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。     

A machine learning approach to investigate the reasons behind species extinction

Species extinction is one of the most important phenomena in conservation biology. Many factors are involved in the disappearance of species, including stochastic population fluctuations, habitat change, resource depletion, and inbreeding. Due to the complexity of the interactions between these various factors and the lengthy time period required to make empirical observations, studying the phenomenon of species extinction can prove to be very difficult in nature. On the other hand, an investigation of the various features involved in species extinction using individual-based simulation modeling and machine learning techniques can be accomplished in a reasonably short period of time. Thus, the aim of this paper is to investigate multiple factors involved in species extinction using computer simulation modeling. We apply several machine learning techniques to the data generated by EcoSim, a predator–prey ecosystem simulation, in order to select the most prominent features involved in species extinction, along with extracting rules that outline conditions that have the potential to be used for predicting extinction. In particular, we used five feature selection methods resulting in the selection of 25 features followed by a reduction of these to 14 features using correlation analysis. Each of the remaining features was placed in one of three broad categories, viz., genetic, environmental, or demographic. The experimental results suggest that factors such as population fluctuation, reproductive age, and genetic distance are important in the occurrence of species extinction in EcoSim, similar to what is observed in nature. We argue that the study of the behavior of species through Individual-Based Modeling has the potential to give rise to new insights into the central factors involved in extinction for real ecosystems. This approach has the potential to help with the detection of early signals of species extinction that could in turn lead to conservation policies to help prevent extinction.     

Power spectra of extinction in the fossil record

Recent Fourier analyses of fossil extinction data have indicated that the power spectrum of extinction during the Phanerozoic may take the form of 1/f noise, a result which, it has been suggested, could be indicative of the presence of `critical dynamics'' in the processes giving rise to extinction. In this paper we examine extinction power spectra in some detail, using family-level data from two widely available compilations. We find that although the average form of the power spectrum roughly obeys the 1/f law, the spectrum can be represented more accurately by dividing it into two regimes: a low-frequency one which is well fit by an exponential, and a high-frequency one in which it follows a power law with a 1/f² form. We give explanations for the occurrence of each of these behaviours and for the position of the crossover between them.     

Extinction and quasi-stationarity in the Verhulst logistic model.

We formulate and analyse a stochastic version of the Verhulst deterministic model for density-dependent growth of a single population. Three parameter regions with qualitatively different behaviours are identified. Explicit approximations of the quasi-stationary distribution and of the expected time to extinction are presented in each of these regions. The quasi-stationary distribution is approximately normal, and the time to extinction is long, in one of these regions. Another region has a short time to extinction and a quasi-stationary distribution that is approximately truncated geometric. A third region is a transition region between these two. Here the time to extinction is moderately long and the quasi-stationary distribution has a more complicated behaviour. Numerical illustrations are given.     

Partitioning the effects of deterministic and stochastic processes on species extinction risk

Species populations are subjected to deterministic and stochastic processes, both of which contribute to their risk of extinction. However, current understanding of the relative contributions of these processes to species extinction risk is far from complete. Here, we address this knowledge gap by analyzing a suite of models representing species populations with negative intrinsic growth rates, to partition extinction risk according to deterministic processes and two broad classes of stochastic processes – demographic and environmental variance. Demographic variance refers to random variations in population abundance arising from random sampling of events given a particular set of intrinsic demographic rates, whereas environmental variance refers to random abundance variations arising from random changes in intrinsic demographic rates over time. When the intrinsic growth rate was not close to zero, we found that deterministic growth was the main driver of mean time to extinction, even when population size was small. This contradicts the intuition that demographic variance is always an important determinant of extinction risk for small populations. In contrast, when the intrinsic growth rate was close to zero, stochastic processes exerted substantial negative effects on the mean time to extinction. Demographic variance had a greater effect than environmental variance at low abundances, with the reverse occurring at higher abundances. In addition, we found that the combined effects of demographic and environmental variance were often substantially lower than the sum of their effects in isolation from each other. This sub-additivity indicates redundancy in the way the two stochastic processes increase extinction risk, and probably arises because both processes ultimately increase extinction risk by boosting variation in abundance over time.     

