Chris Cosner - Profile on Academia.edu (original) (raw)

Papers by Chris Cosner

Theoretical Ecology, Aug 23, 2022

Consumers must track and acquire resources in complex landscapes. Much discussion has focused on ... more Consumers must track and acquire resources in complex landscapes. Much discussion has focused on the concept of a 'resource gradient' and the mechanisms by which consumers can take advantage of such gradients as they navigate their landscapes in search of resources. However, the concept of tracking resource gradients means different things in different contexts. Here, we take a synthetic approach and consider six different definitions of what it means to search for resources based on density or gradients in density. These include scenarios where consumers change their movement behavior based on the density of conspecifics, on the density of resources, and on spatial or temporal gradients in resources. We also consider scenarios involving non-local perception and a form of memory. Using a continuous space, continuous time model that allows consumers to switch between resource-tracking and random motion, we investigate the relative performance of these six different strategies. Consumers' success in matching the spatiotemporal distributions of their resources differs starkly across the six scenarios. Movement strategies based on perception and response to temporal (rather than spatial) resource gradients afforded consumers with the best opportunities to match resource distributions. All scenarios would allow for optimization of resource-matching in terms of the underlying parameters, providing opportunities for evolutionary adaptation, and links back to classical studies of foraging ecology.

Effects of domain size on the persistence of populations in a diffusive food-chain model with Beddington-DeAngelis functional response

ABSTRACT. A food chain consisting of species at three trophic levels is modeled using Beddington‐... more ABSTRACT. A food chain consisting of species at three trophic levels is modeled using Beddington‐DeAngelis functional responses as the links between trophic levels. The dispersal of the species is modeled by diffusion, so the resulting model is a three component reaction‐diffusion system. The behavior of the system is described in terms of predictions of extinction or persistence of the species. Persistence is characterized via permanence, i.e., uniform persistence plus dissi‐pativity. The way that the predictions of extinction or persistence depend on domain size is studied by examining how they vary as the size (but not the shape) of the underlying spatial domain is changed.

Mathematical biosciences, Nov 1, 2018

Roughly speaking, a population is said to have an ideal free distribution on a spatial region if ... more Roughly speaking, a population is said to have an ideal free distribution on a spatial region if all of its members can and do locate themselves in a way that optimizes their fitness, allowing for the effects of crowding. Dispersal strategies that can lead to ideal free distributions of populations using them have been shown to exist and to be evolutionarily stable in a number of modeling contexts in the case of habitats that vary in space but not in time. Those modeling contexts include reaction-diffusion-advection models and the analogous models using discrete diffusion or nonlocal dispersal described by integro-differential equations. Furthermore, in the case of reaction-diffusion-advection models and their nonlocal analogues, there are strategies that allow populations to achieve an ideal free distribution by using only local information about environmental quality and/or gradients. We show that in the context of reactiondiffusion-advection models for time-periodic environments with spatially varying resource levels, where the total level of resources in an environment remains fixed but its location varies seasonally, there are strategies that allow populations to achieve an ideal free distribution. We also show that those strategies are evolutionarily stable. However, achieving an ideal free distribution in a time-periodic environment requires the use of nonlocal information about the environment such as might be derived from experience and memory, social learning, or genetic programming. This is joint work with Chris Cosner.

Mathematics, Mar 11, 2020

In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage st... more In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model's predictions of persistence or extinction for the population. In the case of a population without stage structure, faster diffusion is typically detrimental. In contrast to that, we find that, in a stage structured population, it can be either detrimental or helpful. If the regions where adults can reproduce are the same as those where juveniles can mature, typically slower diffusion will be favored, but if those regions are separated, then faster diffusion may be favored. Our analysis consists primarily of estimates of principal eigenvalues of the linearized system around (0, 0) and results on their asymptotic behavior for large or small diffusion rates. The model we study is not in general a cooperative system, but if adults only compete with other adults and juveniles with other juveniles, then it is. In that case, the general theory of cooperative systems implies that, when the model predicts persistence, it has a unique positive equilibrium. We derive some results on the asymptotic behavior of the positive equilibrium for small diffusion and for large adult reproductive rates in that case.

