On evolutionary stability of carrying capacity driven dispersal in competition with regularly diffusing populations

Two competing populations in spatially heterogeneous but temporarily constant environment are investigated: one is subject to regular movements to lower density areas (random diffusion) while the dispersal of the other is in the direction of the highest per capita available resources (carrying capacity driven diffusion). The growth of both species is subject to the same general growth law which involves Gilpin–Ayala, Gompertz and some other equations as particular cases. The growth rate, carrying capacity and dispersal rate are the same for both population types, the only difference is the dispersal strategy. The main result of the paper is that the two species cannot coexist (unless the environment is spatially homogeneous), and the carrying capacity driven diffusion strategy is evolutionarily stable in the sense that the species adopting this strategy cannot be invaded by randomly diffusing population. Moreover, once the invasive species inhabits some open nonempty domain, it would spread over any available area bringing the native species diffusing randomly to extinction. One of the important technical results used in the proofs can be interpreted in the form that the limit solution of the equation with a regular diffusion leads to lower total population fitness than the ideal free distribution.     

Effects of diffusion on total biomass in heterogeneous continuous and discrete-patch systems

Theoretical models of populations on a system of two connected patches previously have shown that when the two patches differ in maximum growth rate and carrying capacity, and in the limit of high diffusion, conditions exist for which the total population size at equilibrium exceeds that of the ideal free distribution, which predicts that the total population would equal the total carrying capacity of the two patches. However, this result has only been shown for the Pearl-Verhulst growth function on two patches and for a single-parameter growth function in continuous space. Here, we provide a general criterion for total population size to exceed total carrying capacity for three commonly used population growth rates for both heterogeneous continuous and multi-patch heterogeneous landscapes with high population diffusion. We show that a sufficient condition for this situation is that there is a convex positive relationship between the maximum growth rate and the parameter that, by itself or together with the maximum growth rate, determines the carrying capacity, as both vary across a spatial region. This relationship occurs in some biological populations, though not in others, so the result has ecological implications.     

The evolution of phenotypic plasticity in spatially structured environments: implications of intraspecific competition, plasticity costs and environmental characteristics

We model the evolution of reaction norms focusing on three aspects: frequency-dependent selection arising from resource competition, maintenance and production costs of phenotypic plasticity, and three characteristics of environmental heterogeneity (frequency of environments, their intrinsic carrying capacity and the sensitivity to phenotypic maladaptation in these environments). We show that (i) reaction norms evolve so as to trade adaptation for acquiring resources against cost avoidance; (ii) maintenance costs cause reaction norms to better adapt to frequent rather than to infrequent environments, whereas production costs do not; and (iii) evolved reaction norms confer better adaptation to environments with low rather than with high intrinsic carrying capacity. The two previous findings contradict earlier theoretical results and originate from two previously unexplored features that are included in our model. First, production costs of phenotypic plasticity are only incurred when a given phenotype is actually produced. Therefore, they are proportional to the frequency of environments, and these frequencies thus affect the selection pressure to avoid costs just as much as the selection pressure to improve adaptation. This prevents the frequency of environments from affecting the evolving reaction norm. Secondly, our model describes the evolution of plasticity for a phenotype determining an individual's capability to acquire resources, and thus its realized carrying capacity. When individuals are distributed randomly across environments, they cannot avoid experiencing environments with intrinsically low carrying capacity. As selection pressures arising from the need to improve adaptation are stronger under such extreme conditions than under mild ones, better adaptation to environments with low rather than with high intrinsic carrying capacity results.     

Effect of migration and environmental heterogeneity on the maintenance of quantitative genetic variation: a simulation study

