June 25, 2018

Workshop on Adaptive Movement
of Interacting Species
September 10-13, 2009
at the Fields Institute
222 College Street, Toronto

Organizing Committee:
Peter A. Abrams, Department of Ecology and Evolutionary Biology, University of Toronto
Yuan Lou, Department of Mathematics, The Ohio State University

Canadian Institute of Ecology & Evolution

Speaker Abstracts

Peter Abrams (talk 1, Thursday, Sept. 10)
A review of research on adaptive movement and an overview of open questions

Abstract: This is a relatively short talk intended to provide some background on why adaptive movement requires more attention from mathematical biologists. It reviews some of the work that has been done which indicates potentially large differences between the ecological and/or evolutionary consequences of adaptive and random movement in spatially heterogeneous systems.

Peter Abrams (talk 2, Saturday Sept. 12)
Impacts of movement costs on between-patch movements and ecological interactions

Abstract: This talk concentrates on some ecological implications of adaptive movement of small numbers of interacting species in environments consisting of small numbers of habitat patches. I review some earlier work on the importance of various aspects of the rules governing adaptive dynamics for the ecological dynamics of the system. The time scale of movement, the accuracy of estimating local fitness, and the possibility of benefiting from or being harmed by conspecifics are important determinants of the population dynamics of the system. Some of this earlier work is extended to cases in which there is an energetic or mortality cost to moving between patches. This makes it difficult to deduce a proper fitness comparison for deciding whether to move, and also can produce alternative or polymorphic movement strategies.

Priyanga Amarasekare
Non-random dispersal strategies in multi-trophic communities

Abstract: I investigate the effects of non-random dispersal strategies on coexistence and species distributions in multi-trophic communities with competition and predation. I conduct a comparative analysis of dispersal strategies with random and fitness-dependent dispersal at the extremes and two intermediate strategies that rely on cues (density and habitat quality) that serve as proxies for fitness. The most important finding is an asymmetry between consumer species in their dispersal effects. The dispersal strategy of inferior resource competitors that are less susceptible to predation have a large effect on both coexistence and species distributions, but the dispersal strategy of the superior resource competitor that is more susceptible to predation has little or no effect on dispersal. I explore the consequences of this asymmetry for the evolution of dispersal.

Steve Cantrell
How biased density dependent movement of a species at the boundary of a habitat patch mediates its within-patch dynamics

Abstract: In this talk we will discuss some reaction-diffusion models for the propagation of a species' density in a bounded habitat. The particular models we will consider are of diffusive logistic type in the interior of the patch, subject to a nonlinear condition on the boundary of the patch of the form

a(u) * grad (u) . n + ( 1 -a(u))* u = 0.

Here a(u) is a non-decreasing nonnegative function of the species' density that takes values between 0 and 1 when u is between 0 and the local carrying capacity of the species under the logistic growth law, which is presumed to be constant on the patch. When a(u) is identically constant, the prediction of the model is that all nonnegative nontrivial initial species density profiles evolve to 0 in the case of extinction or to a unique positive equilibrium profile in the case of survival. By way of contrast, in the case when a(u) is non-constant, the dynamics at the scale of the patch may be more complicated. In particular, such a(u) may mediate Allee effects at the scale of the patch, consistent with empirical results for the Glanville fritillary butterfly. The models demonstrate how meso-scale effects locally at the boundary of a habitat patch may mediate macro-scale effects on the patch as a whole.

This work is joint with Chris Cosner and Salome Martinez.

Peter Chesson
The effects of adaptive predator movement on coexistence of prey species in a spatially varying environment

Predation can have important roles in species coexistence, undermining coexistence from competition-based mechanisms, replacing competition-based mechanisms with predation-based mechanisms, adding to competition-based mechanisms or interacting with competition to create new mechanisms, depending on the circumstances. When predation occurs in a spatially varying environment, the role that it has in species coexistence depends greatly on the ability of the predator to track prey density, which it may do as a consequence of natural selection fostering adaptive movements. We study these effects in a model of seed predation in an annual plant community with spatially and spatio-temporally varying conditions for the germination and growth of the various plant species. We are able to quantify the magnitudes of competition-based and predation-based coexistence mechanisms to show how predation-based and competition-based coexistence mechanisms interact. Most important, the effects of adaptive movement of the predator emerge through coefficients that control the magnitudes of predation-based versions of the coexistence mechanisms termed the spatial storage effect, and fitness-density covariance.


