Local extinction and the evolution of dispersal rates: causes and correlations

We present the results of individual-based simulation experiments on the evolution of dispersal rates of organisms living in metapopulations. We find conflicting results regarding the relationship between local extinction rate and evolutionarily stable (ES) dispersal rate depending on which principal mechanism causes extinction: if extinction is caused by environmental catastrophes eradicating local populations, we observe a positive correlation between extinction and ES dispersal rate; if extinction is a consequence of stochastic local dynamics and environmental fluctuations, the correlation becomes ambiguous; and in cases where extinction is caused by dispersal mortality, a negative correlation between local extinction rate and ES dispersal rate emerges. We conclude that extinction rate, which both affects and is affected by dispersal rates, is not an ideal predictor for optimal dispersal rates.     

Effects of demographic parameters on metapopulation size and persistence: an analytical stochastic model

An analytical stochastic metapopulation model is developed. It describes how individuals will be distributed among patches as a function of density-dependent birth, death and emigration rates, and the probability of successful dispersal. The model includes demographic stochasticity, but not catastrophes, environmental stochasticity or variation in patch size and suitability. All patches are equally likely to be colonized by migrants. The model predicts: (a) mean and variance of the number of individuals per patch; (b) probability distribution of individuals per patch; (c) mean number of individuals in transit; and (d) turn-over rate and expected persistence time of a single patch. The model shows that (a) dispersal rates must be intermediate in order to ensure metapopulation persistence; (b) the mean number of individuals per patch is often well below the carrying capacity; (c) long transit times and/or high mortality during dispersal reduce the mean number of individuals per patch; (d) density-dependent emigration responses will usually increase metapopulation size and persistence compared with density-independent dispersal; (e) an increase in the per capita net growth rate can both increase and decrease metapopulation size and persistence depending on whether dispersal rates are high or low; (f) density-independent birth, death, and emigration rates lead to a spatial pattern described by the negative binomial distribution.     

The genetic underpinnings of population cyclicity: establishing expectations for the genetic anatomy of cycling populations

Despite extensive research into the mechanisms underlying population cyclicity, we have little understanding of the impacts of numerical fluctuations on the genetic variation of cycling populations. Thus, the potential implications of natural and anthropogenically‐driven variation in population cycle dynamics on the diversity and evolutionary potential of cyclic populations is unclear. Here, we use Canada lynx Lynx canadensis matrix population models, set up in a linear stepping‐stone, to generate demographic replicates of biologically realistic cycling populations. Overall, increasing cycle amplitude predictably reduced genetic diversity and increased genetic differentiation, with cyclic effects increased by population synchrony. Modest dispersal rates (1–3% of the population) between high and low amplitude cyclic populations did not diminish these effects suggesting that spatial variation in cyclic amplitude should be reflected in patterns of genetic diversity and differentiation at these rates. At high dispersal rates (6%) groups containing only high amplitude cyclic populations had higher diversity and lower differentiation than those mixed with low amplitude cyclic populations. Negative density‐dependent dispersal did not impact genetic diversity, but did homogenize populations by reducing differentiation and patterns of isolation by distance. Surprisingly, temporal changes in diversity and differentiation throughout a cycle were not always consistent with population size. In particular, negative density‐dependent dispersal simultaneously decreased differences in genetic diversity while increasing differences in genetic differentiation between numerical peaks and nadirs. Combined, our findings suggest demographic changes at fine temporal scales can impact genetic variation of interacting populations and provide testable predictions relating population cyclicty to genetic variation. Further, our results suggest that including realistic demographic and dispersal parameters in population genetic models and using information from temporal changes in genetic variation could help to discern complex demographic scenarios and illuminate population dynamics at fine temporal scales.     

The evolution of dispersal – the importance of information about population density and habitat characteristics

The evolution of mobility patterns and dispersal strategies depend on different population, habitat and life history characteristics. The ability to perceive and make use of information about the surrounding environment for dispersal decisions will also differ between organisms. To investigate the evolutionary consequences of such differences, we have used a simulation model with nearest-neighbour dispersal in a metapopulation to study how variation in the ability to obtain and make use of information about habitat quality and conspecific density affects the evolution of dispersal strategies. We found a rather strong influence of variation in information on the overall rate of dispersal in a metapopulation. The highest emigration rate evolved in organisms with no information about either density or habitat quality and the lowest rate was found in organisms with information about both the natal and the neighbouring patches. For organisms that can make use of information about conspecific density, positively density-dependent dispersal evolved in the majority of cases, with the strongest density dependence occurring when an individual only has information about density in the natal patch. However, we also identified situations, involving strong local population fluctuations and frequent local extinctions, where negatively density-dependent dispersal evolved.     

