Relationship between resource selection, distribution, and abundance: a test with implications to theory and conservation

Much of applied and theoretical ecology is concerned with the interactions of habitat quality, animal distribution, and population abundance. We tested a technique that uses resource selection functions (RSF) to scale animal density to the relative probability of selecting a patch of habitat. Following an accurate survey of a reference block, the habitat-based density estimator can be used to predict population abundance for other areas with no or unreliable survey data. We parameterized and tested the technique using multiple years of radiotelemetry locations and survey data collected for woodland caribou across four landscape-level survey blocks. The habitat-based density estimator performed poorly. Predictions were no better than those of a simple area estimator and in some cases deviated from the observed by a factor of 10. We developed a simulation model to investigate factors that might influence prediction success. We experimentally manipulated population density, caribou distribution, ability of animals to track carrying capacity, and precision of the estimation equation. Our simulations suggested that interactions between population density, the size of the reference block, and the pattern of distribution can lead to large discrepancies between observed and predicted population numbers. Over- or undermatching patch carrying capacity and precision of the estimator can influence predictions, but the effect is much less extreme. Although there is some empirical and theoretical evidence to support a relationship between animal abundance and resource selection, our study suggests that a number of factors can seriously confound these relationships. Habitat-based density estimators might be effective where a stable, isolated population at equilibrium is used to generate predictions for areas with similar population parameters and ecological conditions.     

A stochastic metapopulation model accounting for habitat dynamics

A stochastic metapopulation model accounting for habitat dynamics is presented. This is the stochastic SIS logistic model with the novel aspect that it incorporates varying carrying capacity. We present results of Kurtz and Barbour, that provide deterministic and diffusion approximations for a wide class of stochastic models, in a form that most easily allows their direct application to population models. These results are used to show that a suitably scaled version of the metapopulation model converges, uniformly in probability over finite time intervals, to a deterministic model previously studied in the ecological literature. Additionally, they allow us to establish a bivariate normal approximation to the quasi-stationary distribution of the process. This allows us to consider the effects of habitat dynamics on metapopulation modelling through a comparison with the stochastic SIS logistic model and provides an effective means for modelling metapopulations inhabiting dynamic landscapes.     

Extinction conditions for isolated populations affected by environmental stochasticity

We determine the critical patch size below which extinction occurs for populations living in one-dimensional habitats surrounded by completely hostile environments in the presence of environmental fluctuations. The population dynamics is reformulated in terms of a stochastic reaction–diffusion equation and is reduced to a deterministic equation that incorporates the systematic contributions of the noise. We obtain bifurcation diagrams and relations for the mean population density at the stationary state, the critical patch size, and the mean number of individuals in the habitat. The effect of the noise differs, depending on whether it affects the net growth rate or the intraspecific competition term. Fluctuations in the net growth rate decrease the critical patch size, whereas fluctuations in the competition term do not change the critical patch size. We compare our analytical results with numerical solutions of the stochastic partial differential equations and show that our procedure proves useful in dealing with reaction–diffusion equations with multiplicative noise.     

Effects of habitat quality and size on extinction in experimental populations

Stochastic population theory makes clear predictions about the effects of reproductive potential and carrying capacity on characteristic time-scales of extinction. At the same time, the effects of habitat size and quality on reproduction and regulation have been hotly debated. To trace the causal relationships among these factors, we looked at the effects of habitat size and quality on extinction time in experimental populations of Daphnia magna. Replicate model systems representative of a broad-spectrum consumer foraging on a continuously supplied resource were established under crossed treatments of habitat size (two levels) and habitat quality (three levels) and monitored until eventual extinction of all populations. Using statistically derived estimates of key parameters, we related experimental treatments to persistence time through their effect on carrying capacity and the population growth rate. We found that carrying capacity and the intrinsic rate of increase were each influenced similarly by habitat size and quality, and that carrying capacity and the intrinsic rate of increase were in turn both correlated with time to population extinction. We expected habitat quality to have a greater influence on extinction. However, owing to an unexpected effect of habitat size on reproductive potential, habitat size and quality were similarly important for population persistence. These results support the idea that improving the population growth rate or carrying capacity will reduce extinction risk and demonstrate that both are possible by improving habitat quality or increasing habitat size.     