The paradox of high genetic variation observed in traits under stabilizing selection is a long‐standing problem in evolutionary theory, as mutation rates appear too low to explain observed levels of standing genetic variation under classic models of mutation–selection balance. Spatially or temporally heterogeneous environments can maintain more standing genetic variation within populations than homogeneous environments, but it is unclear whether such conditions can resolve the above discrepancy between theory and observation. Here, we use individual‐based simulations to explore the effect of various types of environmental heterogeneity on the maintenance of genetic variation (V_A) for a quantitative trait under stabilizing selection. We find that V_A is maximized at intermediate migration rates in spatially heterogeneous environments and that the observed patterns are robust to changes in population size. Spatial environmental heterogeneity increased variation by as much as 10‐fold over mutation–selection balance alone, whereas pure temporal environmental heterogeneity increased variance by only 45% at max. Our results show that some combinations of spatial heterogeneity and migration can maintain considerably more variation than mutation–selection balance, potentially reconciling the discrepancy between theoretical predictions and empirical observations. However, given the narrow regions of parameter space required for this effect, this is unlikely to provide a general explanation for the maintenance of variation. Nonetheless, our results suggest that habitat fragmentation may affect the maintenance of V_A and thereby reduce the adaptive capacity of populations.     

Surprisingly little population genetic structure in a fungus‐associated beetle despite its exploitation of multiple hosts

In heterogeneous environments, landscape features directly affect the structure of genetic variation among populations by functioning as barriers to gene flow. Resource‐associated population genetic structure, in which populations that use different resources (e.g., host plants) are genetically distinct, is a well‐studied example of how environmental heterogeneity structures populations. However, the pattern that emerges in a given landscape should depend on its particular combination of resources. If resources constitute barriers to gene flow, population differentiation should be lowest in homogeneous landscapes, and highest where resources exist in equal proportions. In this study, we tested whether host community diversity affects population genetic structure in a beetle (Bolitotherus cornutus) that exploits three sympatric host fungi. We collected B. cornutus from plots containing the three host fungi in different proportions and quantified population genetic structure in each plot using a panel of microsatellite loci. We found no relationship between host community diversity and population differentiation in this species; however, we also found no evidence of resource‐associated differentiation, suggesting that host fungi are not substantial barriers to gene flow. Moreover, we detected no genetic differentiation among B. cornutus populations separated by several kilometers, even though a previous study demonstrated moderate genetic structure on the scale of a few hundred meters. Although we found no effect of community diversity on population genetic structure in this study, the role of host communities in the structuring of genetic variation in heterogeneous landscapes should be further explored in a species that exhibits resource‐associated population genetic structure.     

Long‐term breeding demography and density dependence in an increasing population of Golden Eagles Aquila chrysaetos

Few studies have quantified the dynamics of recovering populations of large raptors using long‐term, spatially explicit studies. Using data collected over 37 years in the western Italian Alps, we assessed the trends in distribution, abundance, fecundity and breeding population structure of Golden Eagles Aquila chrysaetos. Using the spatial distribution of territory centroids in 2007, we found that the spatial distribution of eagle territories was over‐dispersed up to 3 km. Although population size and total productivity increased from 1972 to 2008, the proportion of pairs that laid eggs showed a strong decline, falling to no more than 50% after 2003. On average, 15% of successful nests produced two fledglings, and productivity also declined over time. No significant relationship between population growth rate and total population size was detected, but the percentage of pairs that bred and breeding success showed evidence of density dependence, as they declined significantly with increasing density. Our results suggest that density dependence, operating across heterogeneous habitats, is currently regulating this population, while the carrying capacity may still be increasing. This may explain the apparent paradox of reduced breeding effort despite increasing total productivity.     

Spatial covariation of fish population vital rates in a stream network

Animal populations are spatially structured in heterogeneous landscapes, in which local patches with differing vital rates are connected by dispersal of individuals to varying degrees. Although there is evidence that vital rates differ among local populations, much less is understood about how vital rates covary among local patches in spatially heterogeneous landscapes. In this study, we conducted a nine-year annual mark–recapture survey to characterize spatial covariation of survival and growth for two Japanese native salmonids, white-spotted charr Salvelinus leucomaenis japonicus and red-spotted masu salmon Oncorhynchus masou ishikawae, in a headwater stream network composed of distinctly different tributary and mainstem habitats. Spatial structure of survival and growth differed by species and age class, but results provided support for negative covariation between vital rates, where survival was higher in the tributary habitat but growth was higher in the mainstem habitat. Thus, neither habitat was apparently more important than the other, and local habitats with complementary vital rates may make this spatially structured population less vulnerable to environmental change (i.e. portfolio effect). Despite the spatial structure of vital rates and possibilities that fish can exploit spatially distributed resources, movement of fish was limited due partly to a series of low-head dams that prevented upstream movement of fish in the study area. This study shows that spatial structure of vital rates can be complex and depend on species and age class, and this knowledge is likely paramount to elucidating dynamics of spatially structured populations.     

