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"Biological invasions Mathematical models."
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The Physics of Foraging
Do the movements of animals, including humans, follow patterns that can be described quantitatively by simple laws of motion? If so, then why? These questions have attracted the attention of scientists in many disciplines, and stimulated debates ranging from ecological matters to queries such as 'how can there be free will if one follows a law of motion?' This is the first book on this rapidly evolving subject, introducing random searches and foraging in a way that can be understood by readers without a previous background on the subject. It reviews theory as well as experiment, addresses open problems and perspectives, and discusses applications ranging from the colonization of Madagascar by Austronesians to the diffusion of genetically modified crops. The book will interest physicists working in the field of anomalous diffusion and movement ecology as well as ecologists already familiar with the concepts and methods of statistical physics.
eBook
Ecological niches and geographic distributions
This book provides a first synthetic view of an emerging area of ecology and biogeography, linking individual- and population-level processes to geographic distributions and biodiversity patterns. Problems in evolutionary ecology, macroecology, and biogeography are illuminated by this integrative view. The book focuses on correlative approaches known as ecological niche modeling, species distribution modeling, or habitat suitability modeling, which use associations between known occurrences of species and environmental variables to identify environmental conditions under which populations can be maintained. The spatial distribution of environments suitable for the species can then be estimated: a potential distribution for the species. This approach has broad applicability to ecology, evolution, biogeography, and conservation biology, as well as to understanding the geographic potential of invasive species and infectious diseases, and the biological implications of climate change.
The authors lay out conceptual foundations and general principles for understanding and interpreting species distributions with respect to geography and environment. Focus is on development of niche models. While serving as a guide for students and researchers, the book also provides a theoretical framework to support future progress in the field.
eBook
Invading with biological weapons: the importance of disease-mediated invasions
1. Invasive organisms and emerging wildlife disease pose two of the greatest threats to global biodiversity and ecosystem functioning. 2. Typically, when parasites are considered in invasion biology, it is in the context of the enemy release hypothesis, wherein a non-indigenous species has greater probability of invasion success by virtue of leaving its natural enemies, including parasites, behind. 3. It is also possible that native parasites may prevent invasions, but it is clear that invasive organisms may bring infectious diseases with them that can infect native competitors (via spillover), or act as competent hosts for native diseases, increasing disease prevalence among native species (via spillback). 4. If the shared disease (either via spillover or spillback) has higher virulence in the native host (which is particularly likely with introduced parasites), there is the potential that the disease can act as a 'biological weapon' leading to a disease-mediated invasion (DMI). 5. Here, we review cases where disease may have been an important factor mediating a wide range of invasions in vertebrates, invertebrates and plants. 6. We then focus on the invasion of the grey squirrel into the UK as a case study of a DMI, and we discuss how mathematical models have helped us to understand the importance of this shared disease and its implications for the management of invasive species. 7. We conclude that (i) DMIs are a widespread phenomenon, that (ii) spillover is more common in animal invasions and spillback more common among plant invasions and that (iii) spillover DMIs are particularly important in explaining the replacement of native animals with phylogenetically similar non-indigenous species.
Journal Article
Direct and indirect effects of invasive species: Biodiversity loss is a major mechanism by which an invasive tree affects ecosystem functioning
1. Global change, such as exotic invasions, dramatically affects ecosystem functioning. However, the mechanisms behind the impacts are often unclear and despite extensive experimental work, we know little about the importance of biodiversity loss as a component of global change effects in real-world ecosystems. 2. We disentangled several mechanisms by which an exotic invader affected ecosystem functioning in East African drylands in Kenya and Ethiopia. We used structural equation modelling to separate direct effects of a woody invader Prosopis juliflora on a range of ecosystem functions from indirect effects mediated through changes in biodiversity (plant species richness) and ecosystem functioning (herbaceous biomass). We analysed effects on ecosystem functions linked to soil biogeochemical cycling and transfer of energy between trophic levels. 3. We found that the mean size of individual indirect effects mediated by biodiversity and herbaceous biomass was about twice as large as the mean size of individual direct effects of Prosopis on ecosystem functions, showing that indirect effects are an important component of the invader's overall environmental impacts. Changes in both herbaceous biomass and biodiversity were approximately equally important as drivers of indirect effects, indicating that we need to expand our view of indirect effects to consider a wider range of mechanisms. Simple univariate models failed to capture some Prosopis invader effects because positive direct effects on soil stability and predatory invertebrates were counteracted by negative indirect effects on biodiversity or biomass loss. The majority of effects were similar in both study systems. Suggestions that woody invaders are able to increase certain ecosystem functions may therefore have arisen because these negative indirect effects were not considered. 4. Synthesis. Our study indicates that successful management of exotic invasions is likely to require not only control of the invader but also restoration of diverse and productive herbaceous communities as they are important for many ecosystem functions. This highlights the importance of biodiversity as a driver of ecosystem functioning also in real-world systems.
