The intermediate dispersal principle in spatially explicit metapopulations

Casagrandi, Renato; Gatto, Marino

doi:10.1016/j.jtbi.2005.07.009

Cited by 23 publications

(15 citation statements)

References 35 publications

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“…Possible examples include directly transmitted human diseases (i.e., pathologies that are transmitted through airborne or fecal-oral contact), in which the intertwining of mobility and social networks may play a key role in spreading the epidemic, and vector-borne/zoonotic diseases, in which spatial interactions of both host and vector/carrier populations might be relevant. In general, the mathematical framework outlined in this work can be used to approach other (apparently unrelated) topics in spatial and conservation ecology, such as the persistence of populations living in fragmented landscapes (e.g., Casagrandi and Gatto 1999Gatto , 2002Gatto , 2006, advective environments (e.g., Speirs and Gurney 2001;Pachepsky et al 2005), dendritic networks (Campbell Grant et al 2007, and webs of marine protected areas (e.g., White et al 2010;Aiken and Navarrete 2011;Watson et al 2011). In all these cases, in fact, population persistence can be established by properly accounting for the relevant spatial interactions and studying the conditions under which the extinction equilibrium becomes stable or unstable.…”

Section: Discussionmentioning

confidence: 99%

Spatially Explicit Conditions for Waterborne Pathogen Invasion

Gatto

Mari

Bertuzzo

et al. 2013

The American Naturalist

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Waterborne pathogens cause many possibly lethal human diseases. We derive the condition for pathogen invasion and subsequent disease outbreak in a territory with specific, space-inhomogeneous characteristics (hydrological, ecological, demographic, and epidemiological). The criterion relies on a spatially explicit model accounting for the density of susceptible and infected individuals and the pathogen concentration in a network of communities linked by human mobility and the water system. Pathogen invasion requires that a dimensionless parameter, the dominant eigenvalue of a generalized reproductive matrix J 0 , be larger than unity. Conditions for invasion are studied while crucial parameters (population density distribution, contact and water contamination rates, pathogen growth rates) and the characteristics of the networks (connectivity, directional transport, water retention times, mobility patterns) are varied. We analyze both simple, prototypical test cases and realistic landscapes, in which optimal channel networks mimic the water systems and gravitational models describe human mobility. Also, we show that the dominant eigenvector of J 0 effectively portrays the geography of epidemic outbreaks, that is, the areas of the studied territory that will be initially affected by an epidemic. This is important for planning an efficient spatial allocation of interventions (e.g., improving sanitation and providing emergency aid and medicines).

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Section: Discussionmentioning

confidence: 99%

Spatially Explicit Conditions for Waterborne Pathogen Invasion

Gatto

Mari

Bertuzzo

et al. 2013

The American Naturalist

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“…On the one hand, dispersal may help species escape local catastrophes [7]; on the other hand, dispersal of common species may endanger rarer ones by 'stepping over' their geographical distributions, and limited dispersal favours divergence among allopatric populations. From a more applied viewpoint, understanding why certain species or genotypes disperse more than others might help to understand shifts in species distributions because of global change [8], to understand constraints on the adaptation of species to changing environmental conditions [9], to plan conservation strategies for threatened species or communities [10,11] and to design strategies for the management of invasive species [12] that build upon our knowledge of their evolutionary histories.…”

Section: Introductionmentioning

confidence: 99%

An empiricist's guide to theoretical predictions on the evolution of dispersal

2013

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Dispersal, the tendency for organisms to reproduce away from their parents, influences many evolutionary and ecological processes, from speciation and extinction events, to the coexistence of genotypes within species or biological invasions. Understanding how dispersal evolves is crucial to predict how global changes might affect species persistence and geographical distribution. The factors driving the evolution of dispersal have been well characterized from a theoretical standpoint, and predictions have been made about their respective influence on, for example, dispersal polymorphism or the emergence of dispersal syndromes. However, the experimental tests of some theories remain scarce partly because a synthetic view of theoretical advances is still lacking. Here, we review the different ingredients of models of dispersal evolution, from selective pressures and types of predictions, through mathematical and ecological assumptions, to the methods used to obtain predictions. We provide perspectives as to which predictions are easiest to test, how theories could be better exploited to provide testable predictions, what theoretical developments are needed to tackle this topic, and we place the question of the evolution of dispersal within the larger interdisciplinary framework of eco-evolutionary dynamics.

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“…A good reference to find the underlying mathematical theory is the textbook by Allen (2003) and its references. As examples of recent applications of continuous-time Markov chains in population biology, we mention some papers published in this journal (Casagrandi and Gatto, 2006;Fouchet et al, 2008;Stirk et al, 2008;Xu et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Quasi-stationary and ratio of expectations distributions: A comparative study

Artalejo

Lopez-Herrero

2010

Journal of Theoretical Biology

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Abstract. Many stochastic systems, including biological applications, use Markov chains in which there is a set of absorbing states. It is then needed to consider analogues of the stationary distribution of an irreducible chain. In this context, quasi-stationary distributions play a fundamental role to describe the long-term behavior of the system. The rationale for using quasi-stationary distribution is well established in the abundant existing literature. The aim of this study is to reformulate the ratio of means approach Seneta, 1965, 1967) which provides a simple alternative. We have a two-fold objective. The first objective is viewing quasi-stationarity and ratio of expectations as two different approaches for understanding the dynamics of the system before absorption. At this point, we remark that the quasi-stationary distribution and a ratio of means distribution may give or not give similar information. In this way, we arrive to the second objective; namely, to investigate the possibility of using the ratio of expectations distribution as an approximation to the quasistationary distribution. This second objective is explored by comparing both distributions in some selected scenarios, which are mainly inspired in stochastic epidemic models. Previously, the rate of convergence to the quasi-stationary regime is taking into account in order to make meaningful the comparison.

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The intermediate dispersal principle in spatially explicit metapopulations

Cited by 23 publications

References 35 publications

Spatially Explicit Conditions for Waterborne Pathogen Invasion

Spatially Explicit Conditions for Waterborne Pathogen Invasion

An empiricist's guide to theoretical predictions on the evolution of dispersal

Quasi-stationary and ratio of expectations distributions: A comparative study

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