Effects of dispersal rates in a two-stage reaction-diffusion system

Journal of Mathematical Biology, Feb 3, 2023

The Effect of Directed Movement on the Strong Allee Effect

Siam Journal on Applied Mathematics, 2021

It is well known that movement strategies in ecology and in economics can make the difference bet... more It is well known that movement strategies in ecology and in economics can make the difference between extinction and persistence. We present a unifying model for the dynamics of ecological populati...

Theoretical Ecology, Jun 15, 2019

Animals use different modes of movement at different times, in different locations, and on differ... more Animals use different modes of movement at different times, in different locations, and on different scales. Incorporating such context dependence in mathematical models represents a substantial increase in complexity, but creates an opportunity to more fully integrate key biological features. Here, we consider the spatial dynamics of a population of foragers with two subunits. In one subunit, foragers move via diffusion (random search) whereas in the other, foragers move via advection (gradient-following search). Foragers switch back and forth between the subunits as functions of their spatial context (i.e., depending on whether they are inside or outside of a patch, or depending on whether or not they can detect a gradient in resource density). We consider a onedimensional binary landscape of resource patches and non-habitat and gauge success in terms of how well the mobile foragers overlap with the distribution of resources. Actively switching between dispersal modes can sometimes greatly enhance this spatial overlap relative to the spatial overlap possible when foragers merely blend advection and diffusion modes at all times. Switching between movement modes is most beneficial when organism's gradient-following abilities are weak compared to its overall capacity for movement, but switching can actually be quite detrimental for organisms that can rapidly follow resource gradients. An organism's perceptual range plays a critical role in determining the conditions under which switching movement modes benefits versus disadvantages foragers as they seek out resources.

Journal of Mathematical Biology, Sep 13, 2019

Based on a Ross-Macdonald type model with a number of identical patches, we study the role of the... more Based on a Ross-Macdonald type model with a number of identical patches, we study the role of the movement of humans and/or mosquitoes on the persistence of malaria and many other vector-borne diseases. By using a theorem on line-sum symmetric matrices, we establish an eigenvalue inequality on the product of a class of nonnegative matrices and then apply it to prove that the basic reproduction number of the multipatch model is always greater than or equal to that of the single patch model. Biologically, this means that habitat fragmentation or patchiness promotes disease outbreaks and intensifies disease persistence. The risk of infection is minimized when the distribution of mosquitoes is proportional to that of humans. Numerical examples for the two-patch submodel are given to investigate how the multipatch reproduction number varies with human and/or mosquito movement. The reproduction number can surpass any given value whenever an appropriate travel pattern is chosen. Fast human and/or mosquito movement decreases the infection risk, but may increase the total number of infected humans.

Discrete and Continuous Dynamical Systems-series B, Sep 1, 2016

West Nile virus (WNV) was first detected in the United States (U.S.) during an outbreak in New Yo... more West Nile virus (WNV) was first detected in the United States (U.S.) during an outbreak in New York City in 1999 with 62 human cases including seven deaths. In 2001, the first human case in Florida was identified, and in Texas and California it was 2002 and 2004, respectively. WNV has now been spread to almost all states in the US. In 2015, the Center for Disease Control and Prevention (CDC) reported 2,175 human cases, including