Journal Article
Controlling Biological Invasions: A Stochastic Host–Generalist Parasitoid Model
On a global scale, biological invasions are seriously destroying the stability of ecosystem, sharply decreasing biodiversity and even endangering human health and causing huge economic losses. However, there exist few effective measures controlling biological invasions. To more accurately examine the prevention and control effects of biological control on biological invasions in real environments of random fluctuations, we construct a stochastic host–generalist parasitoid model. We first establish, respectively, the sufficient conditions for the persistence and extinction of invasive hosts and generalist parasitoids, including (1) only the intrusive hosts go extinct; (2) only the generalist parasitoids are extinct, and (3) the intrusive hosts and generalist parasitoids are both extinct or persistent. Then, we perform a series of numerical simulations to verify the validity of the theoretical results obtained, based on which we further discuss the impacts of stochastic environmental fluctuations on the control of intrusive hosts, especially the possible changes of qualitative behavior caused by environmental noises in the bistable scenario. Our theoretical and numerical results indicate that compared with the invasive hosts, the generalist parasitoids are more vulnerable to environmental noises, and the prevention and control effects of biological control on invasive hosts are closely dependent to the initial population sizes. Thus, improving the ability of early detection of ecosystems, including the initial densities of biological populations and their dynamic characteristics, will provide effective predictive guidance for the prevention and control of alien host invasions.
Journal Article
A review of operations research models in invasive species management: state of the art, challenges, and future directions
Invasive species are a major threat to the economy, the environment, health, and thus human well-being. The international community, including the United Nations’ Global Invasive Species Program (GISP), National Invasive Species Council (NISC), and Center for Invasive Species Management (CISM), has called for a rapid control of invaders in order to minimize their adverse impacts. The effective management of invasive species is a highly complex problem requiring the development of decision tools that help managers prioritize actions most efficiently by considering corresponding bio-economic costs, impacts on ecosystems, and benefits of control. Operations research methods, such as mathematical programming models, are powerful tools for evaluating different management strategies and providing optimal decisions for allocating limited resources to control invaders. In this paper, we summarize the mathematical models applied to optimize invasive species prevention, surveillance, and control. We first define key concepts in invasive species management (ISM) in a framework that characterizes biological invasions, associated economic and environmental costs, and their management. We then present a spatio-temporal optimization model that illustrates various biological and economic aspects of an ISM problem. Next, we classify the relevant literature with respect to modeling methods: optimal control, stochastic dynamic programming, linear programming, mixed-integer programming, simulation models, and others. We further classify the ISM models with respect to the solution method used, their focus and objectives, and the specific application considered. We discuss limitations of the existing research and provide several directions for further research in optimizing ISM planning. Our review highlights the fact that operations research could play a key role in ISM and environmental decision-making, in particular closing the gap between the decision-support needs of managers and the decision-making tools currently available to management.
