Consequences of the Allee Effect and Intraspecific Competition on Population Persistence under Adverse Environmental Conditions

The impact of intraspecific interactions on ecological stability and population persistence in terms of steady state(s) existence is considered theoretically based on a general competition model. We compare persistence of a structured population consisting of a few interacting (competitive) subpopulations, or groups, to persistence of the corresponding unstructured population. For a general case, we show that if the intra-group competition is stronger than the inter-group competition, then the structured population is less prone to extinction, i.e. it can persist in a parameter range where the unstructured population goes extinct. For a more specific case of a population with hierarchical competition, we show that relative viability of structured and unstructured populations depend on the type of density dependence in the population growth. Namely, while in the case of logistic growth, structured and unstructured populations exhibit equivalent persistence; in the case of Allee dynamics, the persistence of a hierarchically structured population is shown to be higher. We then apply these results to the case of behaviourally structured populations and demonstrate that an extreme form of individual aggression can be beneficial at the population level and enhance population persistence.     

栖息地毁坏与动物物种灭绝关系的模拟研究

利用多个物种共存模式模拟了不同情况下的不同动物种群演化的动力学特性,研究结果表明：（1）由于栖息地的毁坏所导致的动手的种灭绝是依赖于对物种死亡率和有关平衡态的假设的,不同的假设下,既使栖息地的破坏率相同,灭绝的物种可能是竞争能力最强的若干物种,也可能是竞争能力相对较弱的若干物种,既不象传统的物种进化理论所认为的必是弱的物种先灭绝,也不象Tilman等人所认为的一定是最强的若干物种先灭绝;（2）如果弱的物种具有较高的平均死亡率,则当栖息地受到一定的毁坏时,将有较多强的物种灭绝,而且物种灭绝时间将大大缩短;（3）在物种死亡率不变的情形下,物种在未受毁坏栖息地上的平衡态和大占有率pl^0,将有利于物种的生存。     

集合种群动态对栖息地毁坏时空异质性的响应

栖息地毁坏既有时间异质性,也有空间异质性,而以往的研究往往只关注其中的一种。将两种不同的异质性共同引入到元胞自动机中,模拟了集合种群动态对栖息地毁坏时空异质性的响应。发现,在随机离散的栖息地毁坏下,由于物种的迁移繁殖力受栖息地毁坏的影响很大,迁移繁殖力弱而竞争力强的物种先灭绝。在连续的栖息地毁坏下,物种的迁移繁殖力受栖息地毁坏的影响较小,物种的灭绝由竞争力和迁移繁殖力共同决定:在有绝对优势种的群落里,种间竞争显著,弱物种先灭绝,而在没有绝对优势种的群落里,种间竞争较小,则以强物种先灭绝。因此,随机毁坏不利于强物种续存,而连续毁坏则不利于具有绝对优势种群的群落里的弱物种续存。在实际开发某一栖息地时,根据集合种群结构和被保护的对象采取相应的开发模式。     

Ontogenetic antagonism–mutualism coupling: perspectives on resilience of stage‐structured communities

Organisms typically change their diets ontogenetically. Recent studies have shown that an ontogenetic diet shift undermines the resilience of stage‐structured food webs. Here, we study the integration of stage‐structured food‐web theory into theory of hybrid community (i.e. mixture of different interaction types), considering that not only diet but also interaction type often changes because of ontogenetic niche shift (e.g. the metamorphosis of pollinating insects, in which juveniles and adults are herbivores and pollinators, respectively). We developed and mathematically analysed a one‐consumer two‐resource model in which juvenile and adult consumers utilise different resources as antagonists and mutualists, respectively. Model analyses illustrated that the consumer either goes extinct or coexists with the resources depending on the initial condition when the resources have low carrying capacities while their community dynamics always converge to a single steady state when the resources have high carrying capacities. These dynamic features are different from those of the corresponding purely antagonistic module in previous studies, in which the consumer always goes extinct for low resource carrying capacities while the dynamics converge to either juvenile‐dominated or adult‐dominated state depending on the initial conditions for high resource carrying capacities. Taken together, we can suggest that ontogenetic antagonism–mutualism coupling is stabilising in that it increases the potential for species coexistence in unproductive environments while improving community resilience in productive environments. Further, these effects are generally robust to interaction nonlinearity. Beyond the previous concern of the instability in stage‐structured food‐webs, our results suggest that antagonism–mutualism coupling can play a crucial role in stabilising stage‐structured hybrid (e.g. plant–animal) communities under environmental changes. The present study represents an important first step in understanding how interaction type diversity can mediate the dynamics of stage‐structured communities.     

