Evolution of specialization in resource utilization in structured metapopulations

We study the evolution of resource utilization in a structured discrete-time metapopulation model with an infinite number of patches, prone to local catastrophes. The consumer faces a trade-off in the abilities to consume two resources available in different amounts in each patch. We analyse how the evolution of specialization in the utilization of the resources is affected by different ecological factors: migration, local growth, local catastrophes, forms of the trade-off and distribution of the resources in the patches. Our modelling approach offers a natural way to include more than two patch types into the models. This has not been usually possible in the previous spatially heterogeneous models focusing on the evolution of specialization.     

On the evolution of specialization with a mechanistic underpinning in structured metapopulations

We analyze the evolution of specialization in resource utilization in a discrete-time metapopulation model using the adaptive dynamics approach. The local dynamics in the metapopulation are based on the Beverton-Holt model with mechanistic underpinnings. The consumer faces a trade-off in the abilities to consume two resources that are spatially heterogeneously distributed to patches that are prone to local catastrophes. We explore the factors favoring the spread of generalist or specialist strategies. Increasing fecundity or decreasing catastrophe probability favors the spread of the generalist strategy and increasing environmental heterogeneity enlarges the parameter domain where the evolutionary branching is possible. When there are no catastrophes, increasing emigration diminishes the parameter domain where the evolutionary branching may occur. Otherwise, the effect of emigration on evolutionary dynamics is non-monotonous: both small and large values of emigration probability favor the spread of the specialist strategies whereas the parameter domain where evolutionary branching may occur is largest when the emigration probability has intermediate values. We compare how different forms of spatial heterogeneity and different models of local growth affect the evolutionary dynamics. We show that even small changes in the resource dynamics may have outstanding evolutionary effects to the consumers.     

Evolutionary suicide and evolution of dispersal in structured metapopulations

 We study the evolution of dispersal in a structured metapopulation model. The metapopulation consists of a large (infinite) number of local populations living in patches of habitable environment. Dispersal between patches is modelled by a disperser pool and individuals in transit between patches are exposed to a risk of mortality. Occasionally, local catastrophes eradicate a local population: all individuals in the affected patch die, yet the patch remains habitable. We prove that, in the absence of catastrophes, the strategy not to migrate is evolutionarily stable. Under a given set of environmental conditions, a metapopulation may be viable and yet selection may favor dispersal rates that drive the metapopulation to extinction. This phenomenon is known as evolutionary suicide. We show that in our model evolutionary suicide can occur for catastrophe rates that increase with decreasing local population size. Evolutionary suicide can also happen for constant catastrophe rates, if local growth within patches shows an Allee effect. We study the evolutionary bifurcation towards evolutionary suicide and show that a discontinuous transition to extinction is a necessary condition for evolutionary suicide to occur. In other words, if population size smoothly approaches zero at a boundary of viability in parameter space, this boundary is evolutionarily repelling and no suicide can occur. Received: 10 November 2000 / Revised version: 13 February 2002 / Published online: 17 July 2002     

Evolutionary branching of dispersal strategies in structured metapopulations

 Dispersal polymorphism and evolutionary branching of dispersal strategies has been found in several metapopulation models. The mechanism behind those findings has been temporal variation caused by cyclic or chaotic local dynamics, or temporally and spatially varying carrying capacities. We present a new mechanism: spatial heterogeneity in the sense of different patch types with sufficient proportions, and temporal variation caused by catastrophes. The model where this occurs is a generalization of the model by Gyllenberg and Metz (2001). Their model is a size-structured metapopulation model with infinitely many identical patches. We present a generalized version of their metapopulation model allowing for different types of patches. In structured population models, defining and computing fitness in polymorphic situations is, in general, difficult. We present an efficient method, which can be applied also to other structured population or metapopulation models. Received: 6 March 2001 / Revised version: 12 February 2002 / Published online: 17 July 2002     

Spatial heterogeneity, source-sink dynamics, and the local coexistence of competing species