Modeling the presence probability of invasive plant species with nonlocal dispersal

Mathematical models for the spread of invading plant organisms typically utilize population growth and dispersal dynamics to predict the time-evolution of a population distribution. In this paper, we revisit a particular class of deterministic contact models obtained from a stochastic birth process for invasive organisms. These models were introduced by Mollison (J R Stat Soc 39(3):283, 1977). We derive the deterministic integro-differential equation of a more general contact model and show that the quantity of interest may be interpreted not as population size, but rather as the probability of species occurrence. We proceed to show how landscape heterogeneity can be included in the model by utilizing the concept of statistical habitat suitability models which condense diverse ecological data into a single statistic. As ecologists often deal with species presence data rather than population size, we argue that a model for probability of occurrence allows for a realistic determination of initial conditions from data. Finally, we present numerical results of our deterministic model and compare them to simulations of the underlying stochastic process.     

Temporal resource variability and the habitat-matching rule

Summary The ideal free distribution of competitors in a heterogeneous environment often predicts habitat matching, where the equilibrium number of consumers in a patch is proportional to resource abundance in that patch. We model the interaction between habitat matching and temporal variation in resource abundance. In one patch the rate of resource input follows a Markov chain; a second patch does not vary temporally. We predict patch use by scaling transition rates in the variable patch to the time that consumers require to respond to changes in rates of resource input. If consumers respond very quickly, habitat matching tracks temporal variability. If resource input fluctuates faster than consumers respond, habitat matching averages over the equilibrium of the Markov chain. Tracking and averaging produce the same mean resource consumption for individuals, but long-term mean occupation of the patches differs. When habitat matching tracks temporal variability in resources, consumer density in the variable patch has a lower mean and a higher variance than when habitat matching reflects only average rates of resource input.We tested our model by feeding free-living mallard ducks (Anas platyrynchos) at two artificial patches. The foragers' behavior satisfied the quantitative predictions of the model in each of two experiments.     

Rethinking edge effects: the unaccounted role of geometric constraints

Edge effects strongly affect the abundance and distribution of organisms across landscapes, with wide‐ranging implications in ecology and conservation biology. The extensive literature on the subject has traditionally considered that edge effects result from the active avoidance or preference of organisms for certain portions of the habitat patch, assuming that abundance is uniform across a patch when environmental conditions are uniform. We demonstrate that this assumption is incorrect due to the so‐far ignored ‘geometric edge effect’ (GEE). In the absence of environmental gradients, abundance of any organism living in a bounded habitat patch will tend to be lower in areas located near the edges compared to areas in the centre of the patch, simply because the areas in the centre receive individuals from all directions, whereas areas near the edge do not receive individuals from outside the patch. This geometric effect was already known for species richness at large geographic scales, the mid‐domain effect, but its importance in the literature of edge effects remained neglected so far. Using simulations, we show that the GEE tends to reduce population abundance and community richness near the edges of bounded habitat patches, and that apparently neutral or negative responses to the edge may occur even when habitat quality is higher near the edges. A published study that detected significant edge effects is reanalyzed, demonstrating that interpreting observed abundance patterns without taking the GEE into account – as traditionally done in the vast literature on edge effects – could provide misleading conclusions. The incorporation of the GEE into sampling and analytical protocols of future studies could advance substantially our ability to understand and predict edge effects in heterogeneous landscapes.     

Trophic disruption: a meta‐analysis of how habitat fragmentation affects resource consumption in terrestrial arthropod systems

Habitat fragmentation is a complex process that affects ecological systems in diverse ways, altering everything from population persistence to ecosystem function. Despite widespread recognition that habitat fragmentation can influence food web interactions, consensus on the factors underlying variation in the impacts of fragmentation across systems remains elusive. In this study, we conduct a systematic review and meta‐analysis to quantify the effects of habitat fragmentation and spatial habitat structure on resource consumption in terrestrial arthropod food webs. Across 419 studies, we found a negative overall effect of fragmentation on resource consumption. Variation in effect size was extensive but predictable. Specifically, resource consumption was reduced on small, isolated habitat fragments, higher at patch edges, and neutral with respect to landscape‐scale spatial variables. In general, resource consumption increased in fragmented settings for habitat generalist consumers but decreased for specialist consumers. Our study demonstrates widespread disruption of trophic interactions in fragmented habitats and describes variation among studies that is largely predictable based on the ecological traits of the interacting species. We highlight future prospects for understanding how changes in spatial habitat structure may influence trophic modules and food webs.     