Spatially structured intraspecific trait variation can foster biodiversity in disturbed,heterogeneous environments

Trait variation within populations is an important area of research for empirical and theoretical ecologists. While differences between individuals are doubtlessly ubiquitous, their role for species coexistence is much less clear and highly debated. Both unstructured (random) and structured (linked to space, time or inheritance) intraspecific trait variation (ITV) may modify species interactions with nontrivial consequences for emerging community compositions. In many ecosystems, these compositions are further driven by prevalent disturbance regimes. I therefore explored the effects of unstructured as well as spatially structured ITV under disturbances in a generic ecological model of competing sessile species. Using spatially explicit, individual‐based simulations, I studied how intraspecific variation in life history traits together with interspecific tradeoffs and disturbance regimes shape long‐term community composition. I found that 1) unstructured ITV does not affect species coexistence in the given context, 2) spatially structured ITV may considerably increase coexistence, but 3) spatially clumped disturbances reduce this effect of spatially structured ITV, especially if interspecific tradeoffs involve dispersal distance. The findings suggest that spatially structured ITV with individual trait responses to local habitat conditions differing among species may create or expand humps in disturbance–diversity relationships. Hence, if present, these forms of spatially structured ITV should be included in ecological models and will be important for reliably assessing community responses to environmental heterogeneity and change.     

Extinction of species in age-structured, discrete noncooperative systems

Using a multi-species model of Ebenman for the dynamics of a discretely reproducing population that consists of noncooperation between juveniles and adults, we obtain exclusion principles by Lyapunov function methods. In the very general age-structured model, we show that, if there is an adult whose growth function is always larger than that of all the other species in the system, then it dominates the system by driving all the others to extinction. This result confirms a general folklore. We also develop a quasi-dominance concept and show that it implies the extinction of all the quasi-dominated species. The quasi-dominance concept applies even if there is no species whose adults always grow faster than all the others. In addition, a notion of weak dominance is developed. We show with specific examples that weak dominance does not necessarily imply extinction of species. If all the growth functions are exponential functions, then weak dominance is equivalent to quasi-dominance.     

Extinct or still out there? Disentangling influences on extinction and rediscovery helps to clarify the fate of species on the edge

Each year, two or three species that had been considered to be extinct are rediscovered. Uncertainty about whether or not a species is extinct is common, because rare and highly threatened species are difficult to detect. Biological traits such as body size and range size are expected to be associated with extinction. However, these traits, together with the intensity of search effort, might influence the probability of detection and extinction differently. This makes statistical analysis of extinction and rediscovery challenging. Here, we use a variant of survival analysis known as cure rate modelling to differentiate factors that influence rediscovery from those that influence extinction. We analyse a global data set of 99 mammals that have been categorized as extinct or possibly extinct. We estimate the probability that each of these mammals is still extant and thus estimate the proportion of missing (presumed extinct) mammals that are incorrectly assigned extinction. We find that body mass and population density are predictors of extinction, and body mass and search effort predict rediscovery. In mammals, extinction rate increases with body mass and population density, and these traits act synergistically to greatly elevate extinction rate in large species that also occurred in formerly dense populations. However, when they remain extant, larger‐bodied missing species are rediscovered sooner than smaller species. Greater search effort increases the probability of rediscovery in larger species of missing mammals, but has a minimal effect on small species, which take longer to be rediscovered, if extant. By separating the effects of species characteristics on extinction and detection, and using models with the assumption that a proportion of missing species will never be rediscovered, our new approach provides estimates of extinction probability in species with few observation records and scant ecological information.     

Co-Extinctions of Tropical Butterflies and their Hostplants

The co‐extinction of interdependent species in relation to massive, long–term habitat disturbance has not been thoroughly investigated. Using logistic regression analyses, we examined the relationship between the loss of butterflies and their specific hostplants from the tropical island of Singapore and report the probable occurrence of their co–extinctions at the community level. Our simulation shows that the number of extinct butterfly species is expected to increase exponentially with that of extinct hostplants. The close association between butterflies and their hostplants suggests that the preservation of whole habitats is urgently needed if we are to avoid the possible cascading effects of species (co‐)extinctions.     