Chris Cosner
Evolutionary aspects of directed movement in reaction-advection-diffusion models and their discrete analogues

Abstract: A number of mathematical models suggest that in spatially varying but temporally constant environments there should be selection against dispersal strategies that do not depend on local conditions. For example, in reaction-diffusion models for two competing populations that are ecologically identical, the population with the smaller diffusion rate will exclude the faster diffuser. However, that is not necessarily the case if the dispersal strategies can take local conditions into account. Advection along environmental gradients can sometimes confer an advantage or provide a mechanism for coexistence. It is possible to formulate dispersal strategies that lead to population equilibria where individuals in all locations have the same fitness as measured by the local population growth rate, and where there is no net movement of individuals, that is, the dispersal terms in the model become zero at equilibrium. These features would be observed in a population distributed according to the ideal free distribution. In some cases these features characterize evolutionarily stable dispersal strategies.

Ross Cressman
Time Scales and Stability in Models of Coevolution

Abstract: Coevolution of behavior (or strategy) structured populations is often analyzed by separating the time scale of behavioral evolution from that of population dynamics. For instance, the canonical equation of adaptive dynamics studies the evolution of the population mean strategy assuming that fast population dynamics instantaneously track stable equilibrium densities for the current strategy. In other models of coevolution (e.g. habitat selection models), it is more realistic to assume that behavioral changes act much faster than the density dynamics. The talk will discuss stability of equilibria in both of these extremes as well as for models that do not assume a separation of time scales.

Sam Flaxman
Coevolution of predator and prey movement mechanisms in an individual based model

Abstract: Predator-prey interactions are the links that determine energy and resource
flows in ecological communities. In spite of decades of study however, we still know surprisingly little about the ways in which these interactions shape habitat use and spatial distributions. I examine simple, generalized movement mechanisms that predators and prey can use to move in response to environmental features and each other. Intriguing results emerged when these mechanisms were allowed to evolve in individual based simulation models. First, in spite of the multiple, potentially conflicting challenges that predators and prey face, predators and prey evolved movement mechanisms that allowed both to simultaneously achieve spatial distributions that are predicted by game theoretic models. This occurred even though (i) predators and prey use only limited, local information to guide their movements and (ii) individual predators and prey both sometimes make movements in the "wrong" direction. Second, as a result of coevolution, prey movements were generally influenced only weakly by environmental features and very weakly by the distribution of predators, while predators by contrast responded strongly to the distribution of prey. As such, at the ecological time scale, it was mainly the behavior of predators that determined the spatial distributions of both predators and prey.

John Fryxell
Sociality, movement, and predator-prey dynamics in the Serengeti ecosystem

Abstract: Both social and spatial processes potentially influence the frequency distribution of predator and prey encounters, but their interaction is rarely considered. I will illustrate these processes using observational data from Serengeti National Park. Fission-fusion models will be used to predict patterns of herbivore grouping and these models in turn will be used to predict predation rates by lions based on the group-dependent functional response model outlined in Fryxell et al. (2007). These trophic models will linked to data on both between-season migration and within-season nomadic movements by herbivores to consider the dynamical impact of both adaptive social and movement processes.

