Long-term persistence of species and the SLOSS problem

The single large or several small (SLOSS) problem has been addressed in a large number of empirical and theoretical studies, but no coherent conclusion has yet been reached. Here I study the SLOSS problem in the context of metapopulation dynamics. I assume that there is a fixed total amount A(0) of habitat available, and I derive formulas for the optimal number n and area A of habitat patches, where n=A(0)/A. I consider optimality in two ways. First, I attempt to maximize the time to metapopulation extinction, which is a relevant measure for metapopulation viability for rare and threatened species. Second, I attempt to maximize the metapopulation capacity of the habitat patch network, which corresponds both with maximizing the distance to the deterministic extinction threshold and with maximizing the fraction of occupied patches. I show that in the typical case, a small number of large patches maximizes the metapopulation capacity, while an intermediate number of habitat patches maximizes the time to extinction. The main conclusion stemming from the analysis is that the optimal number of patches is largely affected by the relationship between habitat patch area and rates of immigration, emigration and local extinction. Here this relationship is summarized by a single factor zeta, termed the patch area scaling factor.     

Logic for designing nature reserves for multiple species

We examine the logic of designing nature reserves to understand better how to integrate the concepts of representativeness and persistence. Simple models of viability are used to evaluate how the expected number of species in the reserve system changes with variation in the risk of extinction among species, their rate of occurrence, and the distribution of species. The optimal size of individual reserves increased with the mean and variance of the probability of extinction among species and with the rate at which the risk of extinction declines with the cost of each reserve. In contrast, the rate of occurrence of species within reserves and their rate of accumulation with increasing reserve area had a relatively minor influence on the optimal size of reserves. Patterns of endemism were most important for the location of reserves. Including differences among species in the analysis reduced the optimal number of individual reserves (and increased the size of each) when operating under a fixed budget compared with reserve designs based on single species. A case study in the city of Melbourne, Australia, demonstrates the conservation value of small (approximately 1 ha) grassland reserves and the underrepresentation of Melbourne's volcanic plains in the region's conservation network.     

破碎景观建立保护区面积-数量模式界定

由于生境丧失日益严重,很难找到一片未被破坏的生境建立自然保护区,因而在设计保护区时,必须处理生境丧失带来的影响。在一个已经遭受过生境丧失的景观上,选取一片正方形的区域,并调整区域的面积以保证其中未被破坏生境的面积为一个固定常数,探讨将未被破坏的生境建设成大量小保护区还是少量大保护区。结果表明:(1)随机的生境丧失下,生境丧失比例越高,少量大保护区模式的优势越明显。(2)即使生境丧失比例恒定,被破坏生境的空间分布形式也有重要影响——被破坏生境的空间聚集程度越高,大量小保护区模式的优势越明显。(3)增加扩散率或降低扩散死亡率可导致从少量大保护区更有利于物种到大量小保护区更有利的转变,且被破坏生境的聚集程度越高,转变的程度越高。以上结论为自然保护区设计提供了理论依据。     

Catastrophes,connectivity and Allee effects in the design of marine reserve networks

Catastrophic events, like oil spills and hurricanes, occur in many marine systems. One potential role of marine reserves is buffering populations against disturbances, including the potential for disturbance-driven population collapses under Allee effects. This buffering capacity depends on reserves in a network providing rescue effects, setting up a tradeoff where reserves need to be connected to facilitate rescue, but also distributed in space to prevent simultaneous extinction. We use a set of population models to examine how dispersal ability and the disturbance regime interact to determine the optimal reserve spacing. We incorporate fishing in a spatially-explicit model to understand the effect of objective choice (e.g. conservation versus fisheries yield) on the optimal reserve spacing. We show that the optimal spacing between reserves increases when accounting for catastrophes with larger spacing needed when Allee effects interact with catastrophes to increase the probability of extinction. We also show that classic tradeoffs between conservation and fishing objectives disappear in the presence of catastrophes. Specifically, we found that at intermediate levels of disturbance, it is optimal to spread out reserves in order to increase both population persistence and to maximize spillover into non-reserve areas.     

Habitat destruction in mutualistic metacommunities

We investigate a mutualistic metacommunity where the strength of the mutualistic interaction between species is measured by the extent to which the presence of one species on a patch either reduces the extinction rate of the others present on the same patch or increases their ability to colonize other patches. In both cases, a strong enough mutualism enables all species to persist at habitat densities where they would all be extinct in the absence of the interaction. However, a mutualistic interaction that enhances colonization enables the species to persist at lower habitat density than one that suppresses extinction. All species abruptly go extinct (catastrophe) when the habitat density is decreased infinitesimally below a critical value. A comparison of the mean field or spatially implicit case with unrestricted dispersal and colonization to all patches in the system with a spatially explicit case where dispersal is restricted to the immediate neighbours of the original patch leads to the intriguing conclusion that restricted dispersal can be favourable for species that have a beneficial effect on each other when habitat conditions are adverse. When the mutualistic interaction is strong enough, the extinction threshold or critical amount of habitat required for the persistence of all species is lower when the dispersal is locally restricted than when unrestricted ! The persistence advantage for all species created by the mutualistic interaction increases substantially with the number of species in the metacommunity, as does the advantage for restricted dispersal over global dispersal.     