Patch occupancy theory predicts that a trade-off between competition and dispersal should lead to regional coexistence of competing species. Empirical investigations, however, find local coexistence of superior and inferior competitors, an outcome that cannot be explained within the patch occupancy framework because of the decoupling of local and spatial dynamics. We develop two-patch metapopulation models that explicitly consider the interaction between competition and dispersal. We show that a dispersal-competition trade-off can lead to local coexistence provided the inferior competitor is superior at colonizing empty patches as well as immigrating among occupied patches. Immigration from patches that the superior competitor cannot colonize rescues the inferior competitor from extinction in patches that both species colonize. Too much immigration, however, can be detrimental to coexistence. When competitive asymmetry between species is high, local coexistence is possible only if the dispersal rate of the inferior competitor occurs below a critical threshold. If competing species have comparable colonization abilities and the environment is otherwise spatially homogeneous, a superior ability to immigrate among occupied patches cannot prevent exclusion of the inferior competitor. If, however, biotic or abiotic factors create spatial heterogeneity in competitive rankings across the landscape, local coexistence can occur even in the absence of a dispersal-competition trade-off. In fact, coexistence requires that the dispersal rate of the overall inferior competitor not exceed a critical threshold. Explicit consideration of how dispersal modifies local competitive interactions shifts the focus from the patch occupancy approach with its emphasis on extinction-colonization dynamics to the realm of source-sink dynamics. The key to coexistence in this framework is spatial variance in fitness. Unlike in the patch occupancy framework, high rates of dispersal can undermine coexistence, and hence diversity, by reducing spatial variance in fitness.     

Trade-offs and spatial life-history strategies in classical metapopulations

The metapopulation concept dichotomizes space into the local scale of an ephemeral patch and the broader scale of the persistent multipatch system. Here, we consider how the "best" (i.e., optimal or noninvasible) life history of asexually reproducing organisms might address this dichotomy along environmental gradients via shifts in two key trade-offs. The expansion-survival trade-off expresses the relation between the combined growth and propagule production rate and the mortality rate. The accumulation-export trade-off partitions expansion into a local accumulation of growth plus propagules retained within the patch and the potential-colonist propagules dispersed to other patches, although the dispersal linkages among patches are assumed to be weak (a characteristic of "classical" metapopulations). We identify the best life histories along gradients of productivity, stress, and patch extinction rates for a metapopulation with and without lottery or overgrowth competition, and we compare them with results for an isolated immortal patch. The two trade-offs interact in determining best life histories, but this effect is generally small, supporting the validity of studies addressing the trade-offs separately. The accumulation-export trade-off responds strongly to the three gradients, increasing export with productivity and with patch extinction rate when this rate is high but decreasing export with higher stress; the expansion-survival trade-off increases expansion with productivity but fails to respond to stress and patch extinction rate gradients, except when the other trade-off does not occur. By linking the trade-offs to life-history strategies (i.e., colonization, exploitation, and tolerance), we separate strategies from phenomenology (i.e., from export, accumulation, and survival) along the gradients.     

Dispersal and the evolution of specialisation in a two-habitat type metapopulation

Metapopulation theory for the evolution of specialisation is virtually absent. In this article, therefore, we study a metapopulation model for consumers with a fitness trade-off between two habitats. We focus on effects of habitat abundance, dispersal rate and trade-off strength on the evolution of specialisation under two types of trade-off. Adaptation affects either the intrinsic growth rates r or the carrying capacities K. Depending on dispersal rate and trade-off strength, evolution can result in one generalist, one specialist or two specialist types. Higher dispersal rate and a weaker trade-off favour the evolution of a generalist, for both trade-off structures. However, we also find differences between the two trade-off structures. Our results are qualitatively similar to analyses of two-patch models, suggesting that insights from such simpler models can be extrapolated to metapopulation models. Additional effects, however, occur because in classical metapopulations patch lifetime depends on extinction rate. Counterintuitively, this favours the evolution of specialisation when the trade-off affects r.     

