graph considered before promotes stability, with
populations of cooperators or defectors being relatively hard to replace. By contrast, the star graph promotes instability,
and often neither type of population can resist replacement. We discuss potential reasons for this in terms of network
topology.
Coauthors: Johann Bauer, Mark Broom, Karan Pattni and
Jan Rychtar.
Coevolutionary graphs are simple, mechanistic models in which node states and graph topology are intertwined. The
rich space of possible dynamics includes opinion-updates, epidemic containment, and evolutionary games. Despite their
simplicity, this class of models tends to exhibit a rich class of behaviors. These include disconnected homogeneous
subgraphs – reminiscent of the formation of “echo-chambers” or geographically isolated speciation – as well as persistent,
interacting heterogeneity. These regimes are usually separated by a critical point, whose calculation has been a topic of
intense study over the last fifteen years. We will give a brief survey of this class of literature and discuss some new results
for several variants of an opinion-based model.
Coauthor: Peter Mucha (UNC Chapel Hill).
In the face of an epidemic, policies may be put in place to alter the behavior of the population (e.g. quarantining) for the good of the public health. While classical compartmental models and measures such as R_0 have provided insights into epidemics, which can be adopted into relevant policies, adaptive human behavior is usually not explicitly considered, even though humans often change economic activities and social plans during, and in anticipation of an outbreak. Considering contact rate to be the control variable, we pose a mathematical model of this problem as a deterministic mean-field game with discrete states and continuous time. In addition to the SIR dynamics, each compartment solves the optimal control problem, considering the tradeoff between present and future utility, as well as the strategies of the other compartments. We can compute the mean-field equilibrium, which is the fixed point of the coupled system of Bellman equations and the SIR differential equations. In addition, we compare the mean-field equilibrium with the socially optimal solution and prove that the contact rate of the infected should always be lowered to achieve social optimum. We also compute the price of anarchy of this system along the different parameters to find the characteristics of a disease, which in the case of an outbreak, we may benefit more by moving towards the social optimum via public policy.
Back to schedule
In structured populations of plants and animals, populations grow at a constant rate once they reach a stable stage
distribution. Transient dynamics refer to how changes in stage structure affect short-term population dynamics. Although
a number of ecological population models have explored properties of transient dynamics, their importance has rarely
been tested in experiments. We propose that bumble bee colony growth is an excellent model system for studying
transient dynamics of structured populations. We demonstrate this utility using colonies of the common western bumble
bee, Bombus vosnesenskii. We explore empirically based models of transient dynamics and compare model predictions
to experimental manipulation of resource pulses that affect both colony growth rates and stage structure. Models and
experiments produce broadly concordant results, suggesting a number of directions for future mathematical and empirical
research.
Coauthors: Natalie Z Kerr (Duke Unviersity), Rosemary L Malfi, (University of Massachusetts, Amherst), and Neal M Williams (University of California, Davis).
In the study of the evolution of cooperation, many mechanisms have been proposed to help overcome the self-interested cheating that is individually optimal in the Prisoners’ Dilemma and other social dilemmas. These mechanisms include assortative or networked social interactions, reciprocity rules to establish cooperation as a social norm, or simultaneous competition between individuals favoring cheaters and competition between groups favoring cooperators. Here, we build on recent mathematical tools describing the dynamics of multilevel selection to consider the role that assortment and reciprocity mechanisms play in facilitating cooperation in concert with multilevel selection. We explore a deterministic partial differential equation variant of the replicator equation which the effects of within-group and between-group competition, and we demonstrate the synergistic effects between population structure within groups and the competitive ability of cooperative groups when groups compete according to collective payoff.
Back to scheduleFormatting for the schedule and abstracts sections was adapted from the webpage for the Princeton Theoretical Ecology Lab Tea.