Structured Metapopulation Model Research Articles

Effects of predator modulation and vector preference on pathogen transmission in plant populations

Biological control programs frequently rely on predators to control vector-borne pathogens by consumptive effects on vector abundance in agroecosystems. Meanwhile, the spread of vectored disease depends on the vector preference for host status (healthy or infected hosts). Yet, it is unclear how vector preferences alter the controlled effectivity of predators in pathogen transmission. Therefore, we here addressed the plant-vector-pathogen models assessing how pathogen transmission in plant was affected by variable predation rates and vector preferences for host status. Specifically, we discussed effects of predators on vector abundance and pathogen transmission under both a non-spatial model and a spatially structured metapopulation model. We showed that predators can decrease the vector abundance and inhibit pathogen prevalence, whereas vector preference contributes profoundly to the controlled effectivity of predators on the spread of vector-borne pathogens. Moreover, predation can increase oscillation amplitude of the pathogen prevalence in both plant and vector; suggesting that the inclusion of predator can amplify the effects of environmental stochasticity on pathogen dynamics. In conclusion, our results support the prediction of theoretical disease models showing predator can be a natural enemy for pathogen control, and also extend that predatory interactions interacting with vector preferences play the singularly joint effects on the spread of vector-borne pathogens.

Examining the impact of ICU population interaction structure on modeled colonization dynamics of Staphylococcus aureus.

Complex transmission models of healthcare-associated infections provide insight for hospital epidemiology and infection control efforts, but they are difficult to implement and come at high computational costs. Structuring more simplified models to incorporate the heterogeneity of the intensive care unit (ICU) patient-provider interactions, we explore how methicillin-resistant Staphylococcus aureus (MRSA) dynamics and acquisitions may be better represented and approximated. Using a stochastic compartmental model of an 18-bed ICU, we compared the rates of MRSA acquisition across three ICU population interaction structures: a model with nurses and physicians as a single staff type (SST), a model with separate staff types for nurses and physicians (Nurse-MD model), and a Metapopulation model where each nurse was assigned a group of patients. The proportion of time spent with the assigned patient group (γ) within the Metapopulation model was also varied. The SST, Nurse-MD, and Metapopulation models had a mean of 40.6, 32.2 and 19.6 annual MRSA acquisitions respectively. All models were sensitive to the same parameters in the same direction, although the Metapopulation model was less sensitive. The number of acquisitions varied non-linearly by values of γ, with values below 0.40 resembling the Nurse-MD model, while values above that converged toward the Metapopulation structure. Inclusion of complex population interactions within a modeled hospital ICU has considerable impact on model results, with the SST model having more than double the acquisition rate of the more structured metapopulation model. While the direction of parameter sensitivity remained the same, the magnitude of these differences varied, producing different colonization rates across relatively similar populations. The non-linearity of the model's response to differing values of a parameter gamma (γ) suggests simple model approximations are appropriate in only a narrow space of relatively dispersed nursing assignments. Simplifying assumptions around how a hospital population is modeled, especially assuming random mixing, may overestimate infection rates and the impact of interventions. In many, if not most, cases more complex models that represent population mixing with higher granularity are justified.

Contextualizing the relative importance of habitat connectivity for metapopulation persistence: A case study of a critically endangered fish

AbstractLocal population characteristics and habitat connectivity both have important influences on metapopulation persistence; however, the relative importance of each can vary depending on the ecological context, making it difficult to apply general ‘rules‐of‐thumb’ for conservation actions. This is particularly true in dendritic networks, where habitat connections are constrained.By constructing a metapopulation model that specifically accounts for the unique characteristics and ecological system of a target species, the relative influence of local population characteristics and habitat connectivity on metapopulation persistence can be assessed more accurately.This modelling approach was used to improve conservation outcomes for the Canterbury mudfish (kо̄waroNeochanna burrowsius), a critically endangered and poorly understood species that is endemic to the Canterbury Plains of Aotearoa/New Zealand. A spatially structured metapopulation model ofN. burrowsiuswas used to investigate the relationship between habitat patch connectivity, rate of population growth as limited by habitat quality (rconditional), and metapopulation persistence.N. burrowsiusmetapopulation persistence increased most strongly under increases inrconditional, but increases in habitat connectivity also had positive effects (94% metapopulation persistence for highly connected networks vs. 39% metapopulation persistence for poorly connected networks whererconditional = 1.3).Although rates of population growth were more influential than increases in habitat connectivity in this case study, both will be important to consider for effectively allocating conservation resources for metapopulations in dendritic networks, depending on what managers could effectively manipulate to enhance metapopulation persistence.

