Spatial Population Models in Spatiotemporally Structured Environments

Spatial effects, such as habitat fragmentation and the location and size of disturbance events, play a key role in the dynamics of populations. This is true in natural populations (such as herbs living under a forest canopy) as well as human-dominated systems (for example, crop pests in agricultural landscapes). Focusing on the development of spatial population models, the project seeks to better understand how and why spatially autocorrelated disturbances affect the dynamics of populations with mixtures of short- and long-distance dispersal. A variety of disturbances are considered, including (1) static disturbance, representing habitat heterogeneity across a landscape; (2) short-term disturbance whereby populations are removed from sites which may then be recolonized, e.g. representing short-term control of agricultural crop pests, and (3) landscapes with specified spatial and temporal autocorrelation, whereby blocks of sites become unsuitable and cannot be recolonized until some time has elapsed. The primary objectives of the computational side of the project are to improve the simulation methodology used for these types of spatial models, to enable more rapid/complete exploration of the parameter space and the use of simulation models in Monte Carlo parameter estimation techniques.Spatial disturbances and heterogeneities play a fundamental role in any ecological system. This project develops mathematical models and computational tools to be used in the study of various types of disturbances. Possible applications include the modeling of understory plant species in a forest where gap formation renders a group of sites unsuitable until the canopy regenerates, or the application of pesticides over a region which leaves those sites unsuitable for recolonization by pests for some time. The project will include collaboration with entomologists and other biologists to study the effects of different strategies for controlling pests across agricultural landscapes, such as maggot flies in commercial blueberry fields. The effects of changing habitat distributions on populations, due to factors such as changing land-use patterns and global climate change, will also be considered. Significant undergraduate research training will be included in the project, including participation in a summer research program primarily aimed at underrepresented minority groups

CAREER: Dynamics of Hierarchical HouseholdStructured Epidemiological Models

Mathematical and computational models will be used to study populations hierarchically segregated into groups referred to as households . These households may represent patches within an agricultural field, fields within a landscape, dorms within a school, schools within a city, cities within a region, or even subnetworks within larger computer networks. Population models and epidemiological models will be explored within this framework, complementing other work with lattice-structured populations. In the models, interactions within a household occur much more often than interactions between different households. Primary goals of the models are to better understand how and why spatially targeted and/or clustered treatments affect dynamics of infections, for example varying the rates of pesticide application to crop fields based on the levels of insect infestations among those fields. Factors such as spatially varying resistance (both long-term, due to e.g. mosaic planting of different crops in different fields; and short-term, e.g. as a result of pesticides) will be included in the models. Another application will be better understanding the spread of malicious computer software ( worms ) using biological dispersal strategies in clustered heterogeneous computer networks.Entomologists and other researchers will cooperate with the principal investigator and his students to develop applications of the project such as controlling maggot flies in commercial blueberry fields in Maine, planthoppers in rice fields in China, and other agricultural crop pests. Interdisciplinary courses on modeling and simulation will incorporate various topics from the project. Undergraduate research training will be a significant part of the work, including participation in a summer research program primarily aimed at underrepresented minority groups. Outreach to high school students and teachers will also be included, with the participation of current undergraduates studying to become K-12 teachers

Evolution of predator dispersal in relation to spatio-temporal prey dynamics : how not to get stuck in the wrong place!

Peer reviewedPublisher PD

Moment Closure - A Brief Review

Moment closure methods appear in myriad scientific disciplines in the modelling of complex systems. The goal is to achieve a closed form of a large, usually even infinite, set of coupled differential (or difference) equations. Each equation describes the evolution of one "moment", a suitable coarse-grained quantity computable from the full state space. If the system is too large for analytical and/or numerical methods, then one aims to reduce it by finding a moment closure relation expressing "higher-order moments" in terms of "lower-order moments". In this brief review, we focus on highlighting how moment closure methods occur in different contexts. We also conjecture via a geometric explanation why it has been difficult to rigorously justify many moment closure approximations although they work very well in practice.Comment: short survey paper (max 20 pages) for a broad audience in mathematics, physics, chemistry and quantitative biolog

Can forest management based on natural disturbances maintain ecological resilience?