Fixation probabilities in a spatially heterogeneous environment

 We consider a simple model of a one-locus, two-allele population inhibiting a two-patch system and experiencing spatially heterogeneous viability selection. The populaton size is finite. We use a diffusion approximation and singular perturbation techniques to find the probability of fixation of a mutant allele. We focus on situations in which each allele is advantageous in one patch and deleterious in the other patch. Our theoretical results support the previous conclusions that, under certain conditions, small populations respond faster to selection than do large populations. We emphasize that knowledge of the dependence of migration rates on population size is crucial in evaluating the effects of population size on the rate of evolution.     

Expression of parasite virulence at different host population densities under natural conditions

It has recently been suggested that the expression of parasite virulence depends on host population density, such that infected hosts have a higher sensitivity to density, and thus reach their carrying capacity earlier than uninfected hosts. In this scenario, parasite-induced reduction in fitness (i.e., virulence) increases with host density. We tested this hypothesis experimentally, using outdoor mesocosm populations of Daphnia magna infected by the microsporidian Octosporea bayeri. Contrary to the prediction, virulence was independent of host density. In a competition experiment with initial prevalence of 50%, O. bayeri reduced the competitive ability of infected Daphnia within the asexual growth phase independent of initial host population density. In an additional experiment we set up populations with 100% and 0% prevalence and followed their population dynamics over the whole season. Consistent with the competition experiment, we found no difference in population dynamics within the asexual growth phase of the host, suggesting that infected hosts are not more sensitive to density than uninfected hosts. The additional experiment, however, included more than the initial growth phase as did the competition experiment. Eventually, after 100 days, 100% infected populations assumed a reduced carrying capacity compared to uninfected populations. We identify and discuss three reasons for the discrepancy between our experiment and the predictions.     

Quantitative genetic variance in experimental fly populations evolving with or without environmental heterogeneity

Heterogeneous environments are typically expected to maintain more genetic variation in fitness within populations than homogeneous environments. However, the accuracy of this claim depends on the form of heterogeneity as well as the genetic basis of fitness traits and how similar the assay environment is to the environment of past selection. Here, we measure quantitative genetic (QG) variance for three traits important for fitness using replicated experimental populations of Drosophila melanogaster evolving under four selective regimes: constant salt‐enriched medium (Salt), constant cadmium‐enriched medium (Cad), and two heterogeneous regimes that vary either temporally (Temp) or spatially (Spatial). As theory predicts, we found that Spatial populations tend to harbor more genetic variation than Temp populations or those maintained in a constant environment that is the same as the assay environment. Contrary to expectation, Salt populations tend to have more genetic variation than Cad populations in both assay environments. We discuss the patterns for QG variances across regimes in relation to previously reported data on genome‐wide sequence diversity. For some traits, the QG patterns are similar to the diversity patterns of ecological selected SNPs, whereas the QG patterns for some other traits resembled that of neutral SNPs.     

The island syndrome in isolated populations of a tropical forest rodent

I examined population traits of eight isolated populations of a tropical forest rodent (Proechimys semispinosus, the Central American spiny rat) for 1 year in central Panamá. Populations were sampled by monthly live-trapping, and seven traits (density, population growth rate, adult survival, reproductive effort, age structure, sex ratio, and body mass) were compared among populations. I also compared results with published data from nearby mainland populations. Each isolated population showed characteristics typical of island populations when compared with mainland populations, including higher and more stable densities, reduced reproductive effort, and greater body mass. Densities were the highest yet recorded for this species, and biomass of these island populations was among the highest of any tropical rodent yet studied. Population traits varied not only between island and mainland populations but also among island populations. P. semispinosus have traits that allow individuals in a population to rapidly respond to temporal changes in habitat quality or resource abundance. These traits include a high reproductive rate and an ability to adjust reproductive effort to changes in density. P. semispinosus are therefore able to quickly reach and maintain high densities under favorable conditions, thereby allowing close tracking of temporally and spatially varying resources. This flexibility is predicted for habitat generalists and presumably promotes abundance and persistence in temporally and spatially heterogeneous environments. P. semispinosus, often the most abundant and widely distributed species of rodent in forests throughout their geographic range, therefore have traits that are similar to those of generalist rodents in temperate forests.     