Theoretical Ecology, Nov 29, 2016

There is a great deal of interest in the effects of biotic interactions on geographic distributio... more There is a great deal of interest in the effects of biotic interactions on geographic distributions. Nature contains many different types of biotic interactions (notably mutualism, commensalism, predation, amensalism and competition), and it is difficult to compare the effects of multiple interaction types on species' distributions. To resolve this problem, we analyze a general, flexible model of pairwise biotic interactions that can describe all interaction types. In the absence of strong positive feedback, a species' ability to be present depends on its ability to increase in numbers when it is rare and the species it is interacting with is at equilibrium. This insight leads to counterintuitive conclusions. Notably we often predict the same range limit when the focal species experiences competition, predation or amensalism. Similarly, we often predict the same range margin or when the species experiences mutualism, commensalism or benefits from prey. In the presence of strong positive density dependent feedback different species interactions produce different range limits in our model. In all cases, the abiotic environment can indirectly influence the impact of biotic interactions on range limits. We illustrate the implications of this observation by analyzing a stress gradient where biotic interactions are harmful in benign environments but beneficial in stressful environments. Our results emphasize the need to consider the effects of all biotic interactions on species' range limits, and provide a systematic comparison of when biotic interactions affect distributions.

The American Naturalist, Feb 1, 2016

Climate change drives uneven phenology shifts across taxa, and this can result in changes to the ... more Climate change drives uneven phenology shifts across taxa, and this can result in changes to the phenological match between interacting species. Shifts in the relative phenology of partner species are well documented, but few studies have addressed the effects of such changes on population dynamics. To explore this, we develop a phenologically explicit model describing consumer-resource interactions. Focusing on scenarios for univoltine insects, we show how changes in resource phenology can be reinterpreted as transformations in the yearto-year recursion relationships defining consumer population dynamics. This perspective provides a straightforward path for interpreting the long-term population consequences of phenology change. Specifically, by relating the outcome of phenological shifts to species traits governing recursion relationships (e.g., consumer fecundity or competitive scenario), we demonstrate how changes in relative phenology can force systems into different dynamical regimes, with major implications for resource management, conservation, and other areas of applied dynamics.

On the Allee effect and directed movement on the whole space

Mathematical Biosciences and Engineering, 2023

It is well known that relocation strategies in ecology can make the difference between extinction... more It is well known that relocation strategies in ecology can make the difference between extinction and persistence. We consider a reaction-advection-diffusion framework to analyze movement strategies in the context of species which are subject to a strong Allee effect. The movement strategies we consider are a combination of random Brownian motion and directed movement through the use of an environmental signal. We prove that a population can overcome the strong Allee effect when the signals are super-harmonic. In other words, an initially small population can survive in the long term if they aggregate sufficiently fast. A sharp result is provided for a specific signal that can be related to the Fokker-Planck equation for the Orstein-Uhlenbeck process. We also explore the case of pure diffusion and pure aggregation and discuss their benefits and drawbacks, making the case for a suitable combination of the two as a better strategy.

Linking mathematical models and trap data to infer the proliferation, abundance, and control of Aedes aegypti

Acta Tropica, Mar 1, 2023

Journal of Mathematical Biology, Feb 19, 2019

Many types of organisms disperse through heterogeneous environments as part of their life histori... more Many types of organisms disperse through heterogeneous environments as part of their life histories. For various models of dispersal, including reactionadvection-diffusion models in continuously varying environments, it has been shown by pairwise invasibility analysis that dispersal strategies which generate an ideal free distribution are evolutionarily steady strategies (ESS, also known as evolutionarily stable strategies) and are neighborhood invader strategies (NIS). That is, populations using such strategies can both invade and resist invasion by populations using strategies that do not produce an ideal free distribution. (The ideal free distribution arises from the assumption that organisms inhabiting heterogeneous environments should move to maximize their fitness, which allows a mathematical characterization in terms of fitness equalization.) Classical reaction diffusion models assume that landscapes vary continuously. Landscape ecologists consider landscapes as mosaics of patches where individuals can make movement decisions at sharp interfaces between patches of different quality. We use a recent formulation of reaction-diffusion systems in patchy landscapes to study dispersal strategies by using methods inspired