Journal Article
Mathematical assessment of the role of temperature on desert locust population dynamics
This study presents a novel non-autonomous mathematical model to explore the intricate relationship between temperature and desert locust population dynamics, considering the influence of both solitarious and gregarious phases across all life stages. The model incorporates temperature-dependent parameters for key biological processes, including egg development, hopper growth, adult maturation, and reproduction. Theoretical analysis reveals the model’s capacity for complex dynamical behaviors, such as multiple stable states and backward bifurcations, suggesting the potential for sudden and unpredictable population shifts. Sensitivity analysis identifies temperature-related parameters as critical drivers of population fluctuations, highlighting the importance of accurate temperature predictions for effective management. Numerical simulations demonstrate the significant impact of temperature on population growth, with optimal conditions promoting rapid development and increased survival, while extreme temperatures can hinder population growth and trigger phase transitions. By providing a deeper understanding of temperature-driven population shifts, this model enhances the ability to predict locust outbreaks, optimize control strategies, and reduce the socio-economic and ecological impacts of locust invasions.
Journal Article
Permanence via invasion graphs: incorporating community assembly into modern coexistence theory
To understand the mechanisms underlying species coexistence, ecologists often study invasion growth rates of theoretical and data-driven models. These growth rates correspond to average per-capita growth rates of one species with respect to an ergodic measure supporting other species. In the ecological literature, coexistence often is equated with the invasion growth rates being positive. Intuitively, positive invasion growth rates ensure that species recover from being rare. To provide a mathematically rigorous framework for this approach, we prove theorems that answer two questions: (i) When do the signs of the invasion growth rates determine coexistence? (ii) When signs are sufficient, which invasion growth rates need to be positive? We focus on deterministic models and equate coexistence with permanence, i.e., a global attractor bounded away from extinction. For models satisfying certain technical assumptions, we introduce invasion graphs where vertices correspond to proper subsets of species (communities) supporting an ergodic measure and directed edges correspond to potential transitions between communities due to invasions by missing species. These directed edges are determined by the signs of invasion growth rates. When the invasion graph is acyclic (i.e. there is no sequence of invasions starting and ending at the same community), we show that permanence is determined by the signs of the invasion growth rates. In this case, permanence is characterized by the invasibility of all -i communities, i.e., communities without species i where all other missing species have negative invasion growth rates. To illustrate the applicability of the results, we show that dissipative Lotka-Volterra models generically satisfy our technical assumptions and computing their invasion graphs reduces to solving systems of linear equations. We also apply our results to models of competing species with pulsed resources or sharing a predator that exhibits switching behavior. Open problems for both deterministic and stochastic models are discussed. Our results highlight the importance of using concepts about community assembly to study coexistence.
Journal Article
An evolutionary model of rhythmic accelerando in animal vocal signalling
Animal acoustic communication contains many structural features. Among these, temporal structure, or rhythmicity, is increasingly tested empirically and modelled quantitatively. Accelerando is a rhythmic structure which consists of temporal intervals increasing in rate over a sequence. Why this particular vocal behaviour is widespread in many different animal lineages, and how it evolved, is so far unknown. Here, we use evolutionary game theory and computer simulations to link two rhythmic aspects of animal communication, acceleration and overlap: We test whether rhythmic accelerando could evolve under a pressure for acoustic overlap in time. Our models show that higher acceleration values result in a higher payoff, driven by the higher relative overlap between sequences. The addition of a cost to the payoff matrix models a physiological disadvantage to high acceleration rates and introduces a divergence between an individual’s incentive and the overall payoff of the population. Analysis of the invasion dynamics of acceleration strategies shows a stable, non-invadable range of strategies for moderate acceleration levels. Our computational simulations confirm these results: A simple selective pressure to maximise the expected overlap, while minimising the associated physiological cost, causes an initially isochronous population to evolve towards producing increasingly accelerating sequences until a population-wide equilibrium of rhythmic accelerando is reached. These results are robust to a broad range of parameter values. Overall, our analyses show that if overlap is beneficial, emergent evolutionary dynamics allow a population to gradually start producing accelerating sequences and reach a stable state of moderate acceleration. Finally, our modelling results closely match empirical data recorded from an avian species showing rhythmic accelerando, the African penguin. This shows the productive interplay between theoretical and empirical biology.
Journal Article