Pollen and Resource Limitation in Veratrum nigrum L. （Liliaceae）, an Andromonoecious Herb

Pollen limitation and resource limitation were invoked to account for the pattern that flowering plants produce more flowers and ovules than fruits and seeds. This study aimed to determine their relative importance in Veratrum nigrum, a self-compatible, perennial, andromonoecious herb. In order to determine whether female production was limited by pollen grains on stigmas or by available resources, we performed supplemental hand pollination in three populations, male-flower-bud removal in three other populations, and emasculation of hermaphroditic flowers in still another population, resulting in a total of seven populations experimentally manipulated. Across the three populations, supplemental hand pollination did not significantly increase fruit set, seed number per fruit, and total seed production per individual, nor did emasculation of hermaphroditic flowers. Taken together, our results suggest that pollen grains deposited on stigmas were abundant enough to fertilize all the ovules. Male-flower-bud removal significantly increased the mean size of hermaphroditic flowers in all three populations. Female reproductive success was increased in one population, but not in the other two populations possibly due to heavy flower/seed predation. We concluded that the female reproductive success of V. nigrum was not limited by pollen grains but by available resources, which is consistent with Bateman＇s principle. Furthermore, the female reproduction increase of male-flower-bud removal individuals might suggest a trade-off between male and female sexual functions.     

ECOLOGICAL HISTORY AND EVOLUTION IN A NOVEL ENVIRONMENT: HABITAT HETEROGENEITY AND INSECT ADAPTATION TO A NEW HOST PLANT

Environmental heterogeneity has often been implicated in the maintenance of genetic variation. However, previous research has not considered how environmental heterogeneity might affect the rate of adaptation to a novel environment. In this study, I used an insect-plant system to test the hypothesis that heterogeneous environments maintain more genetic variation in fitness components in a novel environment than do uniform environments. To manipulate recent ecological history, replicate populations of the dipteran leafminer Liriomyza trifolii were maintained for 20 generations in one of three treatments: a heterogeneous environment that contained five species of host plant, and two uniform environments that contained either a susceptible chrysanthemum or tomato. The hypothesis that greater genetic variance for survivorship and developmental time on a new host plant (a leafminer-resistant chrysanthemum) would be maintained in the heterogeneous treatment relative to the uniform environments was then tested with a sib-analysis and a natural selection experiment. Populations from the heterogeneous host plant treatment had no greater genetic variance in either larval survivorship or developmental time on the new host than did populations from either of the other treatments. Moreover, the rate of adaptation to the new host did not differ between the ecological history treatments, although the populations from the uniform chrysanthemum treatment had higher mean survivorship throughout the selection experiment. The estimates of the heritability of larval survivorship from the sib-analysis and selection experiment were quite similar. These results imply that ecologically realistic levels of environmental heterogeneity will not necessarily maintain more genetic variance than uniform environments when traits expressed in a particular novel environment are considered.     

Protein deprivation decreases male survival and the intensity of sexual antagonism in southern field crickets Gryllus bimaculatus

Recent theory predicts that the magnitude of sexual antagonism should depend on how well populations are adapted to their environment. We tested this idea experimentally by comparing intersexual genetic correlations for adult survival in pedigreed populations of southern field crickets (Gryllus bimaculatus) raised on naturally balanced (free‐choice) vs. imbalanced (protein‐deprived) diets. We tested for (1) sex differences in nutritional intake and preference, (2) sex‐specific effects of protein deprivation on survival and (3) diet dependence of the level of sexual antagonism. Adult males and females consumed a similar amount of protein, but protein deprivation decreased male survival but not female survival. Protein deprivation appeared to decrease the degree of sexual antagonism as intersexual genetic correlations were significantly lower than 1 only for the complementary free‐choice diet group but close to 1 for the protein‐deficient diet group. Our findings thereby implied that variation in nutritional environments can alter the magnitude of sexual antagonism. This research represents an important step towards understanding the relationship between sexual antagonism and adaptation in heterogeneous environments.     