Mutators in space: the dynamics of high-mutability clones in a two-patch model

Clones of bacteria possessing high-mutability rates (or mutators) are being observed in an increasing number of species. In a constant environment most mutations are deleterious, and hence the spontaneous mutation rate is generally low. However, mutators may play an important role in the adaptation of organisms to changing environments. To date, theoretical work has focused on temporal variability in the environment, implicitly assuming that environmental conditions are constant through space. Here, we develop a two-patch model to investigate how spatiotemporal environmental variability and dispersal might influence mutator dynamics. Environmental conditions in each patch fluctuate between two states; the rate of fluctuation varies in each patch at differing phase angles. We find that at low and intermediate rates of fluctuation, an increase in dispersal results in a decrease in the density of mutators. However, at high rates of environmental change, dispersal causes an increase in mutator density. For all frequencies of environmental fluctuation these trends are enhanced as the phase angle approaches 180 degrees. We argue that future work, both empirical and theoretical, is needed to improve our understanding of how spatiotemporal variability impacts on mutator densities and dynamics.     

The spatial scale of population fluctuations and quasi-extinction risk

Using a spatially homogeneous population model with migration (random individual dispersal) and spatially autocorrelated environmental noise, we show how migration and local density regulation affect the spatial scale of fluctuations in the log of population sizes as well as the 1-yr differences in these. The difference between the squares of these two spatial scales of population fluctuations does not depend on the spatial scale of the noise but only on migration rate and strength of local density regulation. We also show how migration, local density regulation, and spatially correlated environmental noise affect the realized population process at a specific location. As the migration increases, the realized local density regulation and the expected population size increase, while the realized environmental noise decreases. This approach also enables us to analyze the dynamics of the total population size within quadrats of different sizes. The risk of local quasi extinction is strongly reduced by increasing quadrat size or migration rate, while an increase in environmental stochasticity or spatial correlation in the environmental noise increases the risk of quasi extinction.     

The ability of individuals to assess population density influences the evolution of emigration propensity and dispersal distance

We analyze the simultaneous evolution of emigration and settlement decisions for actively dispersing species differing in their ability to assess population density. Using an individual-based model we simulate dispersal as a multi-step (patch to patch) movement in a world consisting of habitat patches surrounded by a hostile matrix. Each such step is associated with the same mortality risk. Our simulations show that individuals following an informed strategy, where emigration (and settlement) probability depends on local population density, evolve a lower (natal) emigration propensity but disperse over significantly larger distances - i.e. postpone settlement longer - than individuals performing density-independent emigration. This holds especially when variation in environmental conditions is spatially correlated. Both effects can be traced to the informed individuals' ability to better exploit existing heterogeneity in reproductive chances. Yet, already moderate distance-dependent dispersal costs prevent the evolution of multi-step (long-distance) dispersal, irrespective of the dispersal strategy.     

A multivariate analysis of fine-scale species density in the plant communities of a saltwater lagoon – the importance of disturbance intensity

Several factors might influence an organism's tendency or willingness to leave a given patch. One such factor is conspecific density, which may affect the per capita emigration rate. Some previous field studies on butterflies have reported positively density-dependent dispersal (emigration increases with population density) whereas the opposite, negatively density-dependent dispersal, has been found in other species. We investigated the effect of conspecific density on both the tendency to cross a patch boundary and within-patch mobility in Melitaea cinxia , by experimentally manipulating density in large outdoor cages divided into two habitat patches, separated by a barrier of unsuitable habitat. In contrast to previous results for M. cinxia , we found that the butterflies moved away from a patch at higher rates in high conspecific density (positively density-dependent emigration). The within-patch mobility, measured as the distance travelled per time unit, was however unaffected by butterfly density. A possible explanation for the seeming discrepancy with previous results could be that we used higher butterfly densities. For species with fluctuating population dynamics, such as M. cinxia , dispersal activity both at low and at high local density will be important for population phenomena such as fluctuations in distributional range over good and bad years.     