Journal of Mathematical Biology, Nov 3, 2018

We study the evolutionary stability of dispersal strategies, including but not limited to those t... more We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium). The environment is assumed to be variable in space but constant in time. We assume that there is a separation of times scales, so that dispersal occurs on a fast timescale, evolution occurs on a slow timescale, and population dynamics and interactions occur on an intermediate timescale. Starting with advection-diffusion models for dispersal without population dynamics, we use the large time limits of profiles for population distributions together with the distribution of resources in the environment to calculate growth and interaction coefficients in logistic and Lotka-Volterra ordinary differential equations describing population dynamics. We then use a pairwise invasibility analysis approach motivated by adaptive dynamics to study the evolutionary and/or convergence stability of strategies determined by various assumptions about the advection and diffusion terms in the original advection-diffusion dispersal models. Among other results we find that those strategies which can produce an ideal free distribution are evolutionarily stable.

Diffusive Logistic Equations with Indefinite Weights: Population Models in Disrupted Environments II

Siam Journal on Mathematical Analysis, Jul 1, 1991

The dynamics of a population inhabiting a strongly heterogeneous environment are modeled by diffu... more The dynamics of a population inhabiting a strongly heterogeneous environment are modeled by diffusive logistic equations of the form u_1=nablacdot(d(x,u)+nablau)−bfb(x)cdotnablau+m(x)u−cu2u_1 = \nabla \cdot (d(x,u) + \nabla u) - {\bf b}(x) \cdot \nabla u + m(x)u - cu^2 u_1=nablacdot(d(x,u)+nablau)−bfb(x)cdotnablau+m(x)u−cu2 in Omegatimes(0,infty)\Omega \times (0,\infty )Omegatimes(0,infty), where uuu represents the ...

Ideal free dispersal in integrodifference models

Journal of Mathematical Biology, Jul 1, 2022

Spatial Ecology via Reaction-Diffusion Equations

... ED1TOR-IN-CH1EF Simon Levin, Princeton University, USA Spatial Ecology via Reaction-Diffusion... more ... ED1TOR-IN-CH1EF Simon Levin, Princeton University, USA Spatial Ecology via Reaction-Diffusion Equations Robert Stephen Cantrell and ... of Ecology and Evolutionary Biology, Princeton University, USA Associate Editors Zvia Agur, Tel-Aviv University, Israel Odo Diekmann. ...

Research Square (Research Square), Feb 18, 2022

Consumers must track and acquire resources in complex landscapes. Much discussion has focused on ... more Consumers must track and acquire resources in complex landscapes. Much discussion has focused on the concept of a 'resource gradient' and the mechanisms by which consumers can take advantage of such gradients as they navigate their landscapes in search of resources. However, the concept of tracking resource gradients means different things in different contexts. Here we take a synthetic approach and consider six different definitions of what it means to search for resources based on density or gradients in density. These include scenarios where consumers change their movement behavior based on the density of conspecifics, on the density of resources, and on spatial or temporal gradients in resources. We also consider scenarios involving non-local perception and a form of memory. Using a continuous space, continuous time model that allows consumers to switch between resource-tracking and random motion, we investigate the relative performance of these six different strategies. Consumers' success in matching the spatiotemporal distributions of their resources differs starkly across the six scenarios. Movement strategies based on perception and response to temporal (rather than spatial) resource gradients afforded consumers with the best opportunities to match resource distributions. All scenarios would allow for optimization of resource matching in terms of the underlying parameters, providing opportunities for evolutionary adaptation, and links back to classical studies of foraging ecology.

arXiv (Cornell University), Jan 10, 2020

We consider a model for a population in a heterogeneous environment, with logistic-type local pop... more We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reaction-diffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".