Patch-size and isolation effects in the Fisher–Kolmogorov equation

We examine the classical problem of the existence of a threshold size for a patch to allow for survival of a given population in the case where the patch is not completely isolated. The surrounding habitat matrix is characterized by a non-zero carrying capacity. We show that a critical patch size cannot be strictly defined in this case. We also obtain the saturation density in such a patch as a function of the size of the patch and the relative carrying capacity of the outer region. We argue that this relative carrying capacity is a measure of the isolation of the patch. Our results are then compared with conclusions drawn from observations of the population dynamics of understorey birds in fragments of the Amazonian forest and shown to qualitatively agree with them, offering an explanation for the importance of dispersal and isolation in these observations. Finally, we show that a generalized critical patch size can be introduced resorting to threshold densities for the observation of a given species.     

京杭运河邵伯高邮段栖息地破碎化对狗獾种群数量分布的影响

栖息地破碎是生物多样性下降的主要原因之一。栖息地破碎引起的面积效应、隔离效应和边缘效应能影响动物种群的绝灭阈值、分布、多度、种间关系以及生态系统过程, 最终影响动物种群的数量分布。2006年10-11月和2007年10-11月, 利用全球定位系统(GPS)、地理信息系统(GIS)和样方法定量分析京杭运河邵伯至高邮段狗獾栖息地破碎化程度, 确定不同斑块的面积、斑块距离、斑块隔离度以及栖息地质量对斑块中狗獾数量分布的影响。结果表明, 各个斑块内狗獾的洞口数、粪堆数与该斑块的面积显著的正相关(r=0.961, P=0.039; r=0.999, P=0.023), 但与斑块距离、斑块隔离度无显著的相关性(P>0.05)。栖息地的质量也会影响狗獾的数量分布, 多元线性逐步回归分析表明, 人类干扰和与栖息地的郁闭性显著的影响狗獾的数量分布。以上结果说明, 京杭运河邵伯高邮段栖息地的破碎化程度对狗獾的数量分布还没有造成显著的直接影响, 但会间接降低栖息地的质量, 进而影响狗獾的生存。     

Expansion or extinction: deterministic and stochastic two-patch models with Allee effects

We investigate the impact of Allee effect and dispersal on the long-term evolution of a population in a patchy environment. Our main focus is on whether a population already established in one patch either successfully invades an adjacent empty patch or undergoes a global extinction. Our study is based on the combination of analytical and numerical results for both a deterministic two-patch model and a stochastic counterpart. The deterministic model has either two, three or four attractors. The existence of a regime with exactly three attractors only appears when patches have distinct Allee thresholds. In the presence of weak dispersal, the analysis of the deterministic model shows that a high-density and a low-density populations can coexist at equilibrium in nearby patches, whereas the analysis of the stochastic model indicates that this equilibrium is metastable, thus leading after a large random time to either a global expansion or a global extinction. Up to some critical dispersal, increasing the intensity of the interactions leads to an increase of both the basin of attraction of the global extinction and the basin of attraction of the global expansion. Above this threshold, for both the deterministic and the stochastic models, the patches tend to synchronize as the intensity of the dispersal increases. This results in either a global expansion or a global extinction. For the deterministic model, there are only two attractors, while the stochastic model no longer exhibits a metastable behavior. In the presence of strong dispersal, the limiting behavior is entirely determined by the value of the Allee thresholds as the global population size in the deterministic and the stochastic models evolves as dictated by their single-patch counterparts. For all values of the dispersal parameter, Allee effects promote global extinction in terms of an expansion of the basin of attraction of the extinction equilibrium for the deterministic model and an increase of the probability of extinction for the stochastic model.     

