Allee effects and extinction in a lattice model

In the interest of conservation, the importance of having a large habitat available for a species is widely known. Here, we introduce a lattice-based model for a population and look at the importance of fluctuations as well as that of the population density, particularly with respect to Allee effects. We examine the model analytically and by Monte Carlo simulations and find that, while the size of the habitat is important, there exists a critical population density below which the probability of extinction is greatly increased. This has large consequences with respect to conservation, especially in the design of habitats and for populations whose density has become small. In particular, we find that the probability of survival for small populations can be increased by a reduction in the size of the habitat and show that there exists an optimal size reduction.     

Genetic estimates of contemporary effective population size: what can they tell us about the importance of genetic stochasticity for wild population persistence?

Genetic stochasticity due to small population size contributes to population extinction, especially when population fragmentation disrupts gene flow. Estimates of effective population size ( N _e) can therefore be informative about population persistence, but there is a need for an assessment of their consistency and informative relevance. Here we review the body of empirical estimates of N _e for wild populations obtained with the temporal genetic method and published since Frankham's (1995 ) review. Theoretical considerations have identified important sources of bias for this analytical approach, and we use empirical data to investigate the extent of these biases. We find that particularly model selection and sampling require more attention in future studies.
We report a median unbiased N _e estimate of 260 (among 83 studies) and find that this median estimate tends to be smaller for populations of conservation concern, which may therefore be more sensitive to genetic stochasticity. Furthermore, we report a median N _e/ N ratio of 0.14, and find that this ratio may actually be higher for small populations, suggesting changes in biological interactions at low population abundances. We confirm the role of gene flow in countering genetic stochasticity by finding that N _e correlates strongest with neutral genetic metrics when populations can be considered isolated. This underlines the importance of gene flow for the estimation of N _e, and of population connectivity for conservation in general. Reductions in contemporary gene flow due to ongoing habitat fragmentation will likely increase the prevalence of genetic stochasticity, which should therefore remain a focal point in the conservation of biodiversity.     

Dynamics of inbreeding depression due to deleterious mutations in small populations: mutation parameters and inbreeding rate

A multilocus stochastic model is developed to simulate the dynamics of mutational load in small populations of various sizes. Old mutations sampled from a large ancestral population at mutation-selection balance and new mutations arising each generation are considered jointly, using biologically plausible lethal and deleterious mutation parameters. The results show that inbreeding depression and the number of lethal equivalents due to partially recessive mutations can be partly purged from the population by inbreeding, and that this purging mainly involves lethals or detrimentals of large effect. However, fitness decreases continuously with inbreeding, due to increased fixation and homozygosity of mildly deleterious mutants, resulting in extinctions of very small populations with low reproductive rates. No optimum inbreeding rate or population size exists for purging with respect to fitness (viability) changes, but there is an optimum inbreeding rate at a given final level of inbreeding for reducing inbreeding depression or the number of lethal equivalents. The interaction between selection against partially recessive mutations and genetic drift in small populations also influences the rate of decay of neutral variation. Weak selection against mutants relative to genetic drift results in apparent overdominance and thus an increase in effective size (Ne) at neutral loci, and strong selection relative to drift leads to a decrease in Ne due to the increased variance in family size. The simulation results and their implications are discussed in the context of biological conservation and tests for purging.     

Population size and the risk of local extinction: empirical evidence from rare plants

Due to habitat fragmentation many plant species today occur mainly in small and isolated populations. Modeling studies predict that small populations will be threatened more strongly by stochastic processes than large populations, but there is little empirical evidence to support this prediction for plants. We studied the relationship between size of local populations (number of flowering plants) and survival over ten years for 359 populations of eight short-lived, threatened plants in northern Germany ( Lepidium campestre , Thlaspi perfoliatum , Rhinanthus minor , R . serotinus , Melampyrum arvense , M . nemorosum , Gentianella ciliata and G . germanica ). Overall, 27% of the populations became extinct during the study period. Probability of survival of a local population increased significantly with its size in all but one species ( R. minor ). However, estimated population sizes required for 90% probability of survival over 10 years varied widely among species. Survival probability increased with decreasing distance to the nearest conspecific population in R . serotinus , but not in the other species. The mean annual growth rate of surviving populations differed greatly between species, but was only for G . germanica significantly lower than 1, suggesting that there was no general deterministic decline in the number of plants due to deteriorating habitat conditions. We conclude that the extinction of populations was at least partly due to stochastic processes. This is supported by the fact that in all species a considerable proportion of small populations survived and developed into large populations.     