Estimate of population extinction risk and its application to ecological risk management

Environmental threats, such as habitat size reduction or environmental pollution, may not cause immediate extinction of a population but may shorten the expected time to extinction. We developed a method to estimate the mean time to extinction for a density-dependent population with environmental fluctuation and to compare the impacts of different risk factors. We first derived a formula of the mean extinction time for a population with logistic growth and environmental and demographic stochasticities expressed as a stochastic differential equation model (canonical model). The relative importance of different risk factors is evaluated by the decrease in the mean extinction time. We studied an approximated formula for the reduction in habitat size that enhances extinction risk by the same magnitude as a given decrease in survivorship caused by 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 to increase, corresponding to a significant reduction in the habitat size. Finally, we studied an approximate maximum likelihood estimate of three parameters (intrinsic growth rate r, carrying capacity K, and environmental stochasticity σ ² _e ) from time series data. By Monte Carlo sampling, we can remove the bias very effectively and determine the confidence interval. We discuss here how the reliability of the estimate changes with the length of time series. If we know the intrinsic rate of population growth r, the mean extinction time is estimated quite accurately even when only a short time series is available for parameter estimation. Received: March 31, 1999 / Accepted: November 9, 1999     

Integrating the effects of area, isolation, and habitat heterogeneity on species diversity: a unification of island biogeography and niche theory

We present an analytical model that unifies two of the most influential theories in community ecology, namely, island biogeography and niche theory. Our model captures the main elements of both theories by incorporating the combined effects of area, isolation, stochastic colonization and extinction processes, habitat heterogeneity, and niche partitioning in a unified, demographically based framework. While classical niche theory predicts a positive relationship between species richness and habitat heterogeneity, our unified model demonstrates that area limitation and dispersal limitation (the main elements of island biogeography) may create unimodal and even negative relationships between species richness and habitat heterogeneity. We attribute this finding to the fact that increasing heterogeneity increases the potential number of species that may exist in a given area (as predicted by niche theory) but simultaneously reduces the amount of suitable area available for each species and, thus, increases the likelihood of stochastic extinction. Area limitation, dispersal limitation, and low reproduction rates intensify the latter effect by increasing the likelihood of stochastic extinction. These analytical results demonstrate that the integration of island biogeography and niche theory provides new insights about the mechanisms that regulate the diversity of ecological communities and generates unexpected predictions that could not be attained from any single theory.     

Designing nature reserves in the face of uncertainty

Conservation reserves are a fundamental tool for managing biodiversity. The so-called SLOSS debate--should we have a Single Large Or Several Small reserves - is central to conservation theory. Population dynamic models suggest that the design that minimizes the risk of extinction of a species is case-specific, with the optimal number of reserves ranging between one and very many. Uncertainty is pervasive in ecology, but, the previous analyses of the SLOSS debate have not considered how uncertainty in the model of extinction risk might influence the optimal design. Herein, we show that when uncertainty is considered, the SLOSS problem is simplified and driven more by the aspirations of the manager than the population dynamics of the species. In this case, the optimal solution is to have in the order of twenty or fewer reserves for any species. This result shows counter-intuitively that considering uncertainty actually simplifies rather than complicates decisions about designing nature reserves.     

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.     

Spatially-correlated extinction in a metapopulation model of Leadbeater's Possum

The importance of considering spatially-correlated extinction in metapopulation viability analyses was investigated using a model of the population dynamics of Gymnobelideus leadbeateri McCoy (Leadbeater's Possum). Fire caused local extinction of G. leadbeateri and induced changes in the suitability of the habitat over a period of decades and centuries. Spatially-correlated fires, in which the correlation between the incidence of fire declines with distance, and uniformly-correlated fires were simulated. The predicted risk of metapopulation extinction increased: (i) as the variance in the number of fires each year increased, (ii) as the mean fire interval decreased, and (iii) as the mean dispersal distance decreased. Incorporating spatial correlation in the incidence of fires between patches had little effect on the results, provided the variance in the number of fires per year remained the same and fires modified habitat quality. The predicted risk of metapopulation extinction was greater for spatially-correlated fires than for uniformly-correlated fires when fires only caused local extinction but did not change habitat suitability. Incorporating spatial correlation in the incidence of fire within patches, which allowed partial burning of patches, reduced the predicted risk of extinction. This effect was only slight when patches were smaller than about 50 ha. The results of our simulations demonstrate the importance of considering correlations in disturbance regimes in metapopulation models, especially if these models are used to assist the design of nature reserves.     