Theoretical Ecology, Aug 23, 2022

Consumers must track and acquire resources in complex landscapes. Much discussion has focused on ... more Consumers must track and acquire resources in complex landscapes. Much discussion has focused on the concept of a 'resource gradient' and the mechanisms by which consumers can take advantage of such gradients as they navigate their landscapes in search of resources. However, the concept of tracking resource gradients means different things in different contexts. Here, we take a synthetic approach and consider six different definitions of what it means to search for resources based on density or gradients in density. These include scenarios where consumers change their movement behavior based on the density of conspecifics, on the density of resources, and on spatial or temporal gradients in resources. We also consider scenarios involving non-local perception and a form of memory. Using a continuous space, continuous time model that allows consumers to switch between resource-tracking and random motion, we investigate the relative performance of these six different strategies. Consumers' success in matching the spatiotemporal distributions of their resources differs starkly across the six scenarios. Movement strategies based on perception and response to temporal (rather than spatial) resource gradients afforded consumers with the best opportunities to match resource distributions. All scenarios would allow for optimization of resource-matching in terms of the underlying parameters, providing opportunities for evolutionary adaptation, and links back to classical studies of foraging ecology.

Effects of domain size on the persistence of populations in a diffusive food-chain model with Beddington-DeAngelis functional response

ABSTRACT. A food chain consisting of species at three trophic levels is modeled using Beddington‐... more ABSTRACT. A food chain consisting of species at three trophic levels is modeled using Beddington‐DeAngelis functional responses as the links between trophic levels. The dispersal of the species is modeled by diffusion, so the resulting model is a three component reaction‐diffusion system. The behavior of the system is described in terms of predictions of extinction or persistence of the species. Persistence is characterized via permanence, i.e., uniform persistence plus dissi‐pativity. The way that the predictions of extinction or persistence depend on domain size is studied by examining how they vary as the size (but not the shape) of the underlying spatial domain is changed.

Mathematical biosciences, Nov 1, 2018

Roughly speaking, a population is said to have an ideal free distribution on a spatial region if ... more Roughly speaking, a population is said to have an ideal free distribution on a spatial region if all of its members can and do locate themselves in a way that optimizes their fitness, allowing for the effects of crowding. Dispersal strategies that can lead to ideal free distributions of populations using them have been shown to exist and to be evolutionarily stable in a number of modeling contexts in the case of habitats that vary in space but not in time. Those modeling contexts include reaction-diffusion-advection models and the analogous models using discrete diffusion or nonlocal dispersal described by integro-differential equations. Furthermore, in the case of reaction-diffusion-advection models and their nonlocal analogues, there are strategies that allow populations to achieve an ideal free distribution by using only local information about environmental quality and/or gradients. We show that in the context of reactiondiffusion-advection models for time-periodic environments with spatially varying resource levels, where the total level of resources in an environment remains fixed but its location varies seasonally, there are strategies that allow populations to achieve an ideal free distribution. We also show that those strategies are evolutionarily stable. However, achieving an ideal free distribution in a time-periodic environment requires the use of nonlocal information about the environment such as might be derived from experience and memory, social learning, or genetic programming. This is joint work with Chris Cosner.

Mathematics, Mar 11, 2020

In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage st... more In this article, we study how the rates of diffusion in a reaction-diffusion model for a stage structured population in a heterogeneous environment affect the model's predictions of persistence or extinction for the population. In the case of a population without stage structure, faster diffusion is typically detrimental. In contrast to that, we find that, in a stage structured population, it can be either detrimental or helpful. If the regions where adults can reproduce are the same as those where juveniles can mature, typically slower diffusion will be favored, but if those regions are separated, then faster diffusion may be favored. Our analysis consists primarily of estimates of principal eigenvalues of the linearized system around (0, 0) and results on their asymptotic behavior for large or small diffusion rates. The model we study is not in general a cooperative system, but if adults only compete with other adults and juveniles with other juveniles, then it is. In that case, the general theory of cooperative systems implies that, when the model predicts persistence, it has a unique positive equilibrium. We derive some results on the asymptotic behavior of the positive equilibrium for small diffusion and for large adult reproductive rates in that case.