Both population size and patch quality affect local extinctions and colonizations

Currently, the habitat of many species is fragmented, resulting in small local populations with individuals occasionally dispersing between the remaining habitat patches. In a solitary bee metapopulation, extinction probability was related to both local bee population sizes and pollen resources measured as host plant population size. Patch size, on the other hand, had no additional predictive power. The turnover rate of local bee populations in 63 habitat patches over 4 years was high, with 72 extinction events and 31 colonization events, but the pollen plant population was stable with no extinctions or colonizations. Both pollen resources and bee populations had strong and independent effects on extinction probability, but connectivity was not of importance. Colonizations occurred more frequently within larger host plant populations. For metapopulation survival of the bee, large pollen plant populations are essential, independent of current bee population size.     

Population consequences of changes in an ant-seed mutualism in Sanguinaria canadensis

Summary Seed dispersal by ants was studied in three populations of the myrmecochore, Sanguinaria canadensis, located in three habitats, each of which showed a different level of disturbance. Frequency of seed removal and the distances seeds were carried by ants were related to plant density, dispersion and the relative proportions of sexual and asexual reproduction in each population. Seeds in the least disturbed habitat were removed frequently and carried, by a wide variety of ants, distances of up to 12 m. Plant density was low and clone size was small. There was a relatively low level of sexual (seed) reproduction but seeds were generally transported well beyond the boundaries of the parent clones. By contrast, at the most disturbed site, plant density was high and clone size was very large. While there was a high level of seed production, seeds were rarely moved by ants and since removal distances were short, the probability of a seed being relocated beyond the limits of the parent clone was miniscule. The third population from a habitat which was intermediate in disturbance yielded data intermediate to the others. The data show that habitat disturbance, in disrupting the ant fauna and hence the ant-seed mutualism, has profound effects upon population density, dispersion and patterns of reproduction. Density-dependent regulation of sexual output predicted, for example, by the Strawberry-Coral model (Williams 1975), is maladaptive when the antseed mutualism is disturbed. We discuss the implications of this for theoretical modeling, the significance of mutualisms and the assessment of disturbance for conservation.     

Habitat quality matters for the distribution of an endangered leaf beetle and its egg parasitoid in a fragmented landscape

Fragmentation, deterioration, and loss of habitat patches threaten the survival of many insect species. Depending on their trophic level, species may be differently affected by these factors. However, studies investigating more than one trophic level on a landscape scale are still rare. In the present study we analyzed the effects of habitat size, isolation, and quality for the occurrence and population density of the endangered leaf beetle Cassida canaliculata Laich. (Coleoptera: Chrysomelidae) and its egg parasitoid, the hymenopteran wasp Foersterella reptans Nees (Hymenoptera: Tetracampidae). C. canaliculata is strictly monophagous on meadow sage (Salvia pratensis), while F. reptans can also parasitize other hosts. Both size and isolation of habitat patches strongly determined the occurrence of the beetle. However, population density increased to a much greater extent with increasing host plant density ( = habitat quality) than with habitat size. The occurrence probability of the egg parasitoid increased with increasing population density of C. canaliculata. In conclusion, although maintaining large, well-connected patches with high host plant density is surely the major conservation goal for the specialized herbivore C. canaliculata, also small patches with high host plant densities can support viable populations and should thus be conserved. The less specialized parasitoid F. reptans is more likely to be found on patches with high beetle density, while patch size and isolation seem to be less important.     