NO EFFECT OF ENVIRONMENTAL HETEROGENEITY ON THE MAINTENANCE OF GENETIC VARIATION IN WING SHAPE IN DROSOPHILA MELANOGASTER

Theory suggests that heterogeneous environments should maintain more genetic variation within populations than homogeneous environments, yet experimental evidence for this effect in quantitative traits has been inconsistent. To examine the effect of heterogeneity on quantitative genetic variation, we maintained replicate populations of Drosophila melanogaster under treatments with constant temperatures, temporally variable temperature, or spatially variable temperature with either panmictic or limited migration. Despite observing differences in fitness and divergence in several wing traits between the environments, we did not find any differences in the additive genetic variance for any wing traits among any of the treatments. Although we found an effect of gene flow constraining adaptive divergence between cages in the limited migration treatment, it did not tend to increase within‐population genetic variance relative to any of the other treatments. The lack of any clear and repeatable patterns of response to heterogeneous versus homogeneous environments across several empirical studies suggests that a single general mechanism for the maintenance of standing genetic variation is unlikely; rather, the relative importance of putative mechanisms likely varies considerably from one trait and ecological context to another.     

The mixotroph Ochromonas tuberculata may invade and suppress specialist phago- and phototroph plankton communities depending on nutrient conditions

Mixotrophic organisms combine light, mineral nutrients, and prey as supplementary resources. Based on theoretical assumptions and field observations, we tested experimentally the hypothesis that mixotrophs may invade established plankton communities depending on the trophic status of the system, and investigated possible effects on food web structure, species diversity, and nutrient dynamics. To test our hypothesis, we inoculated the mixotrophic nanoflagellate Ochromonas tuberculata into established planktonic food webs, consisting of specialist phototrophs, specialist phagotrophs, and bacteria at different supplies of soluble inorganic nutrients and dissolved organic carbon. Oligotrophic systems facilitated the invasion of O. tuberculata in two different ways. First, the combination of photosynthesis and phagotrophy gave mixotrophs a competitive advantage over specialist phototrophs and specialist phagotrophs. Second, low nutrient supplies supported the growth of small plankton organisms that fell into the food size spectrum of mixotrophs. Conversely, high nutrient supplies prevented O. tuberculata from successfully invading the food webs. Two important conclusions were derived from our experiments. First, in contrast to a paradigm of ecology, specialization may not necessarily be the most successful strategy for survival under stable conditions. Indeed, the use of several resources with lower efficiency can be an equally, or even more, successful strategy in nature. Second, when limiting nutrients promote the growth of bacterio- and picophytoplankton, invading mixotrophs may have a habitat-ameliorating effect for higher trophic levels, gauged in terms of food quantity and quality. Using given resources more efficiently, O. tuberculata generated higher biomasses and expressed an increased nutritional value for potential planktivores, due to decreased cellular carbon to phosphorus (C:P) ratios compared to specialized plankton taxa. Our findings may help to explain why energy transfer efficiency between phytoplankton and higher trophic levels is generally higher in oligotrophic systems than in nutrient rich environments.     

Life-history evolution in guppies viii: the demographics of density regulation in guppies (poecilia reticulata)

In prior research, we found the way guppy life histories evolve in response to living in environments with a high or low risk of predation is consistent with life-history theory that assumes no density dependence. We later found that guppies from high-predation environments experience higher mortality rates than those from low-predation environments, but the increased risk was evenly distributed across all age/size classes. Life-history theory that assumes density-independent population growth predicts that life histories will not evolve under such circumstances, yet we have shown with field introduction experiments that they do evolve. However, theory that incorporates density regulation predicts this pattern of mortality can result in the patterns of life-history evolution we had observed. Here we report on density manipulation experiments performed in populations of guppies from low-predation environments to ask whether natural populations normally experience density regulation and, if so, to characterize the short-term demographic changes that underlie density regulation. Our experiments reveal that these populations are density regulated. Decreased density resulted in higher juvenile growth, decreased juvenile mortality rates, and increased reproductive investment by adult females. Increased density causes reduced offspring size, decreased fat storage by adult females, and increased adult mortality.     