Metapopulation dynamics of the bog fritillary butterfly: modelling the effect of habitat fragmentation

Population viability analysis (PVA) and metapopulation theory are valuable tools to model the dynamics of spatially structured populations. In this article we used a spatially realistic population dynamic model to simulate the trajectory of a Proclossiana eunomia metapopulation in a network of habitat patches located in the Belgian Ardenne. Sensitivity analysis was used to evaluate the relative influence of the different parameters on the model output. We simulated habitat loss by removing a percentage of the original habitat, proportionally in each habitat patch. Additionally, we evaluated isolation and fragmentation effects by removing and dividing habitat patches from the network, respectively. The model predicted a slow decline of the metapopulation size and occupancy. Extinction risks predicted by the model were highly sensitive to environmental stochasticity and carrying capacity. For a determined level of habitat destruction, the expected lifetime of the metapopulation was highly dependent on the spatial configuration of the landscape. Moreover, when the proportion of removed habitat is above 40% of the original habitat, the loss of whole patches invariably leads to the strongest reduction in metapopulation viability.     

Responses of Etiella zinckenella to habitat fragmentation of Caraganas in desert steppe in Ningxia, China

Habitat fragmentation is a common cause for which species becomes threatened or endangered. Existence of viable habitat is critical to the survival of any species, so habitat fragmentation is the main reason for the changes in distribution and abundance of organisms, and is usually considered to have negative effect on the abundance, species richness and population of organisms in a specific landscape. But this effect may also depend on whether some species could use one or more types of habitat in a specific landscape. Because of its well resistance to stress, Caragana is one of predominant shrub in desert region for forest planting and desert preventing, which plays a critical role in desert control and ecosystem stabilization. Baijitan National Nature Reserve, located in Lingwu County, Ningxia Hui Autonomous Region, China, is typical of desert nature reserve in which the Caragana spp., Oxytropisaciphylla and other desert plants are protected. The Caragana woodlands in this region show a pattern of dots, patches and strips separated by natural and cultivated forest, thereby leading to a typical fragmented landscape. Etiellazinckenella (Lepidoptera, Pyralidae) is one of seed pests of Caragana. In order to illuminate the responses of E. zinckenella to the habitat fragmentation of Caraganas woodlands, the present study focused on the effects of habitat area, habitat fragmentation, as well as matrix composition on the population density and damage ratio of E. zinckenella in desert steppe. From May 2008 to June 2009, by using parallel jump sampling method, 13 Caragana woodland patches representing four landscapes from Baijitan National Nature Reserve were investigated and totally 15,117 pods were inspected. Then, the landscape fragmentation indices, population density and damage ratio of E. zinckenella in Caragana woodlands were calculated. The statistic analysis of the data indicated that the four landscapes have a significant difference in the population density and damage ratio of E. zinckenella; and in the same landscape, the neighbor patches also have a significant difference in the damage ratios of E. zinckenella. E. zinckenella seems to prefer some species of Caragana, for instance, the damage ratio of E. zinckenella to Caragana microphylla is found the highest, followed by the damage ratio to Caraganadavazamcidamage, while the damage ratio to Caraganakorshinskii is found the lowest. The coverage of Caragana is found positively related to the damage ratio of E. zinckenella with hinge damage ratio in high coverage of Caragana forest. The regression analysis shows that the latitude (R_s = 0.5724), longitude (R_s = 0.5577), altitude (R_s = 0.4614) and patch area (R = 0.3012) were not significantly associated with population density and damage ratio of E. zinckenella. However, the population density and damage ratio of E. zinckenella decreased with the increasing in patch area. The landscape patch fragmentation index (R = 0.91129) and the patch density index (R = 0.89864) show a positive correlation with damage ratio. The fragmentation shape index (R = ?0.89675) and inside habitat area fragmentation index (R = ?0.77646) show a negative correlation with the damage ratio. As a result, the population of E. zinckenella was suppressed by the landscape fragmentation, but the patch isolation and complementary resources in the landscape matrix may also have a positive impact on the population density of E. zinckenella.     