Effects of patch size and density on flower visitation and seed set of wild plants: a pan-European approach

1.  Habitat fragmentation can affect pollinator and plant population structure in terms of species composition, abundance, area covered and density of flowering plants. This, in turn, may affect pollinator visitation frequency, pollen deposition, seed set and plant fitness.
2.  A reduction in the quantity of flower visits can be coupled with a reduction in the quality of pollination service and hence the plants' overall reproductive success and long-term survival. Understanding the relationship between plant population size and/or isolation and pollination limitation is of fundamental importance for plant conservation.
3.  We examined flower visitation and seed set of 10 different plant species from five European countries to investigate the general effects of plant populations size and density, both within (patch level) and between populations (population level), on seed set and pollination limitation.
4.  We found evidence that the effects of area and density of flowering plant assemblages were generally more pronounced at the patch level than at the population level. We also found that patch and population level together influenced flower visitation and seed set, and the latter increased with increasing patch area and density, but this effect was only apparent in small populations.
5.   Synthesis. By using an extensive pan-European data set on flower visitation and seed set we have identified a general pattern in the interplay between the attractiveness of flowering plant patches for pollinators and density dependence of flower visitation, and also a strong plant species-specific response to habitat fragmentation effects. This can guide efforts to conserve plant–pollinator interactions, ecosystem functioning and plant fitness in fragmented habitats.     

Patterns and processes of population dynamics with fluctuating habitat size: a case study of a marine copepod inhabiting tide pools

The logistic model is a fundamental population model often used as the basis for analyzing wildlife population dynamics. In the classic logistic model, however, population dynamics may be difficult to characterize if habitat size is temporally variable because population density can vary at a constant abundance, which results in variable strength of density‐dependent feedback for a given population size. To incorporate habitat size variability, we developed a general population model in which changes in population abundance, density, and habitat size are taken into account. From this model, we deduced several predictions for patterns and processes of population dynamics: 1) patterns of fluctuation in population abundance and density can diverge, with respect of their correlation and relative variability; and 2) along with density dependence, habitat size fluctuation can affect population growth with a time lag because changes in habitat size result in changes in population density. In order to test these predictions, we applied our model to population dynamics data of 36 populations of Tigriopus japonicus, a marine copepod inhabiting tide pools of variable sizes caused by weather processes. As expected, we found a significant difference in the fluctuation patterns of population abundance and density of T. japonicus populations with respect to the correlation between abundance and density and their relative variability, which correlates positively with the variability of habitat size. In addition, we found direct and lagged‐indirect effects of weather processes on population growth, which were associated with density dependence and impose regulatory forces on local and regional population dynamics. These results illustrate how changes in habitat size can have an impact on patterns and processes of wildlife population dynamics. We suggest that without knowledge of habitat size fluctuation, measures of population size and its variability as well as inferences about the processes of population dynamics may be misleading.     

Potential Component Allee Effects and Their Impact on Wetland Management in the Conservation of Endangered Anurans

Effective management of wetland quantity and quality is crucial for effective conservation of declining amphibian populations. In particular, frogs and toads that employ aggregative breeding strategies may suffer negative population impacts in response to changes in availability of aquatic breeding habitat, including overabundance of suitable habitat, if density of conspecifics attending aggregations is positively correlated with reproductive success. Here we document such a positive relationship, potentially the first example of a component Allee effect in an anuran, in the critically endangered Houston toad (Bufo houstonensis). We assessed the relationship between mean yearly chorus size and reproductive success of males at the pond level using an information theoretic model selection approach and a two-sample t-test. The chosen model contained the single variable of mean yearly chorus size to predict probability of reproduction, as selected using the Akaike Information Criterion corrected for small sample size and Akaike weight. Mean chorus sizes were significantly higher among ponds exhibiting evidence of reproduction than in those that showed no evidence of reproduction. Our results suggest that chorusing alone is a poor proxy for inference of population stability and highlight a need for reassessment of widely-used amphibian monitoring protocols. Further, amphibian conservation efforts should account for potential Allee effects in order to optimize benefits and avoid underestimating critical population thresholds, particularly in species exhibiting rapid population declines.     