Host-range evolution in Aphidius parasitoids: fidelity, virulence and fitness trade-offs on an ancestral host

The diversity of parasitic insects remains one of the most conspicuous patterns on the planet. The principal factor thought to contribute to differentiation of populations and ultimately speciation is the intimate relationship parasites share with hosts and the potential for disruptive selection associated with using different host species. Traits that generate this diversity have been an intensely debated topic of central importance to the evolution of specialization and maintenance of ecological diversity. A fundamental hypothesis surrounding the evolution of specialization is that no single genotype is uniformly superior in all environments. This "trade-off" hypothesis suggests that negative fitness correlations can lead to specialization on different hosts as alternative stable strategies. In this study we demonstrate a trade-off in the ability of the parasitoid, Aphidius ervi, to maintain a high level of fitness on an ancestral and novel host, which suggests a genetic basis for host utilization that may limit host-range expansion in parasitoids. Furthermore, behavioral evidence suggests mechanisms that could promote specialization through induced host fidelity. Results are discussed in the context of host-affiliated ecological selection as a potential source driving diversification in parasitoid communities and the influence of host species heterogeneity on population differentiation and local adaptation.     

Habitat destruction, environmental catastrophes, and metapopulation extinction

The extinction process of fragmented populations, characterized by a small number of conspecifics inhabiting each patch, is heavily affected by natural and human disturbance. To evaluate the risk of extinction we consider a network of identical patches connected by passive or active dispersal and hosting a finite, discrete number of individuals. We discuss three types of disturbance affecting the metapopulation: permanent loss of habitat patches, erosion of existing patches, and random catastrophes that wipe out the entire population of a patch. Starting from an infinite-dimensional Markov model that fully accounts for demographic stochasticity, we reduce it to finite dimension via moment closure with negative-binomial approximation. The compact models obtained in this way account for the dynamics of the fraction of empty patches, the average number of individuals in occupied patches, and the variance of their distribution. After comparing the performance of these compact models with that of the infinite-dimensional model in the case of no disturbances, we then proceed to computing persistence-extinction boundaries as bifurcation lines of the compact models in the space of demographic and disturbance parameters. We consider bifurcations with respect to demographic and environmental parameters and contrast our results with those of previous theories. We find out that environmental catastrophes increase the risk of extinction for both frequent and infrequent dispersers, while the random loss of patches has a much larger influence on frequent dispersers. This influence can be counterbalanced by active dispersal. Local erosion of habitat fragments has a larger influence on infrequent than on frequent dispersers. We finally discuss the important synergistic effects of disturbances acting simultaneously.     

Dispersal-mediated coexistence of competing predators

Models of metapopulations have often ignored local community dynamics and spatial heterogeneity among patches. However, persistence of a community as a whole depends both on the local interactions and the rates of dispersal between patches. We study a mathematical model of a metacommunity with two consumers exploiting a resource in a habitat of two different patches. They are the exploitative competitors or the competing predators indirectly competing through depletion of the shared resource. We show that they can potentially coexist, even if one species is sufficiently inferior to be driven extinct in both patches in isolation, when these patches are connected through diffusive dispersal. Thus, dispersal can mediate coexistence of competitors, even if both patches are local sinks for one species because of the interactions with the other species. The spatial asynchrony and the competition-colonization trade-off are usual mechanisms to facilitate regional coexistence. However, in our case, two consumers can coexist either in synchronous oscillation between patches or in equilibrium. The higher dispersal rate of the superior prompts rather than suppresses the inferior. Since differences in the carrying capacity between two patches generate flows from the more productive patch to the less productive, loss of the superior by emigration relaxes competition in the former, and depletion of the resource by subsidized consumers decouples the local community in the latter.     