From Aggregation to Dispersion: How Habitat Fragmentation Prevents the Emergence of Consensual Decision Making in a Group

In fragmented landscape, individuals have to cope with the fragmentation level in order to aggregate in the same patch and take advantage of group-living. Aggregation results from responses to environmental heterogeneities and/or positive influence of the presence of congeners. In this context, the fragmentation of resting sites highlights how individuals make a compromise between two individual preferences: (1) being aggregated with conspecifics and (2) having access to these resting sites. As in previous studies, when the carrying capacity of available resting sites is large enough to contain the entire group, a single aggregation site is collectively selected. In this study, we have uncoupled fragmentation and habitat loss: the population size and total surface of the resting sites are maintained at a constant value, an increase in fragmentation implies a decrease in the carrying capacity of each shelter. For our model organism, Blattella germanica, our experimental and theoretical approach shows that, for low fragmentation level, a single resting site is collectively selected. However, for higher level of fragmentation, individuals are randomly distributed between fragments and the total sheltered population decreases. In the latter case, social amplification process is not activated and consequently, consensual decision making cannot emerge and the distribution of individuals among sites is only driven by their individual propensity to find a site. This intimate relation between aggregation pattern and landscape patchiness described in our theoretical model is generic for several gregarious species. We expect that any group-living species showing the same structure of interactions should present the same type of dispersion-aggregation response to fragmentation regardless of their level of social complexity.     

Colonization–extinction dynamics of epixylic lichens along a decay gradient in a dynamic landscape

Metapopulation models are often used for understanding and predicting species dynamics in fragmented landscapes. Several models have been proposed depending on e.g. the relative importance of patch dynamics on the metapopulation dynamics. Dead wood is a dynamic substrate patch, and species that are confined to such patches have experienced a high degree of habitat loss in managed forests. Little is, however, known about how the population dynamics of epixylic species are affected by the fast dynamics of their substrate patches. We quantified the effect of local patch conditions and metapopulation processes on colonizations and extinctions of epixylic lichen species in a managed boreal forest landscape. This was done by twice surveying seven lichen metapopulations on 293 stumps in 30 stands of ages covering the duration of the dynamic patches (stumps). We also investigated the relative importance of local stochastic extinctions from stumps that remained available, and deterministic extinctions due to stump surface disappearance. We found importance of a decay gradient, surrounding metapopulation size, and local population sizes, in driving the colonization–extinction dynamics of epixylic lichens. The species were sorted along the stump decay gradient. Increasing surrounding metapopulation size was associated with increased colonization rates, and increasing local population size decreased lichen extinction rates. Finally, both local stochastic extinctions and deterministic extinctions due to patch disappearance occur, confirming that the long‐term persistence of epixylic lichens depends on colonization rates that compensate for stochastic population extinctions as well as deterministic extinctions.     

Estimating breeding season abundance of golden-cheeked warblers in Texas,USA

Population abundance estimates using predictive models are important for describing habitat use and responses to population-level impacts, evaluating conservation status of a species, and for establishing monitoring programs. The golden-cheeked warbler (Setophaga chrysoparia) is a neotropical migratory bird that was listed as federally endangered in 1990 because of threats related to loss and fragmentation of its woodland habitat. Since listing, abundance estimates for the species have mainly relied on localized population studies on public lands and qualitative-based methods. Our goal was to estimate breeding population size of male warblers using a predictive model based on metrics for patches of woodland habitat throughout the species' breeding range. We first conducted occupancy surveys to determine range-wide distribution. We then conducted standard point-count surveys on a subset of the initial sampling locations to estimate density of males. Mean observed patch-specific density was 0.23 males/ha (95% CI = 0.197–0.252, n = 301). We modeled the relationship between patch-specific density of males and woodland patch characteristics (size and landscape composition) and predicted patch occupancy. The probability of patch occupancy, derived from a model that used patch size and landscape composition as predictor variables while addressing effects of spatial relatedness, best predicted patch-specific density. We predicted patch-specific densities as a function of occupancy probability and estimated abundance of male warblers across 63,616 woodland patches accounting for 1.678 million ha of potential warbler habitat. Using a Monte Carlo simulation, our approach yielded a range-wide male warbler population estimate of 263,339 (95% CI: 223,927–302,620). Our results provide the first abundance estimate using habitat and count data from a sampling design focused on range-wide inference. Managers can use the resulting model as a tool to support conservation planning and guide recovery efforts. © 2012 The Wildlife Society.     