Given the increasingly global stresses on forests, many ecologists argue that managers must maintain ecological resilience: the capacity of ecosystems to absorb disturbances without undergoing fundamental change. In this review we ask: Can the emerging paradigm of natural-disturbance-based management (NDBM) maintain ecological resilience in managed forests? Applying resilience theory requires careful articulation of the ecosystem state under consideration, the disturbances and stresses that affect the persistence of possible alternative states, and the spatial and temporal scales of management relevance. Implementing NDBM while maintaining resilience means recognizing that (i) biodiversity is important for long-term ecosystem persistence, (ii) natural disturbances play a critical role as a generator of structural and compositional heterogeneity at multiple scales, and (iii) traditional management tends to produce forests more homogeneous than those disturbed naturally and increases the likelihood of unexpected catastrophic change by constraining variation of key environmental processes. NDBM may maintain resilience if silvicultural strategies retain the structures and processes that perpetuate desired states while reducing those that enhance resilience of undesirable states. Such strategies require an understanding of harvesting impacts on slow ecosystem processes, such as seed-bank or nutrient dynamics, which in the long term can lead to ecological surprises by altering the forest's capacity to reorganize after disturbance

Robustness of metacommunities with omnivory to habitat destruction: disentangling patch fragmentation from patch loss

Habitat destruction, characterized by patch loss and fragmentation, is a major driving force of species extinction, and understanding its mechanisms has become a central issue in biodiversity conservation. Numerous studies have explored the effect of patch loss on food web dynamics, but ignored the critical role of patch fragmentation. Here we develop an extended patch-dynamic model for a tri-trophic omnivory system with trophic-dependent dispersal in fragmented landscapes. We found that species display different vulnerabilities to both patch loss and fragmentation, depending on their dispersal range and trophic position. The resulting trophic structure varies depending on the degree of habitat loss and fragmentation, due to a tradeoff between bottom-up control on omnivores (dominated by patch loss) and dispersal limitation on intermediate consumers (dominated by patch fragmentation). Overall, we find that omnivory increases system robustness to habitat destruction relative to a simple food chain

Markovian Dynamics on Complex Reaction Networks

Complex networks, comprised of individual elements that interact with each other through reaction channels, are ubiquitous across many scientific and engineering disciplines. Examples include biochemical, pharmacokinetic, epidemiological, ecological, social, neural, and multi-agent networks. A common approach to modeling such networks is by a master equation that governs the dynamic evolution of the joint probability mass function of the underling population process and naturally leads to Markovian dynamics for such process. Due however to the nonlinear nature of most reactions, the computation and analysis of the resulting stochastic population dynamics is a difficult task. This review article provides a coherent and comprehensive coverage of recently developed approaches and methods to tackle this problem. After reviewing a general framework for modeling Markovian reaction networks and giving specific examples, the authors present numerical and computational techniques capable of evaluating or approximating the solution of the master equation, discuss a recently developed approach for studying the stationary behavior of Markovian reaction networks using a potential energy landscape perspective, and provide an introduction to the emerging theory of thermodynamic analysis of such networks. Three representative problems of opinion formation, transcription regulation, and neural network dynamics are used as illustrative examples.Comment: 52 pages, 11 figures, for freely available MATLAB software, see http://www.cis.jhu.edu/~goutsias/CSS%20lab/software.htm

Intense or Spatially Heterogeneous Predation Can Select against Prey Dispersal

Dispersal theory generally predicts kin competition, inbreeding, and temporal variation in habitat quality should select for dispersal, whereas spatial variation in habitat quality should select against dispersal. The effect of predation on the evolution of dispersal is currently not well-known: because predation can be variable in both space and time, it is not clear whether or when predation will promote dispersal within prey. Moreover, the evolution of prey dispersal affects strongly the encounter rate of predator and prey individuals, which greatly determines the ecological dynamics, and in turn changes the selection pressures for prey dispersal, in an eco-evolutionary feedback loop. When taken all together the effect of predation on prey dispersal is rather difficult to predict. We analyze a spatially explicit, individual-based predator-prey model and its mathematical approximation to investigate the evolution of prey dispersal. Competition and predation depend on local, rather than landscape-scale densities, and the spatial pattern of predation corresponds well to that of predators using restricted home ranges (e.g. central-place foragers). Analyses show the balance between the level of competition and predation pressure an individual is expected to experience determines whether prey should disperse or stay close to their parents and siblings, and more predation selects for less prey dispersal. Predators with smaller home ranges also select for less prey dispersal; more prey dispersal is favoured if predators have large home ranges, are very mobile, and/or are evenly distributed across the landscape