Competition among plant species that interact with their environment at different spatial scales

Clonal plants that are physiologically integrated might perceive and interact with their environment at a coarser resolution than smaller, non-clonal competitors. We develop models to explore the implications of such scale asymmetries when species compete for multiple depletable resources that are heterogeneously distributed in space across two patches. Species are either 'non-integrators', whose growth in each patch depends on resource levels in that patch alone, or 'integrators', whose growth is equal between patches and depends on average resource levels across patches. Integration carried both benefits and costs. It tended to be advantageous in poorer patches, where the integrators drew resources down further than the non-integrators (more easily excluding competitors) and might persist by using resources from richer adjacent patches. Integration tended to be disadvantageous in richer patches, where integrators did not draw resources down as far (creating an opportunity for competitors) and could be excluded due to the cost of supporting growth in poorer adjacent patches. Complementarity between patches (each rich in a separate resource) favoured integrators. Integration created new opportunities for local coexistence, and for delayed susceptibility of patches to invasion, but eliminated some opportunities for regional coexistence. Implications for the interpretations of species' zero net growth isoclines and Rs are also discussed.     

Conservation of substructures in proteins: interfaces of secondary structural elements in proteasomal subunits

It is observed that during divergent evolution of two proteins with a common phylogenetic origin, the structural similarity of their backbones is often preserved even when the sequence similarity between them decreases to a virtually undetectable level. Here we analyzed, whether the conservation of structure along evolution involves also the local atomic structures in the interfaces between secondary structural elements. We have used as study case one protein family, the proteasomal subunits, for which 17 crystal structures are known. These include 14 different subunits of Saccharomyces cerevisiae, 2 subunits of Thermoplasma acidophilum and one subunit of Escherichia coli. The structural core of the 17 proteasomal subunits has 23 secondary structural elements. Any two adjacent secondary structural elements form a molecular interface consisting of two molecular patches. We found 61 interfaces that occurred in all 17 subunits. The 3D shape of equivalent molecular patches from different proteasomal subunits were compared by superposition. Our results demonstrate that pairs of equivalent molecular patches show an RMSD which is lower than that of randomly chosen patches from unrelated proteins. This is true even when patch comparisons with identical residues were excluded from the analysis. Furthermore it is known that the sequential dissimilarity is correlated to the RMSD between the backbones of the members of protein families. The question arises whether this is also true for local atomic structures. The results show that the correlation of individual patch RMSD values and local sequence dissimilarities is low and has a wide range from 0 to 0.41, however, it is surprising that there is a good correlation between the average RMSD of all corresponding patches and the global sequence dissimilarity. This average patch RMSD correlates slightly stronger than the C(alpha)-trace RMSD to the global sequence dissimilarity.     

Eco-evolutionary metapopulation dynamics and the spatial scale of adaptation

We construct a model that combines extinction-colonization dynamics with the dynamics of local adaptation in a network of habitat patches of dissimilar qualities. We derive a deterministic approximation for the stochastic model that allows the calculation of patch-specific incidences of occupancy and levels of adaptation at steady state. Depending on (i) the strength of local selection, (ii) the amount of genetic variance, (iii) the demographic cost of maladaptation, (iv) the spatial scale of gene flow, and (v) the amount of habitat heterogeneity, the model predicts adaptation at different spatial scales. Local adaptation is predicted when there is much genetic variance and strong selection, while network-level adaptation occurs when the demographic cost of maladaptation is low. For little genetic variance and high cost of maladaptation, the model predicts network-level habitat specialization in species with long-range migration but an intermediate scale of adaptation (mosaic specialization) in species with short-range migration. In fragmented landscapes, the evolutionary dynamics of adaptation may both decrease and enhance metapopulation viability in comparison with no evolution. The model can be applied to real patch networks with given sizes, qualities, and spatial positions of habitat patches.     

Dispersal, disease and life-history evolution

Discrete-time susceptible-infective-susceptible (S-I-S) disease transmission models can exhibit bistability (alternative stable equilibria) over a wide range of parameter values. We illustrate the richness generated by such 'simple' non-linear systems in the study of two patch epidemic models with disease-enhanced or disease-suppressed dispersal. Dispersal between patches can have a profound impact on local patch disease dynamics. In fact, dispersal between patches may give rise to bistability in parameter regimes without bistability in single patch models.     