On optimal size and number of reserves for metapopulation persistence

Habitat fragmentation is generally considered to be detrimental to the persistence of natural populations. In nature management, one therefore tends to prefer few large nature reserves over many small nature reserves having equal total area. This paper examines whether this preference is warranted in a metapopulation framework with circular reserves (patches) by formulating the dependence of metapopulation persistence on the size and number of reserves, both of which depend on reserve radius if the total area is kept constant. Two measures of metapopulation persistence are used: R(0), the number of patches colonized by an occupied patch during its lifetime as an occupied patch, and T(e), the expected time to extinction. These two measures are functions of the extinction and colonization rates of the metapopulation. Several mechanisms for the extinction and colonization processes are formulated from which the dependence of these rates on reserve radius is calculated. It turns out that T(e)generally increases with reserve radius for all mechanisms, which supports the preference of few large reserves. However, R(0)supports this preference only in the case of some special, rather unrealistic, mechanisms. In many other, more realistic, cases an intermediate reserve size exists for which metapopulation persistence measured by R(0)is optimal.     

Habitat loss and mammalian extinction patterns: are the reserves in the Quadrilátero Ferrífero, southeastern Brazil, effective in conserving mammals?

Habitat loss is considered to be the principal cause of the local extinction of mammals worldwide. We assessed the extinction pattern of medium- and large-sized mammals caused by the effects of habitat loss in reserves in the Quadrilátero Ferrífero, southeastern Brazil, and discussed the effectiveness of these natural remnants for conserving mammals. A literature review and field collections were conducted from 2006 to 2011 to estimate the composition and richness of mammals in nine remnants of different sizes, including reserves and non-protected areas. A species–area relation and a nested subset analysis were performed, and a degree of sensitivity to habitat loss was obtained for each species according to its frequency of occurrence. Forty-five species of mammals were recorded. There was a strong species–area relation involving the legal size of reserves. High species richness was associated with large reserves, and the z value was within the range of very isolated continental remnants. The mammalian community exhibited a nested occurrence pattern, suggesting that most species were part of a more continuous ecosystem and that non-random extinction caused by habitat loss occurred in southeastern Brazil. The negative relation found between species frequencies and body weights suggested that selective species loss is associated with decreases in the size of the reserves. The estimated viable size required to conserve all of the sensitive species is greater than the size of the largest reserve inventoried. We recommend the aggregation of neighboring natural remnants and the creation of new reserves to reduce extinction risks.     

Plant extinction risk under climate change: are forecast range shifts alone a good indicator of species vulnerability to global warming?

Models that couple habitat suitability with demographic processes offer a potentially improved approach for estimating spatial distributional shifts and extinction risk under climate change. Applying such an approach to five species of Australian plants with contrasting demographic traits, we show that: (i) predicted climate‐driven changes in range area are sensitive to the underlying habitat model, regardless of whether demographic traits and their interaction with habitat patch configuration are modeled explicitly; and (ii) caution should be exercised when using predicted changes in total habitat suitability or geographic extent to infer extinction risk, because the relationship between these metrics is often weak. Measures of extinction risk, which quantify threats to population persistence, are particularly sensitive to life‐history traits, such as recruitment response to fire, which explained approximately 60% of the deviance in expected minimum abundance. Dispersal dynamics and habitat patch structure have the strongest influence on the amount of movement of the trailing and leading edge of the range margin, explaining roughly 40% of modeled structural deviance. These results underscore the need to consider direct measures of extinction risk (population declines and other measures of stochastic viability), as well as measures of change in habitat area, when assessing climate change impacts on biodiversity. Furthermore, direct estimation of extinction risk incorporates important demographic and ecosystem processes, which potentially influence species’ vulnerability to extinction due to climate change.     

Characteristics of insect populations on habitat fragments: A mini review

Modern human-dominated landscapes are typically characterized by intensive land-use and high levels of habitat destruction, often resulting in sharply contrasted habitat mosaics. Fragmentation of remaining habitat is a major threat to biodiversity. In the present paper, we focus on the different features of habitat fragmentation. First we discuss the importance of pure habitat loss, fragment size, fragment isolation and quality, edge effects, and the importance of landscape structure. Second, we characterize life-history features of fragmentation-sensitive species, showing that rare, specialized, little dispersing species are most affected, as well as species characterized by high population variability and a high trophic position, while the effect of body size is unclear. Third, we discuss the conservation value of habitat fragments. The question arises how to relate studies on population survival to those of community structure and studies on biodiversity to those on ecologicalal functions. Despite the general superiority of large to small reserves, only small or medium-sized reserves are available in many human-dominated landscapes. A great number of small habitats covering a wide range of geographic area should maximize beta diversity and spreading of risk and may be very important for the regional conservation of biodiversity, in contrast to the prevailing arguments in favor of large habitats. Finally, landscape context influences community structure of fragments, and communities are composed of species that experience the landscape on a broad range of spatial scales. Spatial arrangement of habitat fragments in a landscape appears to be important only in simple, not complex landscapes.     