Dick Gomulkiewicz
Evolution of spatial correlations among interacting species

Abstract: Spatial correlations between traits of interacting species have long been used to identify putative cases of coevolution. Here we evaluate the utility of this approach using models to predict correlations that evolve between traits of interacting species for a broad range of interaction types. Our results reveal coevolution is neither a necessary nor sufficient condition for the evolution of spatially correlated traits between species. Specifically, our results show that coevolutionary selection fails to consistently generate statistically significant correlations and, conversely, that non-coevolutionary processes can readily cause significant correlations to evolve. Our results also show that the correlation between traits of interacting species is insensitive to rates of gene flow---which our models assume to be evolutionary fixed. An open question, then, is whether accounting for adaptive changes in movement rates will strengthen the "signal" of coevolutionary interactions in spatial correlation data.

Robert Holt
The influence of adaptive movement on coevolutionary dynamics

Abstract: In 1999 I explored the question of how population dynamics might influence the evolutionary stability of biological control, using as an illustration a host-parasitoid model in which hosts had a partial refuge from parasitism. The refuge could permit this intrinsically highly unstable system to persist, either at a stable equilibrium or with bounded oscillations. An exploration of evolutionary dynamics in the host suggested that unstable dynamics had a strong influence on the evolution of host traits, and could at time make selection on the host negligible to escape parasitism when it was outside the refuge. This arguably might be one mechanism enhancing the evolutionary stability of biological control. In the first part of the talk I revisit this model, and examine the consequences of allowing simultaneous evolution in the host and parasitoid, and adaptive movement by the host (in and out of the refuge). In the second half of the talk I will use this specific model as a springboard to discuss more general issues.

Chris Klausmeier
Adaptive movement of phytoplankton in vertical gradients of light and nutrients

Abstract: Phytoplankton face a dilemma: light comes from above, nutrients come from below, and they need both. Although the name "plankton" comes from the Greek word for "wanderer", many phytoplankton taxa have adaptations to choose their position within the water column and solve this dilemma. Under uniformly poorly mixed conditions, this adaptive movement results in a thin layer of phytoplankton at a depth where it is colimited by nutrients and light. Complications from interspecific competition, more realistic mixing patterns (stratification), and higher trophic levels will be discussed.

Mathew Leibold
A Metacommunity perspective on the consequences of adaptive dispersal

Abstract: Metacommunity ecology is a general framework for understanding how dispersal affects numerous aspects of community and ecosystem structure in an ecological landscape. To date most theory in metacommunity ecology has assumed that dispersal is passive but it is likely that adaptive dispersal will alter expectations about metacommunities. I will review our current understanding about metacommunity ecology, focusing on empirical as well as theoretical aspects. I will then speculate about how adaptive dispersal may alter our understanding of these findings. My goal is to inspire future work on adaptive dispersal to address these issues that are important both to basic scientific understanding and to applied questions in ecology.

Mark Lewis (with Hannah McKenzie and Evelyn Merrill)
First passage time: Connecting random walks to functional responses

In this talk I will outline first passage time analysis for animals undertaking complex movement patterns, and will demonstrate how first passage time can be used to derive functional responses in predator prey systems. The result is a new approach to understanding type III functional responses based on a random walk model. I will extend the analysis to complex heterogeneous environments to assess the effects of linear features on functional responses in wolves and elk.


Yuan Lou
Evolution of conditional dispersal in spatially heterogeneous habitats

Abstract: A general question in the evolution of dispersal is what kind of dispersal strategies can convey competitive advantages and thus will evolve. We consider a two species competition models in which the species are assumed to have the same population dynamics but different dispersal strategies. Both species disperse by random diffusion and advection along certain environmental gradients, with the same random dispersal rates but different advection coe±cients. We found a conditional dispersal strategy which results in the ideal free distribution of species, and show that it is a local evolutionarily stable strategy. We further show that this strategy is also a global convergent stable strategy under suitable assumptions, and our results illustrate how the evolution of conditional dispersal can lead to an ideal free distribution. The underlying biological reason is that the species with this particular dispersal strategy can perfectly match the environmental resource, which leads to its fitness equilibrated across the habitats.