A simple evolutionary model of dormancy and dispersal in heterogeneous patches with special reference to phytophagous lady beetles: I. Stable environments

A simple evolutionary model of dormancy and dispersal is presented with special reference to phytophagous lady beetles. In order to investigate spatially heterogeneous environments, we assume the simplest patch structure, that is, there are only two patches, main and sub. Environments are also assumed to be temporally constant. The main patch is superior to the sub patch, but density effect at the main patch is higher than at the sub patch. Optimal dormancy and dispersal are obtained at the same time by the method of evolutionarily stable strategy (ESS). In the univoltine life cycle, dormancy strategy vanishes because dormant individuals do not reproduce at all but suffer from a certain mortality rate during winter hibernation. In the bivoltine life cycle, the dormancy and dispersal rates constitute a trade-off: the rates change together with a negative correlation when the mortality rate during dispersal or during winter hibernation changes. When suitability of the main patch gradually deteriorates, the optimal strategy changes as follows: neither dormancy nor dispersal is adopted at the most suitable condition, the dispersal rate is increased without dormancy in the intermediate condition, and then the dormancy rate is increased with a constant dispersal rate. We discuss the field observation data of lady beetles in the light of results of our model.     

Spatial heterogeneity in the effects of climate and density-dependence on dispersal in a house sparrow metapopulation

Dispersal plays a key role in the response of populations to climate change and habitat fragmentation. Here, we use data from a long-term metapopulation study of a non-migratory bird, the house sparrow (Passer domesticus), to examine the influence of increasing spring temperature and density-dependence on natal dispersal rates and how these relationships depend on spatial variation in habitat quality. The effects of spring temperature and population size on dispersal rate depended on the habitat quality. Dispersal rate increased with temperature and population size on poor-quality islands without farms, where house sparrows were more exposed to temporal fluctuations in weather conditions and food availability. By contrast, dispersal rate was independent of spring temperature and population size on high-quality islands with farms, where house sparrows had access to food and shelter all the year around. This illustrates large spatial heterogeneity within the metapopulation in how population density and environmental fluctuations affect the dispersal process.     

Metapopulation structure and habitat quality in modelling dispersal in the butterfly Iolana iolas

Quantifying dispersal is fundamental to understanding the effects of fragmentation on populations. Although it has been shown that patch and matrix quality can affect dispersal patterns, standard metapopulation models are usually based on the two basic variables, patch area and connectivity. In 2004 we studied migration patterns among 18 habitat patches in central Spain for the butterfly Iolana iolas, using mark–release–recapture methods. We applied the virtual migration (VM) model and estimated the parameters of emigration, immigration and mortality separately for males and females. During parameter estimation and model simulations, we used original and modified patch areas accounting for habitat quality with three different indices. Two indices were based on adult and larval resources (flowers and fruits) and the other one on butterfly density. Based on unmodified areas, our results showed that both sexes were markedly different in their movements and mortality rates. Females emigrated more frequently from patches, but males that emigrated were estimated to move longer daily dispersal distances and suffer higher mortality than females during migration. Males were more likely to emigrate from small than from large patches, but patch area had no significant effect on female emigration. The effects of area on immigration rate and the within-patch mortality were similar in both sexes. Based on modified areas, the estimated parameter values and the model simulation results were similar to those estimated using the unmodified patch areas. One possible reason for the failure to significantly improve the parameter estimates of the VM model is the fact that resource quantity and butterfly population sizes were strongly correlated with patch area. Our results suggest that the standard VM modelling approach, based on patch area and connectivity, can provide a realistic picture of the movement patterns of I. iolas .     