Evidence based conservation of butterflies

Few results of research aimed at solving questions arising from butterfly conservation are rigorously tested by manipulating populations and habitats in the field. Some factors common to successful conservation projects are analysed. In most non-migratory species, population density may vary by up to two orders of magnitude between sites or over time, and is primarily determined by the extent to which a subset of each species’ foodplant (or ant host) exists in the optimum growth-form or micro-habitat preferred by its larvae. Successful conservation projects have identified the optimum subset of each species’ larval resource before managing sites to increase its representation. In contrast, short-term fluctuations around a site’s carrying capacity or equilibrium level are mainly attributable to variation in weather, and are generally two orders of magnitude smaller than that attributable to larval habitat quality. There is little evidence that changing the abundance of adult resources, apart from shelter, influences population size or trends. The main constraint of the adult stage is the inability of many species to track the generation of new habitat patches that arise across modern landscapes. Within-patch larval habitat quality is again critical at the meta-population scale, explaining slightly more examples of patch occupancy than site isolation. This is because the higher density populations supported by optimum habitat are less likely to go extinct, and immigrants to new high-quality patches have a higher probability of founding new populations. Such patches may also generate up to a hundred times more emigrants per hectare than low-quality source patches.     

Assessing Extinction Risk in Small Metapopulations of Golden‐headed Lion Tamarins (Leontopithecus chrysomelas) in Bahia State,Brazil

Golden‐headed lion tamarins (GHLTs; Leontopithecus chrysomelas) are endangered primates endemic to the Brazilian Atlantic Forest, where loss of forest and its connectivity threaten species survival. Understanding the role of habitat availability and configuration on population declines is critical for guiding proactive conservation for this, and other, endangered species. We conducted population viability analysis to assess vulnerability of ten GHLT metapopulations to habitat loss and small population size. Seven metapopulations had a low risk of extirpation (or local extinction) over the next 100 years assuming no further forest loss, and even small populations could persist with immediate protection. Three metapopulations had a moderate/high risk of extirpation, suggesting extinction debt may be evident in parts of the species’ range. When deforestation was assumed to continue at current rates, extirpation risk significantly increased while abundance and genetic diversity decreased for all metapopulations. Extirpation risk was significantly negatively correlated with the size of the largest patch available to metapopulations, underscoring the importance of large habitat patches for species persistence. Finally, we conducted sensitivity analysis using logistic regression, and our results showed that local extinction risk was sensitive to percentage of females breeding, adult female mortality, and dispersal rate and survival; conservation or research programs that target these aspects of the species’ biology/ecology could have a disproportionately important impact on species survival. We stress that efforts to protect populations and tracts of habitat of sufficient size throughout the species’ distribution will be important in the near‐term to protect the species from continuing decline and extinction.     

Chaotic dynamics may determine the effect of inter-patch migration on metapopulation survival

A simple, strategic model of a system of habitat fragments connected by conservation corridors is presented. The intrinsic dynamics of the population on each fragment are stochastic. In addition, at each generation there is a probability of a catastrophic event occurring which affects all the habitat fragments by greatly reducing the size of the population on each. Global extinction is considered to occur when all the populations simultaneously fall below a threshold value. If the intrinsic dynamics on each fragment are simple cycles or a stable equilibrium, then the addition of conservation corridors does not reduce the frequency of global extinction. This is because migration between fragments induces their populations to have values which are similar to each other. However, if the intrinsic population dynamics are chaotic then the probability of global extinction is greatly reduced by the introduction of conservation corridors. Although local extinction is likely, the chaos acts to oppose the synchronising effect of migration. Often a subset of the populations survive a catastrophe and can recolonize the other patches.     

Spatial ecology of host–parasitoid interactions: a threatened butterfly and its specialised parasitoid