Frithjof Lutscher
Population dynamics of central place foragers

Abstract: Central place foragers are individuals living in a colony at a central place from which they emerge to forage and to which they return to reproduce. Examples include ants, bats, colonial seabirds, and cave crickets. Foraging area and foraging behavior may influence population dynamics at the central place where reproduction occurs.
Typically, deterministic models for population dynamics consider either a nonspatial setting (e.g. ODEs or difference equations), or a spatial setting in which the species in question can reproduce anywhere in the domain (e.g. PDEs and integrodifference equations). Neither of these two frameworks is suited to describe a central-place forager population on the scale of its foraging patch. We therefore introduce a system of two equations in discrete time, one for the spatial distribution of resources and one for the (nonspatial) density of consumers at the central place. The two equations are connected via a `foraging kernel' that captures the foraging behavior of individuals.

We study the resulting population dynamics under various assumptions of foraging
behavior. (1) We assume a fixed foraging behavior in time and consider the minimal patch size required to sustain a population. We show how different foraging behaviors result in qualitatively different population dynamics. (2) We assume adaptation at the population level: foraging behavior is chosen to optimize colony resource intake. Several new dynamical behaviors arise: the minimal patch size becomes zero, and different
bifurcations occur. (3) We assume adaptation at the individual level: foraging is
described by a resource-dependent random walk, from which we derive the resulting spatial distribution of foragers.

Barney Luttbeg
Adaptive predator and prey movement rules in a spatial game

In this talk I will use genetic algorithm models to examine what movement rules predators and prey should use when both are free to move between patches. I will primarily focus on how the game dynamics of predators and prey responding to each other might alter what we think should be adaptive movement. In particular, if predators tend to move to patches that have the highest instantaneous prey fitness, then it can become sub-optimal for prey use movement rules that lead them to those patches.

Kevin McCann
The Critical Role of Movement in Large and Small Ecosystems

Abstract: The dynamics of ecological systems include a bewildering number of biotic interactions that unfold over a vast range of spatial scales. Here, employing simple and general empirical arguments concerning the nature of movement, trophic position and behaviour, I outline a theory concerning the role of space and food web structure on food web dynamics. I argue that consumers link food webs in space and that this spatial structure mediates relatively rapid behavioural responses by consumers that governs food web dynamics. These results suggest that large mobile consumers are of inordinate importance to the dynamics of ecosystems. This theory suggests that these mobile higher order organisms stabilize ecological systems when embedded in a variable, and extensive spatial structure. However, when space is fragmented, or simplified, then large mobile organisms can have an inordinate destabilizing effect.

Roger Nisbet
Adaptive movement and spatial scales in advection-dominated systems

Abstract: Stream and river systems exhibit high spatial and temporal variability, and there has been considerable research devoted to identifying characteristic lengths, in terms of which to characterize conditions for population persistence and the response to disturbances. For populations in a mildly heterogeneous environment, there is a population response length that characterizes the distance downstream over which the impact of a point source perturbation is felt. In the absence of density dependence, the response length is close to the mean distance traveled by an organism in its lifetime. Previous work has shown that density-dependent demographic rates are likely to increase the response length from this default value, and density-dependent dispersal will reduce it. I shall discuss response lengths in prey-predator systems with particular emphasis on the effects of a "fleeing" response of the prey and of predator movement approximating the "ideal free" situation.

Sebastian Schreiber
Evolution of predator and prey movement in heterogeneous environments

In the 1970s, differential spatial distributions of predators and their prey were identified as potentially important stabilizing force for predator-prey dynamics. In the past decade or so, evolutionary mechanisms underlying these differential distributions have been identified and their feedback with predator-prey dynamics have been explored. In this talk, I will provide an idiosyncratic view on these advancements by discussing some results on patch selection strategies and the evolution of random dispersal. For patch-selection strategies, the emphasis will be on understanding how biological elaborations (e.g. handling times, sex-allocation strategies) interact with spatial heterogeneity to select for differential spatial distributions that stabilize predator-prey dynamics. For the evolution of random dispersal, the emphasis will be on understanding how non-equilibrium feedbacks between ecological and evolutionary processes can produce dispersal polymorphisms for one or both of the species. A general framework uniting both types of models will be presented.