Spatial sex segregation in the dioecious grass Poa ligularis in northern Patagonia: the role of environmental patchiness

We examined the effect of environmental patchiness on the spatial segregation of the sexes in the dioecious anemophilus grass Poa ligularis. Because the species is sensitive to grazing, a better understanding of environmental factors that control its spatial distribution and abundance could improve conservation efforts. We hypothesized that (i) males and females are spatially segregated in the microenvironments created by plant patches as the result of sexual specialization in habitat and/or resources use, (ii) sexual specialization is related to different tolerance to competition and reproductive costs of males and females, and (iii) changes in patch structure affect the microenvironment and the intensity of spatial segregation of the sexes. We analyzed the spatial distribution of sexes at three sites with different plant and micro-environmental patchiness and performed a controlled competition experiment with different substitution of males and females. Our results showed that large plant patches created larger sheltered soil fertility islands than small patches. As patch size and their area of influence increased, the density and the spatial segregation of the sexes of P. ligularis also increased, resulting in biased habitat-specific sex ratios. In accordance with their higher reproductive costs, females were more frequent in sheltered (low air evaporative demand) and nitrogen-rich areas inside patch perimeters than males. Females were also better able to tolerate inter-sexual competition than males. In contrast, males tolerated low nitrogen concentration in soil and low sheltering, probably gaining advantage in pollen dispersal. Inter- and intra-sexual competition, however, affected the reproductive output of both sexes. From the point of view of conservation, environmental patchiness is important to the status of P. ligularis populations. The reduction of patch size limits the available microsites, biases the sex ratio towards males inside patches, increases inter- and intra-sexual competition, and it might be expected to decrease overall seed and pollen production and consequently potential recruitment.     

Local orientation and the evolution of foraging: changes in decision making can eliminate evolutionary trade-offs

Information processing is a major aspect of the evolution of animal behavior. In foraging, responsiveness to local feeding opportunities can generate patterns of behavior which reflect or "recognize patterns" in the environment beyond the perception of individuals. Theory on the evolution of behavior generally neglects such opportunity-based adaptation. Using a spatial individual-based model we study the role of opportunity-based adaptation in the evolution of foraging, and how it depends on local decision making. We compare two model variants which differ in the individual decision making that can evolve (restricted and extended model), and study the evolution of simple foraging behavior in environments where food is distributed either uniformly or in patches. We find that opportunity-based adaptation and the pattern recognition it generates, plays an important role in foraging success, particularly in patchy environments where one of the main challenges is "staying in patches". In the restricted model this is achieved by genetic adaptation of move and search behavior, in light of a trade-off on within- and between-patch behavior. In the extended model this trade-off does not arise because decision making capabilities allow for differentiated behavioral patterns. As a consequence, it becomes possible for properties of movement to be specialized for detection of patches with more food, a larger scale information processing not present in the restricted model. Our results show that changes in decision making abilities can alter what kinds of pattern recognition are possible, eliminate an evolutionary trade-off and change the adaptive landscape.     

Patch use in time and space for a meso-predator in a risky world

Predator–prey studies often assume a three trophic level system where predators forage free from any risk of predation. Since meso-predators themselves are also prospective prey, they too need to trade-off between food and safety. We applied foraging theory to study patch use and habitat selection by a meso-predator, the red fox. We present evidence that foxes use a quitting harvest rate rule when deciding whether or not to abandon a foraging patch, and experience diminishing returns when foraging from a depletable food patch. Furthermore, our data suggest that patch use decisions of red foxes are influenced not just by the availability of food, but also by their perceived risk of predation. Fox behavior was affected by moonlight, with foxes depleting food resources more thoroughly (lower giving-up density) on darker nights compared to moonlit nights. Foxes reduced risk from hyenas by being more active where and when hyena activity was low. While hyenas were least active during moon, and most active during full moon nights, the reverse was true for foxes. Foxes showed twice as much activity during new moon compared to full moon nights, suggesting different costs of predation. Interestingly, resources in patches with cues of another predator (scat of wolf) were depleted to significantly lower levels compared to patches without. Our results emphasize the need for considering risk of predation for intermediate predators, and also shows how patch use theory and experimental food patches can be used for a predator. Taken together, these results may help us better understand trophic interactions.     