Spatial heterogeneity lowers rather than increases host–parasite specialization

Abiotic environmental heterogeneity can promote the evolution of diverse resource specialists, which in turn may increase the degree of host–parasite specialization. We coevolved Pseudomonas fluorescens and lytic phage ?2 in spatially structured populations, each consisting of two interconnected subpopulations evolving in the same or different nutrient media (homogeneous and heterogeneous environments, respectively). Counter to the normal expectation, host–parasite specialization was significantly lower in heterogeneous compared with homogeneous environments. This result could not be explained by dispersal homogenizing populations, as this would have resulted in the heterogeneous treatments having levels of specialization equal to or greater than that of the homogeneous environments. We argue that selection for costly generalists is greatest when the coevolving species are exposed to diverse environmental conditions and that this can provide an explanation for our results. A simple coevolutionary model of this process suggests that this can be a general mechanism by which environmental heterogeneity can reduce rather than increase host–parasite specialization.     

Multiscale topoedaphic heterogeneity increases resilience and resistance of a dominant grassland species to extreme drought and climate change

It is argued that the inclusion of spatially heterogeneous environments in biodiversity reserves will be an effective means of encouraging ecosystem resilience and plant community conservation under climate change. However, the resilience and resistance of plant populations to global change, the specific life‐history traits involved and the spatial scale at which environmentally driven demographic variation is expressed remains largely unknown for most plant groups. Here we address these questions by reporting an empirical investigation into the impacts of an unprecedented 3‐year drought on the demography, population growth rates (λ) and biogeographical distribution of core populations of the perennial grassland species Austrostipa aristiglumis in semiarid Australia. We use life‐history analysis and periodic matrix population models to specifically test the hypothesis that patch‐ and habitat‐scale variation in vital life‐history parameters result in spatial differences in the resilience and resistance of A. aristiglumis populations to extreme drought. We show that the development of critical soil water deficits during drought resulted in collapse of adult A. aristiglumis populations (λ?1), rapid interhabitat phytosociological change and overall contraction towards mesic refugia where populations were both more resistant and resilient to perturbation. Population models, combined with climatic niche analysis, suggest that, even in core areas, a significant reduction in size and habitat range of A. aristiglumis populations is likely under climate change expected this century. Remarkably, however, we show that even minor topographic variation (0.2–3 m) can generate significant variation in demographic parameters that confer population‐level resilience and resistance to drought. Our findings support the hypothesis that extreme climatic events have the capacity to induce rapid, landscape‐level shifts in core plant populations, but that the protection of topographically heterogeneous environments, even at small spatial scales, may play a key role in conserving biodiversity under climate change in the coming century.     

Pollinator‐mediated phenotypic selection does not always modulate flower size and number in the large‐flowered Mediterranean shrub Cistus ladanifer (Cistaceae)

Flower size and number usually evolve under pollinator‐mediated selection. However, hot, dry environments can also modulate display, counteracting pollinator attraction. Increased pollen deposition on larger flower displays may not involve higher female fitness. Consequently, stressful conditions may constrain flower size, favouring smaller‐sized flowers. The large‐flowered, self‐incompatible Mediterranean shrub Cistus ladanifer was used to test that: (1) this species suffers pollen limitation; (2) pollinators are spatially–temporally variable and differentially visit plants with more/larger flowers; (3) increased visits enhance reproduction under pollen limitation; (4) stressful conditions reduce female fitness of larger displays; and (5) phenotypic selection on floral display is not just pollinator‐mediated. We evaluated pollen limitation, related floral display to pollinator visits and fruit and seed production and estimated phenotypic selection. Flower size was 7.2–10.5 cm and varied spatially–temporally. Visitation rates (total visits/50 min) ranged from 0.26 to 0.43 and increased with flower size. Fruit set averaged 80% and seed number averaged 855, but only fruit set varied between populations and years. Selection towards larger flowers was detected under conditions of pollen limitation. Otherwise, we detected stabilizing selection on flower size and negative selection on flower number. Our results suggest that selection on floral display is not only pollinator‐dependent through female fitness in C. ladanifer. © 2014 The Linnean Society of London, Botanical Journal of the Linnean Society, 2014, 176 , 540–555.