Sex allocation of parasitic wasps: local mate competition,dispersal before mating and host quality variation

We constructed a sex allocation model for parasitic wasps to explain the wide variation in their sex ratio, considering the effects of local mate competition, partial dispersal of progeny before mating, and heterogeneity in host quality among patches. We conducted an experiment to compare with the predictions of our model. We considered the following situations. First, the hosts are distributed in discrete patches: a number of female wasps visit and oviposit in each patch. Second, all the progeny do not mate within the natal patch; some of them disperse to take part in population-wide random mating. We calculated ES sex ratios in cases where there are two kinds of patches: good ones and poor ones. We examined the dependency of ES sex ratios on several parameters, i.e., 1) the probability that a daughter mates in her natal patch, 2) the ratio of the female fitness of the good patch to that of the poor patch, 3) the proportion of poor patches, and 4) the number of foundresses in a patch. The result of our experiment showed the same tendency as the calculation in case where the LMC effect is high in each patch. We briefly discuss a possible selection pressure for dispersal of progeny, with special reference to the mating structure of parasitic wasps.     

Demography of alpine red squirrel populations in relation to fluctuations in seed crop size

Vertebrate population dynamics, social organisation and space use often are closely associated with the distribution of critical resources, such as food. Tree squirrels are ideal models to study these relationships, since both key demographic parameters (reproduction, survival and dispersal) and spatio-temporal variation in food supplies (measured as seed-crop size) can be reliably estimated. In this paper we test the following two predictions underlying the association between annual food abundance and demography in six alpine red squirrel populations, both with and without time-lag effects: 1) between-season and between-year fluctuations in survival rate, population density and increase parallel those in food availability; and 2) individuals follow a resource tracking strategy and increase in density mainly the year after a rich seed-crop. Red squirrels occurred at higher densities in Scots pine forest, characterised by stable seed-crops, than in Norway spruce with more abundant but more variable seed crops. Fluctuations in numbers were positively correlated with food availability, measured as annual conifer seed-crop sizes. Overall, adult survival rates were higher than those of subadults, and survival substantially fluctuated between seasons and years. Autumn densities and rates of population increase (summer-autumn) were strongly correlated with the same year's autumn seed-crop, while correlations with the previous year's seed-crop (time-lag models) were either weak (population density) or absent (population increase). Results of this paper show that fluctuations in red squirrel densities in habitats with strong temporal variation in seed production are more closely linked with food availability than in more stable habitats. In addition, in the Alpine conifer forests squirrel population sizes, in autumn, increase in synchrony with food resources, eliminating the population lag normally present when resources are produced in pulses.     

Scaling population responses to spatial environmental variability in advection-dominated systems

We model the spatial dynamics of an open population of organisms that disperse solely through advection in order to understand responses to multiscale environmental variability. We show that the distance over which a population responds to a localized perturbation, called the response length, can be characterized as an organisms average lifetime dispersal distance, unless there is strong density‐dependence in demographic or dispersal rates. Continuous spatial fluctuations in demographic rates at scales smaller than the response length will be largely averaged in the population distribution, whereas those in per capita emigration rates will be strongly tracked. We illustrate these results using a parameterized example to show how responses to environmental variability may differ in streams with different average current velocities. Our model suggests an approach to linking local dynamics dominated by dispersal processes to larger‐scale dynamics dominated by births and deaths.     

Evolution of migration rate in a spatially realistic metapopulation model

We use an individual-based, spatially realistic metapopulation model to study the evolution of migration rate. We first explore the consequences of habitat change in hypothetical patch networks on a regular lattice. If the primary consequence of habitat change is an increase in local extinction risk as a result of decreased local population sizes, migration rate increases. A nonmonotonic response, with migration rate decreasing at high extinction rate, was obtained only by assuming very frequent catastrophes. If the quality of the matrix habitat deteriorates, leading to increased mortality during migration, the evolutionary response is more complex. As long as habitat patch occupancy does not decrease markedly with increased migration mortality, reduced migration rate evolves. However, once mortality becomes so high that empty patches remain uncolonized for a long time, evolution tends to increase migration rate, which may lead to an "evolutionary rescue" in a fragmented landscape. Kin competition has a quantitative effect on the evolution of migration rate in our model, but these patterns in the evolution of migration rate appear to be primarily caused by spatiotemporal variation in fitness and mortality during migration. We apply the model to real habitat patch networks occupied by two checkerspot butterfly (Melitaea) species, for which sufficient data are available to estimate rigorously most of the model parameters. The model-predicted migration rate is not significantly different from the empirically observed one. Regional variation in patch areas and connectivities leads to regional variation in the optimal migration rate, predictions that can be tested empirically.     