Body length of bony fishes was not a selective factor during the biggest mass extinction of all time

The Permo‐Triassic mass extinction devastated life on land and in the sea, but it is not clear why some species survived and others went extinct. One explanation is that lineage loss during mass extinctions is a random process in which luck determines which species survive. Alternatively, a phylogenetic signal in extinction may indicate a selection process operating on phenotypic traits. Large body size has often emerged as an extinction risk factor in studies of modern extinction risk, but this is not so commonly the case for mass extinctions in deep time. Here, we explore the evolution of non‐teleostean Actinopterygii (bony fishes) from the Devonian to the present day, and we concentrate on the Permo‐Triassic mass extinction. We apply a variety of time‐scaling metrics to date the phylogeny, and show that diversity peaked in the latest Permian and declined severely during the Early Triassic. In line with previous evidence, we find the phylogenetic signal of extinction increases across the mass extinction boundary: extinction of species in the earliest Triassic is more clustered across phylogeny compared to the more randomly distributed extinction signal in the late Permian. However, body length plays no role in differential survival or extinction of taxa across the boundary. In the case of fishes, size did not determine which species survived and which went extinct, but phylogenetic signal indicates that the mass extinction was not a random field of bullets.     

Stochastic Fluctuations Through Intrinsic Noise in Evolutionary Game Dynamics

A one-step (birth–death) process is used to investigate stochastic noise in an elementary two-phenotype evolutionary game model based on a payoff matrix. In this model, we assume that the population size is finite but not fixed and that all individuals have, in addition to the frequency-dependent fitness given by the evolutionary game, the same background fitness that decreases linearly in the total population size. Although this assumption guarantees population extinction is a globally attracting absorbing barrier of the Markov process, sample trajectories do not illustrate this result even for relatively small carrying capacities. Instead, the observed persistent transient behavior can be analyzed using the steady-state statistics (i.e., mean and variance) of a stochastic model for intrinsic noise that assumes the population does not go extinct. It is shown that there is good agreement between the theory of these statistics and the simulation results. Furthermore, the ESS of the evolutionary game can be used to predict the mean steady state.     

Convergence of a structured metapopulation model to Levins’s model

We consider a structured metapopulation model describing the dynamics of a single species, whose members are located in separate patches that are linked through migration according to a mean field rule. Our main aim is to find conditions under which its equilibrium distribution is reasonably approximated by that of the unstructured model of Levins (1969). We do this by showing that the (positive) equilibrium distribution converges, as the carrying capacity of each population goes to infinity together with appropriate scalings on the other parameters, to a bimodal distribution, consisting of a point mass at 0, together with a positive part which is closely approximated by a shifted Poisson centred near the carrying capacity. Under this limiting régime, we also give simpler approximate formulae for the equilibrium distribution. We conclude by showing how to compute persistence regions in parameter space for the exact model, and then illustrate all our results with numerical examples. Our proofs are based on Steins method.Supported in part by Schweizer Nationalfonds Projekt Nrs 20–61753.00 and 20–67909.02Supported in part by CNR of Italy under Grant n. 00.0142.ST74     

Habitat fragmentation and population extinction of birds

It has not been established that a major cause of extinction in birds or any other taxa is failure of metapopulation dynamics: the collapse of a network of ephemeral but discrete populations as movement between them becomes increasingly infrequent. The few data on who goes where and who mates with whom suggest that most species are structured as either a single large population or a small set of source populations and a larger set of sinks. The extinction of the latter is irrelevant to the persistence of the species. However, regional decline of a species in the face of habitat destruction and fragmentation can mimic a failure of metapopulation dynamics, because distinct aggregations of individuals will disappear much as they would if populations in an interacting network were eliminated one by one. Any species with highly restricted range is at great risk of extinction from spatially localized forces, such as cyclones or deforestation. Restricted range rather than inherent weakness is the main reason that so many island species have gone extinct or are endangered. Species with small populations in contact with much larger heterospecific ones with which they are interfertile are threatened with extinction by hybridization. Finally, the disappearance of a species from a site may be due to subtle habitat change, even if this observation seems superficially consistent with some general population theory, such as the dynamic equilibrium theory of island biogeography. Current theory is an inadequate substitute for intensive field studies as a means to address the conservation problems of individual species.     

