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SCIENTIFIC PROGRAMS AND ACTIVITIES |
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| November 23, 2024 |
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Workshop on Adaptive Movement
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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.