Habitat conservation for threatened temperate insect species is often guided by one of two paradigms: a metapopulation approach focusing on patch area, isolation and number; or a habitat approach focusing on maintaining high quality habitat for the focal species. Recent research has identified the additive and interacting importance of both approaches for maintaining populations of threatened butterflies. For specialised host-parasitoid interactions, understanding the consequences of habitat characteristics for the interacting species is important, because (1) specialised parasitoids are particularly vulnerable to the consequences of fragmentation, and (2) altered interaction frequencies resulting from changes to habitat management or the spatial configuration of habitat are likely to have consequences for host dynamics. The spatial ecology of Cotesia bignellii, a specialist parasitoid of the threatened butterfly Euphydryas aurinia, was investigated at two spatial scales: within habitat patches (at the scale of individual aggregations of larvae, or ‘webs’) and among habitat patches (the scale of local populations). Parasitism rates were investigated in relation to larval web size, vegetation sward height and host density. Within patches, the probability of a larval webs being parasitized increased significantly with increasing number of larvae in the web, and parasitism rates increased significantly with increasing web isolation. The proportion of webs parasitized was significantly and negatively correlated with cluster density. Among habitat patches the proportion of parasitized webs decreased as cluster density increased. Clusters with a high proportion of larval webs parasitized tended to have lower parasitism rates per larval web. These results support the call for relatively large and continuous habitat patches to maintain stable parasitoid and host populations. Conservation efforts directed towards maintenance of high host plant density could allow E. aurinia to reduce parasitism risk, while providing C. bignellii with sufficient larval webs to allow population persistence.     

Effects of Landscape-Scale Environmental Variation on Greater Sage-Grouse Chick Survival

Effective long-term wildlife conservation planning for a species must be guided by information about population vital rates at multiple scales. Greater sage-grouse (Centrocercus urophasianus) populations declined substantially during the twentieth century, largely as a result of habitat loss and fragmentation. In addition to the importance of conserving large tracts of suitable habitat, successful conservation of this species will require detailed information about factors affecting vital rates at both the population and range-wide scales. Research has shown that sage-grouse population growth rates are particularly sensitive to hen and chick survival rates. While considerable information on hen survival exists, there is limited information about chick survival at the population level, and currently there are no published reports of factors affecting chick survival across large spatial and temporal scales. We analyzed greater sage-grouse chick survival rates from 2 geographically distinct populations across 9 years. The effects of 3 groups of related landscape-scale covariates (climate, drought, and phenology of vegetation greenness) were evaluated. Models with phenological change in greenness (NDVI) performed poorly, possibly due to highly variable production of forbs and grasses being masked by sagebrush canopy. The top drought model resulted in substantial improvement in model fit relative to the base model and indicated that chick survival was negatively associated with winter drought. Our overall top model included effects of chick age, hen age, minimum temperature in May, and precipitation in July. Our results provide important insights into the possible effects of climate variability on sage-grouse chick survival.     

Local and Regional Determinants of Colonisation-Extinction Dynamics of a Riparian Mainland-Island Root Vole Metapopulation

The role of local habitat geometry (habitat area and isolation) in predicting species distribution has become an increasingly more important issue, because habitat loss and fragmentation cause species range contraction and extinction. However, it has also become clear that other factors, in particular regional factors (environmental stochasticity and regional population dynamics), should be taken into account when predicting colonisation and extinction. In a live trapping study of a mainland-island metapopulation of the root vole (Microtus oeconomus) we found extensive occupancy dynamics across 15 riparian islands, but yet an overall balance between colonisation and extinction over 4 years. The 54 live trapping surveys conducted over 13 seasons revealed imperfect detection and proxies of population density had to be included in robust design, multi-season occupancy models to achieve unbiased rate estimates. Island colonisation probability was parsimoniously predicted by the multi-annual density fluctuations of the regional mainland population and local island habitat quality, while extinction probability was predicted by island population density and the level of the recent flooding events (the latter being the main regionalized disturbance regime in the study system). Island size and isolation had no additional predictive power and thus such local geometric habitat characteristics may be overrated as predictors of vole habitat occupancy relative to measures of local habitat quality. Our results suggest also that dynamic features of the larger region and/or the metapopulation as a whole, owing to spatially correlated environmental stochasticity and/or biotic interactions, may rule the colonisation – extinction dynamics of boreal vole metapopulations. Due to high capacities for dispersal and habitat tracking voles originating from large source populations can rapidly colonise remote and small high quality habitat patches and re-establish populations that have gone extinct due to demographic (small population size) and environmental stochasticity (e.g. extreme climate events).     