Effects of dispersal rates in a two-stage reaction-diffusion system

Journal of Mathematical Biology, Feb 3, 2023

The Effect of Directed Movement on the Strong Allee Effect

Siam Journal on Applied Mathematics, 2021

It is well known that movement strategies in ecology and in economics can make the difference bet... more It is well known that movement strategies in ecology and in economics can make the difference between extinction and persistence. We present a unifying model for the dynamics of ecological populati...

Theoretical Ecology, Jun 15, 2019

Animals use different modes of movement at different times, in different locations, and on differ... more Animals use different modes of movement at different times, in different locations, and on different scales. Incorporating such context dependence in mathematical models represents a substantial increase in complexity, but creates an opportunity to more fully integrate key biological features. Here, we consider the spatial dynamics of a population of foragers with two subunits. In one subunit, foragers move via diffusion (random search) whereas in the other, foragers move via advection (gradient-following search). Foragers switch back and forth between the subunits as functions of their spatial context (i.e., depending on whether they are inside or outside of a patch, or depending on whether or not they can detect a gradient in resource density). We consider a onedimensional binary landscape of resource patches and non-habitat and gauge success in terms of how well the mobile foragers overlap with the distribution of resources. Actively switching between dispersal modes can sometimes greatly enhance this spatial overlap relative to the spatial overlap possible when foragers merely blend advection and diffusion modes at all times. Switching between movement modes is most beneficial when organism's gradient-following abilities are weak compared to its overall capacity for movement, but switching can actually be quite detrimental for organisms that can rapidly follow resource gradients. An organism's perceptual range plays a critical role in determining the conditions under which switching movement modes benefits versus disadvantages foragers as they seek out resources.

Journal of Mathematical Biology, Sep 13, 2019

Based on a Ross-Macdonald type model with a number of identical patches, we study the role of the... more Based on a Ross-Macdonald type model with a number of identical patches, we study the role of the movement of humans and/or mosquitoes on the persistence of malaria and many other vector-borne diseases. By using a theorem on line-sum symmetric matrices, we establish an eigenvalue inequality on the product of a class of nonnegative matrices and then apply it to prove that the basic reproduction number of the multipatch model is always greater than or equal to that of the single patch model. Biologically, this means that habitat fragmentation or patchiness promotes disease outbreaks and intensifies disease persistence. The risk of infection is minimized when the distribution of mosquitoes is proportional to that of humans. Numerical examples for the two-patch submodel are given to investigate how the multipatch reproduction number varies with human and/or mosquito movement. The reproduction number can surpass any given value whenever an appropriate travel pattern is chosen. Fast human and/or mosquito movement decreases the infection risk, but may increase the total number of infected humans.

Discrete and Continuous Dynamical Systems-series B, Sep 1, 2016

West Nile virus (WNV) was first detected in the United States (U.S.) during an outbreak in New Yo... more West Nile virus (WNV) was first detected in the United States (U.S.) during an outbreak in New York City in 1999 with 62 human cases including seven deaths. In 2001, the first human case in Florida was identified, and in Texas and California it was 2002 and 2004, respectively. WNV has now been spread to almost all states in the US. In 2015, the Center for Disease Control and Prevention (CDC) reported 2,175 human cases, including

Theoretical Ecology, Nov 29, 2016

There is a great deal of interest in the effects of biotic interactions on geographic distributio... more There is a great deal of interest in the effects of biotic interactions on geographic distributions. Nature contains many different types of biotic interactions (notably mutualism, commensalism, predation, amensalism and competition), and it is difficult to compare the effects of multiple interaction types on species' distributions. To resolve this problem, we analyze a general, flexible model of pairwise biotic interactions that can describe all interaction types. In the absence of strong positive feedback, a species' ability to be present depends on its ability to increase in numbers when it is rare and the species it is interacting with is at equilibrium. This insight leads to counterintuitive conclusions. Notably we often predict the same range limit when the focal species experiences competition, predation or amensalism. Similarly, we often predict the same range margin or when the species experiences mutualism, commensalism or benefits from prey. In the presence of strong positive density dependent feedback different species interactions produce different range limits in our model. In all cases, the abiotic environment can indirectly influence the impact of biotic interactions on range limits. We illustrate the implications of this observation by analyzing a stress gradient where biotic interactions are harmful in benign environments but beneficial in stressful environments. Our results emphasize the need to consider the effects of all biotic interactions on species' range limits, and provide a systematic comparison of when biotic interactions affect distributions.

