Diffusion-driven instabilities and emerging spatial patterns in patchy landscapes

Spatial variation in population densities across a landscape is a feature of many ecological systems, from self-organised patterns on mussel beds to spatially restricted insect outbreaks. It occurs as a result of environmental variation in abiotic factors and/or biotic factors structuring the spatial distribution of populations. However the ways in which abiotic and biotic factors interact to determine the existence and nature of spatial patterns in population density remain poorly understood. Here we present a new approach to studying this question by analysing a predator–prey patch-model in a heterogenous landscape. We use analytical and numerical methods originally developed for studying nearest- neighbour (juxtacrine) signalling in epithelia to explore whether and under which conditions patterns emerge. We find that abiotic and biotic factors interact to promote pattern formation. In fact, we find a rich and highly complex array of coexisting stable patterns, located within an enormous number of unstable patterns. Our simulation results indicate that many of the stable patterns have appreciable basins of attraction, making them significant in applications. We are able to identify mechanisms for these patterns based on the classical ideas of long-range inhibition and short-range activation, whereby landscape heterogeneity can modulate the spatial scales at which these processes operate to structure the populations

Dynamics and coexistence in a system with intraguild mutualism

It is a tenet of ecological theory that two competing consumers cannot stably coexist on a single limiting resource in a homogeneous environment. Many mechanisms and processes have since been evoked and studied, empirically and theoretically, to explain species coexistence and the observed biological diversity. Facilitative interactions clearly have the potential to enhance coexistence. Yet, even though mutual facilitation between species of the same guild is widely documented empirically, the subject has received very little theoretical attention. Here, we study one form of intraguild mutualism in the simplest possibly community module of one resource and two consumers. We incorporate mutualism as enhanced consumption in the presence of the other consumers. We find that intraguild mutualism can (a) significantly enhance coexistence of consumers, (b) induce cyclic dynamics, and (c) give rise to a bi-stability (a 'joint' Allee effect) and potentially catastrophic collapse of both consumer species.Fil: Assaneo, María Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Física de Buenos Aires. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Física de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Física. Laboratorio de Sistemas Dinámicos; ArgentinaFil: Coutinho, Renato Mendes. Universidade Estadual Paulista Julio de Mesquita Filho; BrasilFil: Lin, Yangchen. University of Cambridge; Estados UnidosFil: Mantilla, Carlos. Universidad de Carabobo.; VenezuelaFil: Lutscher, Frithjof. University of Ottawa; Canad

Faster movement in non-habitat matrix promotes range shifts in heterogeneous landscapes

Ecologists often assume that range expansion will be fastest in landscapes composed entirely of the highest‐quality habitat. Theoretical models, however, show that range expansion depends on both habitat quality and habitat‐specific movement rates. Using data from 78 species in 70 studies, we find that animals typically have faster movement through lower‐quality environments (73% of published cases). Therefore, if we want to manage landscapes for range expansion, there is a trade‐off between promoting movement with nonhostile matrix, and promoting population growth with high‐quality habitat. We illustrate how this trade‐off plays out with the use of an exemplar species, the Baltimore checkerspot butterfly. For this species, we calculate that the expected rate of range expansion is fastest in landscapes with ~15% high‐quality habitat. Behavioral responses to nonhabitat matrix have often been documented in animal populations, but rarely included in empirical predictions of range expansion. Considering movement behavior could change land‐planning priorities from focus on high‐quality habitat only to integrating high‐ and low‐quality land cover types, and evaluating the costs and benefits of different matrix land covers for range expansion

Recommendations for increasing the use of HIV/AIDS resource allocation models

The article of record as published may be found at: http://dx.doi.org/10.1186/1471-2458-9-S1-S8Background: Resource allocation models have not had a substantial impact on HIV/AIDS resource allocation decisions in spite of the important, additional insights they may provide. In this paper, we highlight six difficulties often encountered in attempts to implement such models in policy settings; these are: model complexity, data requirements, multiple stakeholders, funding issues, and political and ethical considerations. We then make recommendations as to how each of these difficulties may be overcome. Results: To ensure that models can inform the actual decision, modellers should understand the environment in which decision-makers operate, including full knowledge of the stakeholders' key issues and requirements. HIV/AIDS resource allocation model formulations should be contextualized and sensitive to societal concerns and decision-makers' realities. Modellers should provide the required education and training materials in order for decision-makers to be reasonably well versed in understanding the capabilities, power and limitations of the model. Conclusion: This paper addresses the issue of knowledge translation from the established resource allocation modelling expertise in the academic realm to that of policymaking