Population size, self-incompatibility and genetic rescue in diploid and tetraploid races of Rutidosis leptorrhynchoides (Asteraceae)

Self-incompatibility systems function to prevent inbreeding, and work effectively in large, genetically diverse populations. However, a decrease in population size can reduce genetic diversity at the self-incompatibility locus, which leads to a reduction in mate availability and has important demographic implications for small populations. Currently, little is known about the response of self-incompatible polyploid species to a reduction in population size. In Rutidosis leptorrhynchoides there was a significant decrease in the within-population probability of fertilization with a decline in population size for diploid populations and a marginally significant relationship for tetraploid populations, suggesting that in small populations of both chromosome races fertilization success is reduced due to a decrease in self-incompatibility allele (S-allele) diversity. There was no significant difference between the slopes of the fertility-population size relationship for diploid and tetraploid populations which indicates a similar rate of decline in fertilization success with population size for both chromosome races. Fertilization success increased when crosses were undertaken between populations and this was significantly related to population size for diploid and tetraploid populations, indicating that small populations gain the greatest benefit to fertilization success from crossing between populations. For tetraploid populations the benefits of crossing between populations tended to decline more rapidly with increasing population size. These results suggest that for small populations that have reduced fertilization success, genetic rescue by introducing new genetic material from other populations is an important means of ameliorating mate limitation issues associated with reduced S-allele diversity in both diploid and tetraploid races.     

Comparing risk factors for population extinction

Extinction risk of natural populations of animals and plants is enhanced by many different processes, including habitat size reduction and toxic chemical exposure. We develop a method to evaluate different risk factors in terms of the decrease in the mean extinction time. We choose a population model with logistic growth, environmental and demographic stochasticities with three parameters (intrinsic growth rate r, carrying capacity K, and environmental noise sigma(2)(e)). The reduction in the habitat size decreases carrying capacity K only, whilst toxic chemical exposure decreases survivorship (or fertility) and in effect reduces both r and K. We derived a formula for the reduction in habitat size that decrease the mean extinction time by the same magnitude as a given level of toxic chemical exposure. In a large population (large K) or in a slowly growing population (small r), a small decrease in survivorship can cause the extinction risk increase corresponding to a significant reduction in the habitat size. This conclusion depends also on the nonlinearity of dose-effect relationship. To illustrate the method, we analyse a freshwater fish, Japanese crucian carp (Carassius auratus subsp.) in Lake Biwa.     

Connectivity, habitat heterogeneity, and population persistence in Ranunculus nodiflorus, an endangered species in France

Here, we explore the role of habitat spatial structure in the maintenance of metapopulations of Ranunculus nodiflorus. This rare species grows in puddles that can be connected occasionally by flooded corridors. We monitored five locations in the Fontainebleau forest, France, since 2002 and recorded the presence of corridors among puddles and evaluated their impact on puddle demography and plant fitness. We showed that connections increased population size, by increasing both the number of puddles occupied by the species and the density of individuals within puddles, but seemed to have no direct influence on plant fitness. We found no evidence of a large persistent soil seed bank. Natural corridors are likely to decrease the extinction probability of the populations, most probably by allowing recolonization of empty puddles after extinctions. Therefore, the preservation of corridors appears crucial for the conservation of R. nodiflorus in its natural habitat.     

Detection of reduction in population size using data from microsatellite loci

We demonstrate that the mean ratio of the number of alleles to the range in allele size, which we term M, calculated from a population sample of microsatellite loci, can be used to detect reductions in population size. Using simulations, we show that, for a general class of mutation models, the value of M decreases when a population is reduced in size. The magnitude of the decrease is positively correlated with the severity and duration of the reduction in size. We also find that the rate of recovery of M following a reduction in size is positively correlated with post-reduction population size, but that recovery occurs in both small and large populations. This indicates that M can distinguish between populations that have been recently reduced in size and those which have been small for a long time. We employ M to develop a statistical test for recent reductions in population size that can detect such changes for more than 100 generations with the post-reduction demographic scenarios we examine. We also compute M for a variety of populations and species using microsatellite data collected from the literature. We find that the value of M consistently predicts the reported demographic history for these populations. This method, and others like it, promises to be an important tool for the conservation and management of populations that are in need of intervention or recovery.