The American Naturalist, Feb 1, 2016

Climate change drives uneven phenology shifts across taxa, and this can result in changes to the ... more Climate change drives uneven phenology shifts across taxa, and this can result in changes to the phenological match between interacting species. Shifts in the relative phenology of partner species are well documented, but few studies have addressed the effects of such changes on population dynamics. To explore this, we develop a phenologically explicit model describing consumer-resource interactions. Focusing on scenarios for univoltine insects, we show how changes in resource phenology can be reinterpreted as transformations in the yearto-year recursion relationships defining consumer population dynamics. This perspective provides a straightforward path for interpreting the long-term population consequences of phenology change. Specifically, by relating the outcome of phenological shifts to species traits governing recursion relationships (e.g., consumer fecundity or competitive scenario), we demonstrate how changes in relative phenology can force systems into different dynamical regimes, with major implications for resource management, conservation, and other areas of applied dynamics.

On the Allee effect and directed movement on the whole space

Mathematical Biosciences and Engineering, 2023

It is well known that relocation strategies in ecology can make the difference between extinction... more It is well known that relocation strategies in ecology can make the difference between extinction and persistence. We consider a reaction-advection-diffusion framework to analyze movement strategies in the context of species which are subject to a strong Allee effect. The movement strategies we consider are a combination of random Brownian motion and directed movement through the use of an environmental signal. We prove that a population can overcome the strong Allee effect when the signals are super-harmonic. In other words, an initially small population can survive in the long term if they aggregate sufficiently fast. A sharp result is provided for a specific signal that can be related to the Fokker-Planck equation for the Orstein-Uhlenbeck process. We also explore the case of pure diffusion and pure aggregation and discuss their benefits and drawbacks, making the case for a suitable combination of the two as a better strategy.

Linking mathematical models and trap data to infer the proliferation, abundance, and control of Aedes aegypti

Acta Tropica, Mar 1, 2023

Journal of Mathematical Biology, Feb 19, 2019

Many types of organisms disperse through heterogeneous environments as part of their life histori... more Many types of organisms disperse through heterogeneous environments as part of their life histories. For various models of dispersal, including reactionadvection-diffusion models in continuously varying environments, it has been shown by pairwise invasibility analysis that dispersal strategies which generate an ideal free distribution are evolutionarily steady strategies (ESS, also known as evolutionarily stable strategies) and are neighborhood invader strategies (NIS). That is, populations using such strategies can both invade and resist invasion by populations using strategies that do not produce an ideal free distribution. (The ideal free distribution arises from the assumption that organisms inhabiting heterogeneous environments should move to maximize their fitness, which allows a mathematical characterization in terms of fitness equalization.) Classical reaction diffusion models assume that landscapes vary continuously. Landscape ecologists consider landscapes as mosaics of patches where individuals can make movement decisions at sharp interfaces between patches of different quality. We use a recent formulation of reaction-diffusion systems in patchy landscapes to study dispersal strategies by using methods inspired

Journal of Mathematical Biology, Nov 3, 2018

We study the evolutionary stability of dispersal strategies, including but not limited to those t... more We study the evolutionary stability of dispersal strategies, including but not limited to those that can produce ideal free population distributions (that is, distributions where all individuals have equal fitness and there is no net movement of individuals at equilibrium). The environment is assumed to be variable in space but constant in time. We assume that there is a separation of times scales, so that dispersal occurs on a fast timescale, evolution occurs on a slow timescale, and population dynamics and interactions occur on an intermediate timescale. Starting with advection-diffusion models for dispersal without population dynamics, we use the large time limits of profiles for population distributions together with the distribution of resources in the environment to calculate growth and interaction coefficients in logistic and Lotka-Volterra ordinary differential equations describing population dynamics. We then use a pairwise invasibility analysis approach motivated by adaptive dynamics to study the evolutionary and/or convergence stability of strategies determined by various assumptions about the advection and diffusion terms in the original advection-diffusion dispersal models. Among other results we find that those strategies which can produce an ideal free distribution are evolutionarily stable.