保护区的大小和数量效果的模拟研究*

对一个既包含局域种群动态,又包含集合种群侵占率的模型进行了计算机模拟,结果表明:(1)集合种群的存活时间随着保护区数目的增大先增大而后减小,即保护区的数目维持在中等大小时最有利于种群在集合种群水平上的存活。(2)这个最优值与保护区的总面积密切相关。这意味着在自然保护区的设置中,如果保护区的总面积一定,那么最佳决策不是保留一个大的完整的自然保护区,而是建立一个由数目相对较多而面积相对较小的保护区组成的网络。这对于自然保护区的设置有着重要的意义。     

Size of nature reserves: densities of large trees and dead wood indicate high value of small conservation forests in southern Sweden

The optimal size of nature reserves has been debated for some time. Although edge and core habitats are often recognized, it is commonly assumed in theory and in studies of a particular habitat type that reserves or patches of different sizes have similar habitat structure. However, for older, highly fragmented landscapes it has been suggested that small areas are of conservation interest as high-quality remnants, whereas large areas are more degraded. We studied 49 randomly selected forest reserves in the size range 5–230 ha (typical for many highly fragmented landscapes) and 3653 sites of key habitat (unprotected deciduous broadleaf forest). Structures in forest that are generally correlated with value for biodiversity were measured, and reserve objectives were examined from declaration texts. Both the density of large trees and the density of dead wood (snags, logs) decreased with increasing reserve size. The mean size of identified key habitats was very small (1.6 ha). A botanical objective for establishment of reserves was more frequently used for smaller reserves. In contrast, cultural and especially recreational objectives were more commonly used when larger reserves were established, suggesting higher values for recreation in these reserves. For vascular plants, birds and beetles, a literature review indicated that small forest patches do not contain impoverished communities, but are often rich (per unit of area). Small reserves and key habitats have several disadvantages, but they are probably important components of reserve networks for biodiversity in highly fragmented landscapes.     

Evolution of migration rate in a spatially realistic metapopulation model

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

The influence of neighborhood size and habitat shape on the accumulation of deleterious mutations.

To examine the impact of genetic neighborhood size and habitat shape on genetic load and the accumulation of deleterious mutation, individual-based simulations were performed in continuously distributed habitats. The risk of extinction increased as both the area of the habitat and the neighborhood size decreased. When the neighborhood area became smaller than the habitat area, habitat shape also began to influence the risk of extinction by mutation loads, expected time to extinction being shorter in longer and narrower habitats than in a square habitat. Both the number of homozygous deleterious loci per individual and the mutation load in the population increased as the neighborhood size and total population size decreased. Neighborhood size and total population size both independently affected the average number of homozygous deleterious loci per individual. In addition, as the ratio of the long to the short side of the rectangle of a habitat increased, the average number of homozygous deleterious loci increased. When the areas of the habitats were held constant, the average number of homozygous loci and the mutation loads were smallest for a regular square and largest for the longest, narrowest habitat. These results suggest that the spatial genetic structure of an individual is an important factor in the accumulation of deleterious mutations and the risk of extinction by mutation meltdown.     

Distribution and habitat specialization of species affect local extinction in dragonfly Odonata populations

The object of our study was to determine the effect of distribution and habitat specialization of odonate species on local extinction in streams in central Finland. We studied the local extinction of the 20 most abundant dragonfly (Odonata) species in 34 small creeks and brooks in central Finland. The historical presence of each studied species in our research area was confirmed using existing records gathered between 1930 and 1975. A minimum of five records was available for each species. During the summers of 1995 and 1996, we investigated the current persistence of 219 separate populations with historical presence. In total, 98 historical populations were vanished. As predicted, we found that species with a narrow distribution were less persistent than species with a broad distribution. Therefore, the extinction risk of a species was inversely related to the width of its regional distribution. Using reference works, species were categorized into two main breeding habitat types: lotic species or lentic species. The species main habitat type was a significant predictor of local extinction risk after statistical removal of the effect of regional distribution on extinction risk. The lotic species had lower local extinction risk than other species. Altogether, the highest extinction risk was found in habitat-specialist species associated with peatlands, probably due to loss of natural breeding habitat. On the other hand, extinction risk was lower in widely distributed habitat generalist species than true lotic species. The local extinction within species was more common in small dynamic upstream than in larger stable downstream habitats. The results of this study are consistent with meta-population theory.