Consumer movement through differentially subsidized habitats creates a spatial food web with unexpected results

Energy and nutrient flow between habitats, or allochthonous input, can have a significant impact on food web dynamics. Previous theory demonstrated that resource abundance decreases in habitats where consumers are subsidized. Here we examine the effect of subsidies that are available in localized parts of a habitat (such as near the shore in a marine‐subsidized terrestrial ecosystem) with a two‐patch model in which consumers move between patches, resources are stationary, and consumers receive the subsidy in only one of the two patches. In contrast to previous theory, our results show that subsidized consumers can increase resource abundance, though only in the subsidized patch. Furthermore, the total resource population responds positively to increasing consumer movement. These results demonstrate the importance of spatial heterogeneity in food web dynamics and the need for further examination of the role of space in multispecies trophic webs.     

Allee effects and resilience in stochastic populations

Allee effects, or positive functional relationships between a population’s density (or size) and its per unit abundance growth rate, are now considered to be a widespread if not common influence on the growth of ecological populations. Here we analyze how stochasticity and Allee effects combine to impact population persistence. We compare the deterministic and stochastic properties of four models: a logistic model (without Allee effects), and three versions of the original model of Allee effects proposed by Vito Volterra representing a weak Allee effect, a strong Allee effect, and a strong Allee effect with immigration. We employ the diffusion process approach for modeling single-species populations, and we focus on the properties of stationary distributions and of the mean first passage times. We show that stochasticity amplifies the risks arising from Allee effects, mainly by prolonging the amount of time a population spends at low abundance levels. Even weak Allee effects become consequential when the ubiquitous stochastic forces affecting natural populations are accounted for in population models. Although current concepts of ecological resilience are bound up in the properties of deterministic basins of attraction, a complete understanding of alternative stable states in ecological systems must include stochasticity.     

Direct versus indirect effects of habitat fragmentation on community patterns in experimental landscapes

Habitat area and fragmentation are confounded in many ecological studies investigating fragmentation effects. We thus devised an innovative experiment founded on fractal neutral landscape models to disentangle the relative effects of habitat area and fragmentation on arthropod community patterns in red clover (Trifolium pratense). The conventional approach in experimental fragmentation studies is to adjust patch size and isolation to create different landscape patterns. We instead use fractal distributions to adjust the overall amount and fragmentation of habitat independently at the scale of the entire landscape, producing different patch properties. Although habitat area ultimately had a greater effect on arthropod abundance and diversity in this system, we found that fragmentation had a significant effect in clover landscapes with ≤40 % habitat. Landscapes at these lower habitat levels were dominated by edge cells, which had fewer arthropods and lower richness than interior cells. Fragmentation per se did not have a direct effect on local-scale diversity, however, as demonstrated by the lack of a broader landscape effect (in terms of total habitat area and fragmentation) on arthropods within habitat cells. Fragmentation—through the creation of edge habitat—thus had a strong indirect effect on morphospecies richness and abundance at the local scale. Although it has been suggested that fragmentation should be important at low habitat levels (≤20–30 %), we show that fragmentation per se is significant only at intermediate (40 %) levels of habitat, where edge effects were neither too great (as at lower levels of habitat) nor too weak (as at higher levels of habitat).     

Avian responses to forest fragmentation during the breeding and non-breeding seasons

Forest fragmentation represents a threat to several bird species worldwide. Several factors can change across seasons (e.g. bird perception of the landscape, weather conditions, biotic interactions), which can modify the response of bird populations to forest fragmentation. However, most studies have been conducted only during the breeding season. Here we assessed the relationship between forest fragmentation (patch area and patch isolation) with population abundances of resident species during both the breeding and the non-breeding seasons. Bird population abundances (all species in the community, subsets of forest and habitat generalist species and for individual species) were estimated across a gradient of area-isolation in a semi-arid forest in Cordoba, Argentina. Population abundance of the overall avian community and of the subset of forest species declined with patch area reduction independently of the season. By contrast, the subset of habitat generalist species was not affected by patch area reduction or by the increase in patch isolation, either during the breeding or during the non-breeding season. When the analyses were carried out for individual species, we found four forest species and one habitat generalist species whose responses (the relationship between population abundance and patch area or with isolation) were different between breeding and non-breeding seasons. The negative effects of forest fragmentation were found mainly during the breeding season. Our results suggest that reduction of patch area may lead to a reduction of more than 65% of the population abundance of forest bird species, during both the breeding and the non-breeding season. Therefore, there is an urgent need to conserve large forest patches within the region as irreplaceable elements for the conservation of populations of several species.