A stochastic structured metapopulation model to assess recovery scenarios of patchily distributed endangered species: Case study for a Mojave Desert rodent.

While metapopulation theory offers tractable means to understand extinction risks for patchily-distributed endangered species, real systems often feature discrepant patch quality and accessibility, complex influences of environmental stochasticity, and regional and temporal autocorrelation. Spatially structured metapopulation models are flexible and can use real data but often at the cost of generality. Particularly as resources for management of such species are often critically limited, endangered species management guided by metapopulation modeling requires incorporation of biological realism. Here we developed a flexible, stochastic spatially structured metapopulation model of the profoundly endangered Amargosa vole, a microtine rodent with an extant population of only a few hundred individuals within 1km2 of habitat in the Mojave Desert. Drought and water insecurity are increasing extinction risks considerably. We modelled subpopulation demographics using a Ricker-like model with migration implemented in an incidence function metapopulation model. A set of scenarios was used to assess the effect of anthropogenic stressors or management actions on expected time to extinction (Te) including: 1) wildland fire, 2) anthropogenically-mediated losses of hydrologic flows, 3) drought, 4) intentional expansion of existing patches into ‘megamarshes’ (i.e. via restoration/enhancement), and 5) additive impacts of multiple influences. In isolation, marshes could be sources or sinks, but spatial context within the full metapopulation including adjacency could alter relative impacts of subpopulations on all other subpopulations. The greatest reductions in persistence occurred in scenarios simulated with impacts from drought in combination with fire or anthropogenically-mediated losses of hydrologic flows. Optimal actions to improve persistence were to prevent distant and smaller marshes from acting as sinks through strategic creation of megamarshes that act as sources of voles and stepping-stones. This research reinforces that management resources expended without guidance from empirically-based modeling can actually harm species’ persistence. This metapopulation-PVA tool could easily be implemented for other patchily-distributed endangered species and allow managers to maximize scarce resources to improve the likelihood of endangered species persistence.

The Evolution of Immigration Strategies Facilitates Niche Expansion by Divergent Adaptation in a Structured Metapopulation Model.

Local adaptation and habitat choice are two key factors that control the distribution and diversification of species. Here we model habitat choice mechanistically as the outcome of dispersal with nonrandom immigration. We consider a structured metapopulation with a continuous distribution of patch types and determine the evolutionarily stable immigration strategy as the function linking patch type to the probability of settling in the patch on encounter. We uncover a novel mechanism whereby coexisting strains that only slightly differ in their local adaptation trait can evolve substantially different immigration strategies. In turn, different habitat use selects for divergent adaptations in the two strains. We propose that the joint evolution of immigration and local adaptation can facilitate diversification and discuss our results in the light of niche conservatism versus niche expansion.

Heterogeneity in local density allows a positive evolutionary relationship between self-fertilisation and dispersal.

Despite empirical evidence for a positive relationship between dispersal and self-fertilization (selfing), theoretical work predicts that these traits should always be negatively correlated, and the Good Coloniser Syndrome of high dispersal and selfing (Cf. Baker's Law) should not evolve. Critically, previous work assumes that adult density is spatiotemporally homogeneous, so selfing results in identical offspring production for all patches, eliminating the benefit of dispersal for escaping from local resource competition. We investigate the joint evolution of dispersal and selfing in a demographically structured metapopulation model where local density is spatiotemporally heterogeneous due to extinction-recolonization dynamics. Selfing alleviates outcrossing failure due to low local density (an Allee effect) while dispersal alleviates competition through dispersal of propagules from high- to low-density patches. Because local density is spatiotemporally heterogeneous in our model, selfing does not eliminate heterogeneity in competition, so dispersal remains beneficial even under full selfing. Hence the Good Coloniser Syndrome is evolutionarily stable under a broad range of conditions, and both negative and positive relationships between dispersal and selfing are possible, depending on the environment. Our model thus accommodates positive empirical relationships between dispersal and selfing not predicted by previous theoretical work and provides additional explanations for negative relationships.