The role of local species abundance in the evolution of pollinator attraction in flowering plants

We present a population genetic model that incorporates aspects of pollinator efficiency and abundance to examine the effect of the local plant community on the evolution of floral trait specialization. Our model predicts that plant species evolve to be pollinator specialists on the most effective and common pollinators when their abundance is low relative to other plant species in the community (i.e., conspecific pollen is relatively rare) and evolve to be pollinator generalists when they are numerically dominant (i.e., conspecific pollen is abundant). Strong flower constancy also favors generalist floral traits. Furthermore, generalist species are predicted to differentiate when there is a concave trade-off in attracting pollinator species with different floral trait preferences. This result implies that populations that evolve toward a generalist strategy may be more prone to speciation. Ours is the first theoretical model to include local species abundance explicitly, despite the fact that it has been previously identified as an important factor in the evolution of plant specialization. Our results add a layer of ecological complexity to previous models of floral evolution and therefore have the potential to improve our power to predict circumstances under which specialized and generalized plant-pollinator interactions should evolve.     

Behavioral choices based on patch selection: a model using aggregation methods

The aim of this work is to study the influence of patch selection on the dynamics of a system describing the interactions between two populations, generically called 'population N' and 'population P'. Our model may be applied to prey-predator systems as well as to certain host-parasite or parasitoid systems. A situation in which population P affects the spatial distribution of population N is considered. We deal with a heterogeneous environment composed of two spatial patches: population P lives only in patch 1, while individuals belonging to population N migrate between patch 1 and patch 2, which may be a refuge. Therefore they are divided into two patch sub-populations and can migrate according to different migration laws. We make the assumption that the patch change is fast, whereas the growth and interaction processes are slower. We take advantage of the two time scales to perform aggregation methods in order to obtain a global model describing the time evolution of the total populations, at a slow time scale. At first, a migration law which is independent on population P density is considered. In this case the global model is equivalent to the local one, and under certain conditions, population P always gets extinct. Then, the same model, but in which individuals belonging to population N leave patch 1 proportionally to population P density, is studied. This particular behavioral choice leads to a dynamically richer global system, which favors stability and population coexistence. Finally, we study a third example corresponding to the addition of an aggregative behavior of population N on patch 1. This leads to a more complicated situation in which, according to initial conditions, the global system is described by two different aggregated models. Under certain conditions on parameters a stable limit cycle occurs, leading to periodic variations of the total population densities, as well as of the local densities on the spatial patches.     

Patch dynamics in a landscape modified by ecosystem engineers

Ecosystem engineers, organisms that modify the environment, have the potential to dramatically alter ecosystem structure and function at large spatial scales. The degree to which ecosystem engineering produces large-scale effects is, in part, dependent on the dynamics of the patches that engineers create. Here we develop a set of models that links the population dynamics of ecosystem engineers to the dynamics of the patches that they create. We show that the relative abundance of different patch types in an engineered landscape is dependent upon the production of successful colonists from engineered patches and the rate at which critical resources are depleted by engineers and then renewed. We also consider the effects of immigration from either outside the system or from engineers that are present in non-engineered patches, and the effects of engineers that can recolonize patches before they are fully recovered on the steady state distribution of different patch types. We use data collected on the population dynamics of a model engineer, the beaver, to estimate the per-patch production rate of new colonists, the decay rate of engineered patches, and the recovery rate of abandoned patches. We use these estimated parameters as a baseline to determine the effects of varying parameters on the distribution of different patch types. We suggest a number of hypotheses that derive from model predictions and that could serve as tests of the model.