Predictors of light-limited growth and competition of phytoplankton in a well-mixed water column

Based on a model of light limited growth, Huisman and Weissing found that in a well mixed water column with constant light supply (energy reaching the water surface), equilibrium growth and competition of phytoplankton for light can be characterised by a critical light intensity at the base of the column (I*out). The present study attempts to give a further insight into this model. We first analyse the dependence of the critical light intensity on four parameters: initial slope of the photosynthesis-intensity (p-I) curve, maximal photosynthetic rate, the light-saturated parameter Ikand specific carbon loss rate. Increases in the first two parameters tend to reduce the critical light intensity and increases in the last two tend to increase the critical light intensity. Then we analyse the performance of a model under variable light supply with a time-scale of 1 day (24 hr). Within this time-scale, the critical light intensity changes with time. However, the equilibrium growth and the outcome of competition for light can be adequately characterised by critical light extinction defined as the upper limit of total light extinction due to both biomass and non-living matter in the water column. Under constant light supply, a critical light intensity uniquely corresponds to a critical light extinction. Therefore, critical light extinction can be utilised to predict the equilibrium growth and the outcome of competition under both constant and variable light supply. By changing the maximal light supply at noon, seasonal succession of species composition of communities is investigated. The possible effect of two typical photoresponses, photoadaptation and photoinhibition, on growth and competiton are discussed. Copyright 1999 Academic Press.     

Dynamics of escape mutants

We use multi-type Galton-Watson branching processes to model the evolution of populations that, due to a small reproductive ratio of the individuals, are doomed to extinction. Yet, mutations occurring during the reproduction process, may lead to the appearance of new types of individuals that are able to escape extinction. We provide examples of such populations in medical, biological and environmental contexts and give results on (i) the probability of escape/extinction, (ii) the distribution of the waiting time to produce the first individual whose lineage does not get extinct and (iii) the distribution of the time it takes for the number of mutants to reach a high level. Special attention is dedicated to the case where the probability of mutation is very small and approximations for (i)-(iii) are derived.     

On the time to extinction for a two-type version of Bartlett's epidemic model

We are interested in how the addition of type heterogeneities affects the long time behaviour of models for endemic diseases. We do this by analysing a two-type version of a model introduced by Bartlett under the restriction of proportionate mixing. This model is used to describe diseases for which individuals switch states according to susceptible-->infectious-->recovered and immune, where the immunity is life-long. We describe an approximation of the distribution of the time to extinction given that the process is started in the quasi-stationary distribution, and we analyse how the variance and the coefficient of variation of the number of infectious individuals depends on the degree of heterogeneity between the two types of individuals. These are then used to derive an approximation of the time to extinction. From this approximation we conclude that if we increase the difference in infectivity between the two types the expected time to extinction decreases, and if we instead increase the difference in susceptibility the effect on the expected time to extinction depends on which part of the parameter space we are in, and we can also obtain non-monotonic behaviour. These results are supported by simulations.     

Single-species models of the Allee effect: extinction boundaries,sex ratios and mate encounters

We critically review and classify models of single-species population dynamics subject to the demographic Allee effect with emphasis on non-spatial, deterministic approach. Inclusion of spatial movement and stochastic phenomena does not substantially change the behaviour; stochasticity only "blurs" step-like character of the Allee effect into a sigmoidal form. The outcome of all non-spatial, deterministic models is either unconditional extinction, extinction-survival scenario (ES), or unconditional survival. Three major model classes are recognized: (1) one-dimensional heuristic models, (2) one-dimensional models with mating probability and fixed sex ratio, and (3) two-sex models with variable adult sex ratio. Each class is characterized by the shape of extinction boundary which separates extinction from survival in the ES scenario. The latter two classes may give better predictions of extinction thresholds than heuristic models but require specific information and are data intensive. In one-dimensional models with fixed sex ratio, population cannot survive if density/number of males decreases below some threshold while there is no such restriction on females. Individual-based models seem to be most capable of explaining mechanisms leading to the Allee effect.     

The effect of incubation time distribution on the extinction characteristics of a rabies epizootic

The continuous model of Anderson et al. (1981), Nature 289, 765–771, is successful in describing certain characteristics of rabies epizootics, in particular, the secondary recurrences which follow the initial outbreak; however, it also predicts the occurrence of exponentially small minima in the infected population, which would realistically imply extinction of the virus. Here we show that inclusion of a more realistic distribution of incubation times in the model can explain why extinction will not occur, and we give explicit parametric estimates for the minimum infected fox density which will occur in the model, in terms of the incubation time distribution.     

Characterization of the interaction of ophiobolin A and calmodulin

1. The fungal toxin ophiobolin A reacts with the epsilon-amino group of lysine to give a conjugated enamine produce with lambda max at 272 nm and a molar extinction of 19,200 per M/cm. 2. Bovine brain calmodulin reacts with ophiobolin A to give a lambda max at 272 nm. 3. One mol of calmodulin reacts with two moles of ophiobolin A. Reaction of 1 mol of ophiobolin A inactivates 1 mol of calmodulin. 4. Ophiobolin A-treated calmodulin is resistant to tryptic cleavage at lysine 77. 5. Ophiobolin A also inhibits Dictyostelium calmodulin which has glutamine instead of lysine at residue 77.     