Joint evolution of dispersal propensity and site selection in structured metapopulation models

We propose a novel mathematical model for a metapopulation in which dispersal occurs on two levels: juvenile dispersal from the natal site is mandatory but it may take place either locally within the natal patch or globally between patches. Within each patch, individuals live in sites. Each site can be inhabited by at most one individual at a time and it may be of high or low quality. A disperser immigrates into a high-quality site whenever it obtains one, but it immigrates into a low-quality site only with a certain probability that depends on the time within the dispersal season. The vector of these low-quality-site-acceptance probabilities is the site-selection strategy of an individual. We derive a proxy for the invasion fitness in this model and study the joint evolution of long-distance-dispersal propensity and site-selection strategy. We focus on the way different ecological changes affect the evolutionary dynamics and study the interplay between global patch-to-patch dispersal and local site-selection. We show that ecological changes affect site-selection mainly via the severeness of competition for sites, which often leads to effects that may appear counterintuitive. Moreover, the metapopulation structure may result in extremely complex site-selection strategies and even in evolutionary cycles. The propensity for long-distance dispersal is mainly determined by the metapopulation-level ecological factors. It is, however, also strongly affected by the winter-survival of the site-holders within patches, which results in surprising non-monotonous effects in the evolution of site-selection due to interplay with long-distance dispersal. Altogether, our results give new additional support to the recent general conclusion that evolution of site-selection is often dominated by the indirect factors that take place via density-dependence, which means that evolutionary responses can rarely be predicted by intuition.

A spatially structured metapopulation model within a stochastic environment

Populations often exist, either by choice or by external pressure, in a fragmented way, referred to as a metapopulation. Typically, the dynamics accounted for within metapopulation models are assumed to be static. For example, patch occupancy models often assume that the colonisation and extinction rates do not change, while spatially structured models often assume that the rates of births, deaths and migrations do not depend on time. While some progress has been made when these dynamics are changing deterministically, less is known when the changes are stochastic. It can be quite common that the environment a population inhabits determines how these dynamics change over time. Changes to this environment can have a large impact on the survival probability of a population and such changes will often be stochastic. The typical metapopulation model allows for catastrophes that could eradicate most, if not all, individuals on an entire patch. It is this type of phenomenon that this article addresses. A Markov process is developed that models the number of individuals on each patch within a metapopulation. An approximation for the original model is presented in the form of a piecewise-deterministic Markov process and the approximation is analysed to present conditions for extinction.

Finite element approximation of a spatially structured metapopulation PDE model

We present a new fully spatially structured PDE metapopulation model for predator–prey dynamics in d≤3 space dimensions. A nonlinear reaction–diffusion system of Rosenzweig–MacArthur form models predator–prey dynamics in two ‘high’ quality patches embedded in a ‘low’ quality subdomain, where species can diffuse, convect and die. Our model substantially generalizes and improves earlier fully structured metapopulation models. After a nondimensionalization procedure, in order to approximate the metapopulation model we present a fully discrete Galerkin finite element method in two space dimensions, which is a generalization of the finite element method analyzed in a previous single patch predator–prey model. The numerical solutions are illustrated for some test cases using MATLAB. Numerical experiments demonstrate that the initial local extinction of predators in one patch leads to waves of recolonization from another patch. In an appendix we also give an outline for the proof of the well-posedness of the model.

Implications of Fine-Grained Habitat Fragmentation and Road Mortality for Jaguar Conservation in the Atlantic Forest, Brazil.

Jaguar (Panthera onca) populations in the Upper Paraná River, in the Brazilian Atlantic Forest region, live in a landscape that includes highly fragmented areas as well as relatively intact ones. We developed a model of jaguar habitat suitability in this region, and based on this habitat model, we developed a spatially structured metapopulation model of the jaguar populations in this area to analyze their viability, the potential impact of road mortality on the populations' persistence, and the interaction between road mortality and habitat fragmentation. In more highly fragmented populations, density of jaguars per unit area is lower and density of roads per jaguar is higher. The populations with the most fragmented habitat were predicted to have much lower persistence in the next 100 years when the model included no dispersal, indicating that the persistence of these populations are dependent to a large extent on dispersal from other populations. This, in turn, indicates that the interaction between road mortality and habitat fragmentation may lead to source-sink dynamics, whereby populations with highly fragmented habitat are maintained only by dispersal from populations with less fragmented habitat. This study demonstrates the utility of linking habitat and demographic models in assessing impacts on species living in fragmented landscapes.

On fitness in metapopulations that are both size- and stage-structured.