一类具有年龄结构的麦蚜-瓢虫模型的全局分析

研究了一个具有年龄结构的麦蚜-瓢虫模型,其中麦蚜种群被分成两个年龄段,瓢虫种群被分成三个年龄段．应用定性理论可以证明:通过这两个种群的交互作用,可以导致麦蚜种群和瓢虫种群都灭绝或瓢虫种群灭绝,或这两个种群能以正平衡态或振动解的形式共存．通过计算,本文表明这个简单的系统可以产生非常复杂的动力学行为．在这种情形下,要想通过初始值来预测种群的数量是不可能的．应用MATLAB软件,本文展示了这个复杂的动力学行为．     

物种灭绝对不同时间尺度人类活动的响应机制研究

通过修改Tilman的多物种共存的经典模式中栖息地毁坏率（D）,使D随时间的推移呈线性增长情况下,本文模拟了百万年、万年和百年尺度人类活动对栖息地的破坏下,物种灭绝对栖息地毁坏的响应特征。结果表明,大时间尺度人类活动对栖息地毁坏导致物种的强弱关系发生变化,并且强物种先灭绝,而小时间尺度人类活动对栖息地破坏是弱物种先灭绝;在百万年和万年尺度上,物种对栖息地毁坏的响应是减幅振荡衰退直至灭绝,并且最强物种对栖息地的占有率（q）越大,振幅越大,而在百年尺度上,物种的演化几乎是直线衰退;在大时间尺度的栖息地毁坏情况下,q越大,则物种灭绝起始时间和所有物种灭绝的时间越长;而在较小的时间尺度的栖息地毁坏情况下,q越大,灭绝起始时间和所有物种最终灭绝的时间则越短。     

Biotic responses of canids to the terminal Pleistocene megafauna extinction

Trophic downgrading is a major concern for conservation scientists. The largest consumers in many ecosystems have become either rare or extirpated, leading to worry over the loss of their ecosystem function. However, trophic downgrading is not a uniquely modern phenomenon. The extinction of 34 genera of megafauna from North America ～13 000 yr ago must have led to widespread changes in terrestrial ecosystem function. Studies that have examined the event address impacts on vegetative structure, small mammal communities, nutrient cycling, and fire regimes. Relatively little attention has been paid to community changes at the top of the food chain. Here, we examine the response of carnivores in North America to the Pleistocene extinction. We employ fossil data to model the climatic niche of endemic canids, including the extinct dire wolf Canis dirus, over the last 20 000 yr. Quantifying the abiotic niche allows us to account for expected changes due to climate fluctuations over the Late Quaternary; deviations from expected responses likely reveal influences of competition and/or resource availability. We quantify the degree of niche conservatism and interspecific overlap to assess species and community responses among canids. We also include in our analyses a novel introduced predator, the domestic dog Canis lupus familiaris, which accompanied humans into the New World. We find that endemic canid species display low fidelity to their climatic niche through time, We find that survivors increasingly partition their climatic niche throughout the Holocene and, surprisingly, do not expand into niche space presumably vacated by the extinction of very large carnivores. These results suggest that loss of megaherbivores and competition with humans likely outweighed advantages conferred from the loss of very large predators. We also find that wolves and dogs decrease their niche overlap throughout the Holocene, suggesting a distinctive relationship between dogs and man.     

Habitat fragmentation,percolation theory and the conservation of a keystone species

Many species survive in specialized habitats. When these habitats are destroyed or fragmented the threat of extinction looms. In this paper, we use percolation theory to consider how an environment may fragment. We then develop a stochastic, spatially explicit, individual-based model to consider the effect of habitat fragmentation on a keystone species (the army ant Eciton burchelli) in a neo tropical rainforest. The results suggest that species may become extinct even in huge reserves before their habitat is fully fragmented; this has important implications for conservation. We show that sustainable forest-harvesting strategies may not be as successful as is currently thought. We also suggest that habitat corridors, once thought of as the saviour for fragmented environments, may have a detrimental effect on population persistence.     