The return of the Red Queen, or the law of the growth in the mean duration of the existence of genera during evolution

Phanerozoic marine genera apparently do not become less extinction-prone with age. Higher extinction probability in "young" cohorts of genera is better explained by initially different levels of extinction-tolerance of genera in the cohort. This fact agrees with one of the two basic statements of the "Red Queen" hypothesis (Van Valen, 1973). In the second statement (the idea that the increase in fitness lowers extinction probability) the term "fitness" should be changed to "adaptability". The increase of extinction-tolerance, that can be interpreted as the increase of adaptability to unpredictable changes of environment, is found in succession of "generations" of genera that replace one another through time. This increase reveals itself, firstly, in the growth of mean duration of genera, as well as in the decrease of extinction/origination rates, gradual accumulation of long-lived genera and origination of genera with higher duration. The increase of adaptability may be caused by selective extinction of stenotopic, ecologically specialized forms; Cope's law; evolution of ecosystems that involves development of more effective mechanisms of sustaining homeostasis which may stimulate the recovery of a genus after partial extinction.     

Demographic stochasticity, allee effects, and extinction: the influence of mating system and sex ratio

Demographic stochasticity has a substantial influence on the growth of small populations and consequently on their extinction risk. Mating system is one of several population characteristics that may affect this. We use a stochastic pair-formation model to investigate the combined effects of mating system, sex ratio, and population size on demographic stochasticity and thus on extinction risk. Our model is designed to accommodate a continuous range of mating systems and sex ratios as well as several levels of stochasticity. We show that it is not mating system alone but combinations of mating system and sex ratio that are important in shaping the stochastic dynamics of populations. Specifically, polygyny has the potential to give a high demographic variance and to lower the stochastic population growth rate substantially, thus also shortening the time to extinction, but the outcome is highly dependent on the sex ratio. In addition, population size is shown to be important. We find a stochastic Allee effect that is amplified by polygyny. Our results demonstrate that both mating system and sex ratio must be considered in conservation planning and that appreciating the role of stochasticity is key to understanding their effects.     

Measurement error and estimates of population extinction risk

It is common to estimate the extinction probability for a vulnerable population using methods that are based on the mean and variance of the long‐term population growth rate. The numerical values of these two parameters are estimated from time series of population censuses. However, the proportion of a population that is registered at each census is typically not constant but will vary among years because of stochastic factors such as weather conditions at the time of sampling. Here, we analyse how such sampling errors influence estimates of extinction risk and find sampling errors to produce two opposite effects. Measurement errors lead to an exaggerated overall variance, but also introduce negative autocorrelations in the time series (which means that estimates of annual growth rates tend to alternate in size). If time series data are treated properly these two effects exactly counter balance. We advocate routinely incorporating a measure of among year correlations in estimating population extinction risk.     

Invasibility and stochastic boundedness in monotonic competition models

We give necessary and sufficient conditions for stochastically bounded coexistence in a class of models for two species competing in a randomly varying environment. Coexistence is implied by mutual invasibility, as conjectured by Turelli. In the absence of invasibility, a species converges to extinction with large probability if its initial population is small, and extinction of one species must occur with probability one regardless of the initial population sizes. These results are applied to a general symmetric competition model to find conditions under which environmental fluctuations imply coexistence or competitive exclusion.     

Can a More Variable Species Win Interspecific Competition?

An individual-based approach is used to describe population dynamics. Two kinds of models have been constructed with different distributions illustrating individual variability. In both models, the growth rate of an individual and its final body weight at the end of the growth period, which determines the number of offspring, are functions of the amount of resources assimilated by an individual. In the model with a symmetric distribution, the half saturation constant in the Michaelis–Menten function describing the relationship between the growth of individuals and the amount of resources has a normal distribution. In the model with an asymmetric distribution, resources are not equally partitioned among individuals. The individual who acquired more resources in the past, will acquire more resources in the future. A single population comprising identical individuals has a very short extinction time. If individuals differ in the amount of food assimilated, this time significantly increases irrespectively of the type of model describing population dynamics. Individuals of two populations of competing species use common resources. For larger differences in individual variability, the more variable species will have a longer extinction time and will exclude less variable species. Both populations can also coexist when their variabilities are equal or even when they are slightly different, in the latter case under the condition of high variability of both species. These conclusions have a deterministic nature in the case of the model with the asymmetric distribution—repeated simulations give the same results. In the case of the model with the symmetric distribution, these conclusions are of a statistical nature—if we repeat the simulation many times, then the more variable species will have a longer extinction time more frequently, but some results will happen (although less often) when the less variable species has a longer extinction time. Additionally, in the model with the asymmetric distribution, the result of competition will depend on the way of the introduction of variability into the model. If the higher variability is due to an increase in the proportion of individuals with a low assimilation of resources, it can produce a longer extinction time of the less variable species.