A proxy for the invasion fitness in structured metapopulation models has been defined as a metapopulation reproduction ratio, which is the expected number of surviving dispersers produced by a mutant immigrant and a colony of its descendants. When a size-structured metapopulation model involves also individual stages (such as juveniles and adults), there exists a generalized definition for the invasion fitness proxy. The idea is to calculate the expected numbers of dispersers of all different possible types produced by a mutant clan initiated with a single mutant, and to collect these values into a matrix. The metapopulation reproduction ratio is then the dominant eigenvalue of this matrix. The calculation method has been published in detail in the case of small local populations. However, in case of large patches the previously published numerical calculation method to obtain the expected number of dispersers does not generalize as such, which gives us one aim of this article. Here, we thus derive a generalized method to calculate the invasion fitness in a metapopulation, which consists of large local populations, and is both size- and stage-structured. We also prove that the metapopulation reproduction ratio is well-defined, i.e., it is equal to 1 for a mutant with a strategy equal to the strategy of a resident. Such a proof has not been previously published even for the case with only one type of individuals.

Individual and patch behaviour in structured metapopulation models.

Density dependent Markov population processes with countably many types can often be well approximated over finite time intervals by the solution of the differential equations that describe their average drift, provided that the total population size is large. They also exhibit diffusive stochastic fluctuations on a smaller scale about this deterministic path. Here, it is shown that the individuals in such processes experience an almost deterministic environment. Small groups of individuals behave almost independently of one another, evolving as Markov jump processes, whose transition rates are prescribed functions of time. In the context of metapopulation models, we show that 'individuals' can represent either patches or the individuals that migrate among the patches; in host-parasite systems, they can represent both hosts and parasites.

Metapopulation Dynamics and the Evolution of Sperm Parasitism

Amazon molly (Poecilia formosa) females reproduce asexually, but they need sperm to initiate the process. Such gynogenetic reproduction can be called sperm parasitism since the DNA in the sperm is not used. Since all offspring of asexually reproducing females are females, they can locally outcompete sexually reproducing ones, but their persistence is threatened by the lack of males. Therefore, the existence of Amazon mollies is puzzling. A metapopulation structure has been suggested to enable the coexistence of gynogenetic and sexual species. Previously only Levins-type metapopulation models have been used to investigate this question, but thy are not defined on the individual level. Therefore we investigate the evolution of sperm parasitism in a structured metapopulation model, which incorporates both realistic local population dynamics and individual-level dispersal. If the reproduction strategy is freely evolving in a large well-mixed population or in the structured metapopulation model, strong discrimination of asexually reproducing females by males results in evolution to full sexuality, whereas mild discrimination leads to too small probability of sexual reproduction, so that the lack of males causes the extinction of the evolving population, resulting in evolutionary suicide. This classification remains the same also when both sexual reproduction and dispersal are freely evolving. Sexual and asexual behaviour can be observed at the same time in this model in the presence of a trade-off between the reproduction and dispersal traits. However, we do not observe disruptive selection resulting in the evolutionarily stable coexisence of fully sexual and fully asexual females. Instead, the presence of sexual and asexual behaviour is due to females with a mixed reproduction trait.

Human mobility and the worldwide impact of intentional localized highly pathogenic virus release

The threat of bioterrorism and the possibility of accidental release have spawned a growth of interest in modeling the course of the release of a highly pathogenic agent. Studies focused on strategies to contain local outbreaks after their detection show that timely interventions with vaccination and contact tracing are able to halt transmission. However, such studies do not consider the effects of human mobility patterns. Using a large-scale structured metapopulation model to simulate the global spread of smallpox after an intentional release event, we show that index cases and potential outbreaks can occur in different continents even before the detection of the pathogen release. These results have two major implications: i) intentional release of a highly pathogenic agent within a country will have global effects; ii) the release event may trigger outbreaks in countries lacking the health infrastructure necessary for effective containment. The presented study provides data with potential uses in defining contingency plans at the National and International level.

Evaluating the Effects of Anthropogenic Stressors on Source‐Sink Dynamics in Pond‐Breeding Amphibians

Although interwetland dispersal is thought to play an important role in regional persistence of pond-breeding amphibians, few researchers have modeled amphibian metapopulation or source-sink dynamics. Results of recent modeling studies suggest anthropogenic stressors, such as pollution, can negatively affect density and population viability of amphibians breeding in isolated wetlands. Presumably population declines also result in reduced dispersal to surrounding (often uncontaminated) habitats, potentially affecting dynamics of nearby populations. We used our data on the effects of mercury (Hg) on the American toad ( Bufo americanus) as a case study in modeling the effects of anthropogenic stressors on landscape-scale amphibian dynamics. We created a structured metapopulation model to investigate regional dynamics of American toads and to evaluate the degree to which detrimental effects of Hg contamination on individual populations can disrupt interpopulation dynamics. Dispersal from typical American toad populations supported nearby populations that would otherwise have been extirpated over long time scales. Through support of such sink populations, dispersal between wetland-associated subpopulations substantially increased overall productivity of wetland networks, but this effect declined with increasing interwetland distance and decreasing wetland size. Contamination with Hg substantially reduced productivity of wetland-associated subpopulations and impaired the ability of populations to support nearby sinks within relevant spatial scales. Our results add to the understanding of regional dynamics of pond-breeding amphibians, the wide-reaching negative effects of environmental contaminants, and the potential for restoration or remediation of degraded habitats.