Diffusive Logistic Equations with Indefinite Weights: Population Models in Disrupted Environments II

Siam Journal on Mathematical Analysis, Jul 1, 1991

The dynamics of a population inhabiting a strongly heterogeneous environment are modeled by diffu... more The dynamics of a population inhabiting a strongly heterogeneous environment are modeled by diffusive logistic equations of the form u_1=nablacdot(d(x,u)+nablau)−bfb(x)cdotnablau+m(x)u−cu2u_1 = \nabla \cdot (d(x,u) + \nabla u) - {\bf b}(x) \cdot \nabla u + m(x)u - cu^2 u_1=nablacdot(d(x,u)+nablau)−bfb(x)cdotnablau+m(x)u−cu2 in Omegatimes(0,infty)\Omega \times (0,\infty )Omegatimes(0,infty), where uuu represents the ...

Ideal free dispersal in integrodifference models

Journal of Mathematical Biology, Jul 1, 2022

Spatial Ecology via Reaction-Diffusion Equations

... ED1TOR-IN-CH1EF Simon Levin, Princeton University, USA Spatial Ecology via Reaction-Diffusion... more ... ED1TOR-IN-CH1EF Simon Levin, Princeton University, USA Spatial Ecology via Reaction-Diffusion Equations Robert Stephen Cantrell and ... of Ecology and Evolutionary Biology, Princeton University, USA Associate Editors Zvia Agur, Tel-Aviv University, Israel Odo Diekmann. ...

Research Square (Research Square), Feb 18, 2022

Consumers must track and acquire resources in complex landscapes. Much discussion has focused on ... more Consumers must track and acquire resources in complex landscapes. Much discussion has focused on the concept of a 'resource gradient' and the mechanisms by which consumers can take advantage of such gradients as they navigate their landscapes in search of resources. However, the concept of tracking resource gradients means different things in different contexts. Here we take a synthetic approach and consider six different definitions of what it means to search for resources based on density or gradients in density. These include scenarios where consumers change their movement behavior based on the density of conspecifics, on the density of resources, and on spatial or temporal gradients in resources. We also consider scenarios involving non-local perception and a form of memory. Using a continuous space, continuous time model that allows consumers to switch between resource-tracking and random motion, we investigate the relative performance of these six different strategies. Consumers' success in matching the spatiotemporal distributions of their resources differs starkly across the six scenarios. Movement strategies based on perception and response to temporal (rather than spatial) resource gradients afforded consumers with the best opportunities to match resource distributions. All scenarios would allow for optimization of resource matching in terms of the underlying parameters, providing opportunities for evolutionary adaptation, and links back to classical studies of foraging ecology.

arXiv (Cornell University), Jan 10, 2020

We consider a model for a population in a heterogeneous environment, with logistic-type local pop... more We consider a model for a population in a heterogeneous environment, with logistic-type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior has been observed in some natural systems. We study how environmental heterogeneity and the rates of switching and diffusion affect the persistence of the population. The reaction-diffusion systems in the models can be cooperative at some population densities and competitive at others. The results extend our previous work on similar models in homogeneous environments. We also consider competition between two populations that are ecologically identical, but where one population diffuses at a fixed rate and the other switches between two different diffusion rates. The motivation for that is to gain insight into when switching might be advantageous versus diffusing at a fixed rate. This is a variation on the classical results for ecologically identical competitors with differing fixed diffusion rates, where it is well known that "the slower diffuser wins".