物种灭绝对不同时间尺度栖息地毁坏响应的空间模拟

人类活动所引起的栖息地毁坏已成为当前物种多样性丧失的最主要的原因之一。空间显含模型相对于空间隐含模型来说,更加接近于现实,因此,通过元胞自动机,模拟了物种多样性对万年、千年、百年时间尺度人类活动所引起的栖息地毁坏的响应。研究结果表明：万年时间尺度上,物种是由强到弱的灭绝;而在千年时间尺度上,物种灭绝的序受集合种群结构的影响较大;在百年时间尺度上。物种由于栖息地毁坏过于剧烈和迅速,来不及作出响应。在栖息地完全毁坏时集体灭绝。因此,物种灭绝序不只是受竞争-侵占均衡机制的影响,还受不同时间尺度（不同速率）栖息地毁坏的影响。以及集合种群结构的影响。     

Extinction risk of a meta-population: aggregation approach

Aggregation of variables of a complex mathematical model with realistic structure gives a simplified model which is more suitable than the original one when the amount of data for parameter estimation is limited. Here we explore use of a formula derived for a single unstructured population (canonical model) in predicting the extinction time for a population living in multiple habitats. In particular we focus multiple populations each following logistic growth with demographic and environmental stochasticities, and examine how the mean extinction time depends on the migration and environmental correlation. When migration rate and/or environmental correlation are very large or very small, we may express the mean extinction time exactly using the formula with properly modified parameters. When parameters are of intermediate magnitude, we generate a Monte Carlo time series of the population size for the realistic structured model, estimate the "effective parameters" by fitting the time series to the canonical model, and then calculate the mean extinction time using the formula for a single population. The mean extinction time predicted by the formula was close to those obtained from direct computer simulation of structured models. We conclude that the formula for an unstructured single-population model has good approximation capability and can be applicable in estimating the extinction risk of the structured meta-population model for a limited data set.     

Do human activities raise species richness? Contrasting patterns in United States plants and fishes

In a given area, human activities usually cause the extinction of native species and the establishment of non‐native species. A key conservation issue is whether non‐native establishment tends to outpace native species extinction to produce a net gain in species richness. To determine this, empirical data must be accumulated at various scales. I show that, within the United States, the number of established non‐native plant species per state does tend to outpace the number of extinct and threatened species per state. The net gain in plant species is strongly and positively correlated with human population density. Continuation of this trend predicts substantial gains in net plant species richness for all states in the United States as human population grows. This contrasts with freshwater fishes, where most states show a net loss of species diversity as extinct and threatened species exceed established non‐native species. Changes in fish diversity do not correlate strongly with human population or non‐native species but are largely driven by the decline of native fish species.     

Modelling the role of social behavior in the persistence of the alpine marmot Marmota marmota

A general rule of thumb for biological conservation obtained from simple models of hypothetical species is that for populations with strong environmental noise moderate increases in habitat size or quality do not substantially reduce extinction risk. However, whether this rule also holds for real species with complex behavior, such as social species with breeding units and reproductive suppression, is uncertain. Here we present a population viability analysis of the alpine marmot Marmota marmota, which displays marked social behavior, i.e. it lives in social groups of up to twenty individuals. Our analysis is based on a long‐term field study carried out in the Bavarian Alps since 1982. During the first fifteen years of this study, 687 marmots were individually marked and the movements and fate of 98 dispersing marmots were recorded with radio‐telemetry. Thus, in contrast to most other viability analyses of spatially structured populations, good data about dispersal exist. A model was constructed which is individual‐based, spatially explicit at the scale of clusters of neighbouring territories, and spatially implicit at larger scales. The decisive aspect of marmot life history, winter mortality, is described by logistic regression where mortality is increased by age and the severity of winter, and decreased by the number of subdominant individuals present in a group. Model predictions of group size distribution are in good agreement with the results of the field study. The model shows that the effect of sociality on winter mortality is very effective in buffering environmental harshness and fluctuations. This underpins theoretical results stating that the appropriate measure of the strength of environmental noise is the ratio between the variance of population growth rate and the intrinsic rate of increase. The lessons from our study for biological conservation are that simple, unstructured models may not be sufficient to assess the viability of species with complex behavioral traits, and that even moderate increases in habitat capacity may substantially reduce extinction risk even if environmental fluctuations seem high.