Adaptive Dynamics of Altruistic Cooperation in a Metapopulation: Evolutionary Emergence of Cooperators and Defectors or Evolutionary Suicide?

We investigate the evolution of public goods cooperation in a metapopulation model with small local populations, where altruistic cooperation can evolve due to assortment and kin selection, and the evolutionary emergence of cooperators and defectors via evolutionary branching is possible. Although evolutionary branching of cooperation has recently been demonstrated in the continuous snowdrift game and in another model of public goods cooperation, the required conditions on the cost and benefit functions are rather restrictive, e.g., altruistic cooperation cannot evolve in a defector population. We also observe selection for too low cooperation, such that the whole metapopulation goes extinct and evolutionary suicide occurs. We observed intuitive effects of various parameters on the numerical value of the monomorphic singular strategy. Their effect on the final coexisting cooperator-defector pair is more complex: changes expected to increase cooperation decrease the strategy value of the cooperator. However, at the same time the population size of the cooperator increases enough such that the average strategy does increase. We also extend the theory of structured metapopulation models by presenting a method to calculate the fitness gradient in a general class of metapopulation models, and try to make a connection with the kin selection approach.

Comparing large-scale computational approaches to epidemic modeling: Agent-based versus structured metapopulation models

BackgroundIn recent years large-scale computational models for the realistic simulation of epidemic outbreaks have been used with increased frequency. Methodologies adapt to the scale of interest and range from very detailed agent-based models to spatially-structured metapopulation models. One major issue thus concerns to what extent the geotemporal spreading pattern found by different modeling approaches may differ and depend on the different approximations and assumptions used.MethodsWe provide for the first time a side-by-side comparison of the results obtained with a stochastic agent-based model and a structured metapopulation stochastic model for the progression of a baseline pandemic event in Italy, a large and geographically heterogeneous European country. The agent-based model is based on the explicit representation of the Italian population through highly detailed data on the socio-demographic structure. The metapopulation simulations use the GLobal Epidemic and Mobility (GLEaM) model, based on high-resolution census data worldwide, and integrating airline travel flow data with short-range human mobility patterns at the global scale. The model also considers age structure data for Italy. GLEaM and the agent-based models are synchronized in their initial conditions by using the same disease parameterization, and by defining the same importation of infected cases from international travels.ResultsThe results obtained show that both models provide epidemic patterns that are in very good agreement at the granularity levels accessible by both approaches, with differences in peak timing on the order of a few days. The relative difference of the epidemic size depends on the basic reproductive ratio, R0, and on the fact that the metapopulation model consistently yields a larger incidence than the agent-based model, as expected due to the differences in the structure in the intra-population contact pattern of the approaches. The age breakdown analysis shows that similar attack rates are obtained for the younger age classes.ConclusionsThe good agreement between the two modeling approaches is very important for defining the tradeoff between data availability and the information provided by the models. The results we present define the possibility of hybrid models combining the agent-based and the metapopulation approaches according to the available data and computational resources.

Seasonal transmission potential and activity peaks of the new influenza A(H1N1): a Monte Carlo likelihood analysis based on human mobility