Colonization in metapopulations: a review of theory and observations

In metapopulation dynamics turnover of populations in isolated patches may be frequent. Regional survival of a species in such a system with frequent extinctions hinges on its colonization ability. Colonization is more than just dispersal; when a propagule reaches a new patch it faces higher extinction probabilities than does an established population. Extinction models as well as empirical data suggest that a large propagule with a potential for rapid increase in a varying environment, or with a low mortality rate in an environment perceived as constant, has a higher probability of successful colonization. Large variation in population size when it is still small increases the risk of failure. Factors introducing such variation are demographic stochasticity and environmental variation. It is hard to single out demographic traits that ensure good colonizing ability, since colonization can be achieved in many different ways, but generalists and species with self-fertilization seem to be superior.     

The evolution of patch selection in stochastic environments

A null model for habitat patch selection in spatially heterogeneous environments is the ideal free distribution (IFD), which assumes individuals have complete knowledge about the environment and can freely disperse. Under equilibrium conditions, the IFD predicts that local population growth rates are zero in all occupied patches, sink patches are unoccupied, and the fraction of the population selecting a patch is proportional to the patch's carrying capacity. Individuals, however, often experience stochastic fluctuations in environmental conditions and cannot respond to these fluctuations instantaneously. An evolutionary stability analysis for fixed patch-selection strategies reveals that environmental uncertainty disrupts the classical IFD predictions: individuals playing the evolutionarily stable strategy may occupy sink patches, local growth rates are negative and typically unequal in all patches, and individuals prefer higher-quality patches less than predicted by their carrying capacities. Spatial correlations in environmental fluctuations can enhance or marginalize these trends. The analysis predicts that continually increasing environmental variation first selects for range expansion, then selects for persisting coupled sink populations, and ultimately leads to regional extinction. In contrast, continually increasing habitat degradation first selects for range contraction and may select for persisting coupled sink populations before regional extinction. These results highlight the combined roles of spatial and temporal heterogeneity on the evolution of habitat selection.     

The synergistic effects of stochasticity and dispersal on population densities

Using laboratory experiments, simulation models, and analytical techniques, we examined the impact of dispersal on the mean densities of patchily distributed populations. Even when dispersal leads to no net additions or removals of individuals from a population, it may nonetheless increase mean population densities if the net immigration rate is positive when populations are growing and negative when they are declining. As a model system for exploring this phenomenon, we used the yeastlike fungus Aureobasidium pullulans. In a laboratory experiment, we showed that dispersal can both ensure persistence and increase mean population densities even when dispersal among populations causes no direct addition or loss of fungal cells. From the laboratory data, we constructed a plausible model of A. pullulans dynamics among apple leaves within an orchard. This simulation model demonstrated that the effect of dispersal on mean densities is enhanced by three factors: weak density dependence of the dynamics within populations, high environmental variability affecting population growth rates, and lack of synchrony among the fluctuations of populations. Using an analytical model, we showed that the underlying mechanisms for this phenomenon are general, suggesting that a large effect of dispersal on mean population densities is possible in many natural systems.     

Impacts of dispersal on rapid adaptation and dynamic stability of Daphnia in fluctuating environments

Prior ecological research has shown that spatial processes can enhance the temporal stability of populations in fluctuating environments. Less explored is the effect of dispersal on rapid adaptation and its concomitant impact on population dynamics. For asexually reproducing populations, theory predicts that dispersal in fluctuating environments can facilitate asynchrony among clones and enhance stability by reducing temporal variability of total population abundance. This effect is predicted when clones exhibit heritable variation in environmental optima and when fluctuations occur asynchronously among patches. We tested this in the field using artificial ponds and metapopulations composed of a diverse assemblage of Daphnia pulex clones. We directly manipulated dispersal presence/absence and environmental fluctuations in the form of nutrient pulses. Consistent with predictions, dispersal enhanced temporal asynchrony among clones in the presence of nutrient pulses; this in turn stabilized population dynamics. This effect only emerged when patches experienced spatially asynchronous nutrient pulses (dispersal had no effect when patches were synchronously pulsed). Clonal asynchrony was driven by strong positive selection for a single clone that exhibited a performance advantage under conditions of low resource availability. Our work highlights the importance of dispersal as a driver of eco-evolutionary dynamics and population stability in variable environments.