Transient dynamics in equilibrium and non-equilibrium communities

Human activities or natural events may perturb locally stable equilibrium communities. One can ask how long the community will take to return to its equilibrium and how "far" from the equilibrium it may get in the process. To answer those questions, we can measure the "resilience" and "reactivity" of a system. These concepts thus quantify one particular form of transient dynamics in ecological models. I will briefly review these measures and give some examples and known but still surprising insights. Then I will suggest extensions to periodically forced systems and periodic orbits in autonomous systems and examine some of their properties.Non UBCUnreviewedAuthor affiliation: University of OttawaFacult

Prey and generalist predator through the seasons

Non UBCUnreviewedAuthor affiliation: University of OttawaFacult

Modeling moving polarized groups of animals and cells

The striking patterns which can be found in moving polarized groups such as schools of fish or flocks of birds result from a twofold adaptation process: Individuals adapt their orientation of movement to that of their neighbors, a process which is called alignment. Within a moving group individuals also adapt their speed to the speed of the group. Several models for this behavior are derived. They take the form of systems of nonlinear partial differential equations. First, the speed of an individual is assumed constant and in the simplest model individuals move in one dimensional space. They change direction depending on the direction of their neighbors. Still assuming constant speed, the model is generalized to movement in several space dimensions. Then the speed adaptation process is modeled for movement in one dimension. Finally, the two models for alignment and speed adaptation are combined in one dimension. The qualitative behavior of solutions is examined analytically and numerically. Analytical results comprise existence of solutions, stability conditions, invariant domains and description of limit sets. Mathematical tools are dynamical systems theory, linear and nonlinear partial differential equations, a priori estimates, Lyapunov functions, vanishing viscosity solutions. Numerical simulations show that the behavior of solutions can be interpreted as schooling behavior of individuals.The striking patterns which can be found in moving polarized groups such as schools of fish or flocks of birds result from a twofold adaptation process: Individuals adapt their orientation of movement to that of their neighbors, a process which is called alignment. Within a moving group individuals also adapt their speed to the speed of the group. Several models for this behavior are derived. They take the form of systems of nonlinear partial differential equations. First, the speed of an individual is assumed constant and in the simplest model individuals move in one dimensional space. They change direction depending on the direction of their neighbors. Still assuming constant speed, the model is generalized to movement in several space dimensions. Then the speed adaptation process is modeled for movement in one dimension. Finally, the two models for alignment and speed adaptation are combined in one dimension. The qualitative behavior of solutions is examined analytically and numerically. Analytical results comprise existence of solutions, stability conditions, invariant domains and description of limit sets. Mathematical tools are dynamical systems theory, linear and nonlinear partial differential equations, a priori estimates, Lyapunov functions, vanishing viscosity solutions. Numerical simulations show that the behavior of solutions can be interpreted as schooling behavior of individuals

Integrodifference equations in spatial ecology

This book is the first thorough introduction to and comprehensive treatment of the theory and applications of integrodifference equations in spatial ecology. Integrodifference equations are discrete-time continuous-space dynamical systems describing the spatio-temporal dynamics of one or more populations. The book contains step-by-step model construction, explicitly solvable models, abstract theory and numerical recipes for integrodifference equations. The theory in the book is motivated and illustrated by many examples from conservation biology, biological invasions, pattern formation and other areas. In this way, the book conveys the more general message that bringing mathematical approaches and ecological questions together can generate novel insights into applications and fruitful challenges that spur future theoretical developments. The book is suitable for graduate students and experienced researchers in mathematical ecology alike