BackgroundOn 11 June the World Health Organization officially raised the phase of pandemic alert (with regard to the new H1N1 influenza strain) to level 6. As of 19 July, 137,232 cases of the H1N1 influenza strain have been officially confirmed in 142 different countries, and the pandemic unfolding in the Southern hemisphere is now under scrutiny to gain insights about the next winter wave in the Northern hemisphere. A major challenge is pre-empted by the need to estimate the transmission potential of the virus and to assess its dependence on seasonality aspects in order to be able to use numerical models capable of projecting the spatiotemporal pattern of the pandemic.MethodsIn the present work, we use a global structured metapopulation model integrating mobility and transportation data worldwide. The model considers data on 3,362 subpopulations in 220 different countries and individual mobility across them. The model generates stochastic realizations of the epidemic evolution worldwide considering 6 billion individuals, from which we can gather information such as prevalence, morbidity, number of secondary cases and number and date of imported cases for each subpopulation, all with a time resolution of 1 day. In order to estimate the transmission potential and the relevant model parameters we used the data on the chronology of the 2009 novel influenza A(H1N1). The method is based on the maximum likelihood analysis of the arrival time distribution generated by the model in 12 countries seeded by Mexico by using 1 million computationally simulated epidemics. An extended chronology including 93 countries worldwide seeded before 18 June was used to ascertain the seasonality effects.ResultsWe found the best estimate R0 = 1.75 (95% confidence interval (CI) 1.64 to 1.88) for the basic reproductive number. Correlation analysis allows the selection of the most probable seasonal behavior based on the observed pattern, leading to the identification of plausible scenarios for the future unfolding of the pandemic and the estimate of pandemic activity peaks in the different hemispheres. We provide estimates for the number of hospitalizations and the attack rate for the next wave as well as an extensive sensitivity analysis on the disease parameter values. We also studied the effect of systematic therapeutic use of antiviral drugs on the epidemic timeline.ConclusionThe analysis shows the potential for an early epidemic peak occurring in October/November in the Northern hemisphere, likely before large-scale vaccination campaigns could be carried out. The baseline results refer to a worst-case scenario in which additional mitigation policies are not considered. We suggest that the planning of additional mitigation policies such as systematic antiviral treatments might be the key to delay the activity peak in order to restore the effectiveness of the vaccination programs.

Informed participation in a randomised controlled trial of computed tomography screening for lung cancer

The actual lung cancer (screening) knowledge, attitudes, risk perceptions, reasons to participate in or decline participation, and informed decisions of subjects who decided to or decided not to participate in the Dutch-Belgian randomised controlled trial for lung cancer screening in high-risk subjects (the NELSON trial) were evaluated. A total of 2,500 high-risk subjects were asked to complete a questionnaire 3 weeks after they had received a brochure with information about the trial. Differences in knowledge, attitude and risk perception between participants and nonparticipants were analysed with logistic regression analyses adjusted for sex and smoking status. The questionnaire response of trial participants was 80% (n = 889) whereas the response of nonparticipants was low (7%, n = 97) and selective. Participants' responses to knowledge items on lung cancer as a disease were on average more often correct (mean+/-sd 68+/-17%) than items on lung cancer screening (49+/-29%). Participants had adequate knowledge on lung cancer screening (51%) more often than the nonparticipants (38%; p = 0.009). Of the decisions regarding participation, 49% were uninformed, mainly due to insufficient knowledge. Most of the participants (99%) and 64% of the nonparticipants had a positive attitude towards lung cancer screening. Additional efforts are required to improve the knowledge and understanding of subjects who are in the process of decision-making regarding participation in a lung cancer screening trial.

A novel fitness proxy in structured locally finite metapopulations with diploid genetics, with an application to dispersal evolution

Many studies of evolutionarily stable strategies (ESS) for technical reasons make the simplification that reproduction is clonal. A post-hoc justification is that in the simplest eco-evolutionary models more realistic genetic assumptions, such as haploid sexual or diploid sexual cases, yield results compatible with the clonal ones. For metapopulations the technical reasons were even more poignant thanks to the lack of accessible fitness proxies for the diploid case. However, metapopulations are also precisely the sort of ecological backdrop for which one expect discrepancies between the evolutionary outcomes derived from clonal reproduction and diploid genetics, because substantially many mutant homozygotes appear locally even though the mutant is rare globally. In this paper we devise a fitness proxy applicable to the haploid sexual and diploid sexual case, in the style of Metz and Gyllenberg [Metz, J.A.J., Gyllenberg, M., 2001. How should we define fitness in structured metapopulation models? Including an application to the calculation of ES dispersal strategies. Proc. R. Soc. Lond. B 268, 499–508], that can cope with local population fluctuations due to environmental and demographic stochasticity. With the use of this fitness proxy we find that in dispersal evolution the studied clonal model is equivalent with the haploid sexual model, and that there are indeed many differences between clonal and diploid ESS dispersal rates. In a homogenous landscape the discrepancy is but minor (less than 2%), but the situation is different in a heterogeneous landscape: Not only is the quantitative discrepancy between the two types of ESSs appreciable (around 10%–20%), but more importantly, at the same parameter values, evolutionarily stability properties may differ. It is possible, that the singular strategy is evolutionarily stable in the clonal case but not in the diploid case, and vice versa.