     

Resurgence: the role of extinction

Three hens were trained to door push and three were trained to head bob using food as the reinforcer (Behaviour 1 training). A period of extinction followed. Each hen was then trained to perform the other behaviour (Behaviour 2) and this was followed by seven sessions of extinction. This whole sequence was repeated six times, with two sessions of extinction following Behaviour 1 training. Over the repeated extinction conditions there were decreases in responding early in extinction, for both Behaviours 1 and 2, compared with the first condition. Behaviour in the later extinction sessions could be studied for Behaviour 2 only, and it was found to increase relative to the first condition, over repeated extinction conditions. The occurrence of Behaviour 1 during the extinction following the training of Behaviour 2, that is the resurgence of Behaviour 1, both over the whole of and in the first session of each extinction phase, was variable and tended to increase over these six conditions. Thus it is possible to study resurgence using a within-subject design but the effect of repeated extinction conditions needs to be considered. The period of extinction immediately following Behaviour 1 training was then increased to nine sessions for two replications of the whole sequence. This was followed by two repeats of the sequence with no sessions of this extinction and then by another repeat, with nine sessions of this extinction phase. Over these five conditions the total resurgence of Behaviour 1 was generally greater when there were no sessions of extinction immediately following Behaviour 1 training, than when there were nine sessions. This result was more marked for the resurgence of Behaviour 1 in the first session of the extinction of Behaviour 2. Thus, these data support the hypothesis that the resurgence of Behaviour 1 is the result of the prevention of the extinction of Behaviour 1 by training Behaviour 2. At a similar point in extinction, the number of occurrences of Behaviour 1 in its own extinction was not significantly different from the number of occurrences of Behaviour 1 during the extinction of Behaviour 2. This fails to support the hypothesis that resurgence is induced by the extinction of Behaviour 2.     

Rules of thumb for conservation of metapopulations based on a stochastic winking-patch model

From a theoretical viewpoint, nature management basically has two options to prolong metapopulation persistence: decreasing local extinction probabilities and increasing colonization probabilities. This article focuses on those options with a stochastic, single-species metapopulation model. We found that for most combinations of local extinction probabilities and colonization probabilities, decreasing the former increases metapopulation extinction time more than does increasing the latter by the same amount. Only for relatively low colonization probabilities is an effort to increase these probabilities more beneficial, but even then, decreasing extinction probabilities does not seem much less effective. Furthermore, we found the following rules of thumb. First, if one focuses on extinction, one should preferably decrease the lowest local extinction probability. Only if the extinction probabilities are (almost) equal should one prioritize decreases in the local extinction probability of the patch with the best direct connections to and from other patches. Second, if one focuses on colonization, one should preferably increase the colonization probability between the patches with the lowest local extinction probability. Only if the local extinction probabilities are (almost) equal should one instead prioritize increases in the highest colonization probability (unless extinction probabilities and colonization probabilities are very low). The rules of thumb have an important common denominator: the local extinction process has a greater bearing on metapopulation extinction time than colonization.     

Extinction times and size of the surviving species in a two-species competition process

We investigate a stochastic model for the competition between two species. Based on percentiles of the maximum number of individuals in the ecosystem, we present an approximating model for which the extinction time can be thought of as a phase-type random variable. We determine formulae for the probabilities of extinction and the moments of the extinction time. We discuss the use of several quasi-stationary assumptions. We include a comparative study between existing asymptotic results, results obtained from a simulation of the process, and our solution.     

Effects of inter-trial interval length on food-hoarding partial reinforcement of running behaviour in the golden hamster

Food-hoarding provides an adequate motivation in sated hamsters for the acquisition of a two-way running response. This learning was studied using a discrete-trial procedure, in continuous (CR) and partial reinforcement (PR) conditions, with two different inter-trial interval (ITI) lengths. The dependent variables were: the time spent by Ss in the goal section of the runway, and the number of their runs during extinction.The PR training had two effects on goal times: a slow decrease in acquisition on non-reinforced trials, and then a stabilization at this level during the extinction phase, as contrasted with the sudden increase found in CR-trained Ss when they were switched from acquisition to extinction conditions. However, the PR effects on number of runs depended upon ITI length: resistance to extinction of PR-trained Ss was superior to that of CR-trained Ss with spaced, but not with massed, trials. In the latter case, CR-trained Ss persisted as much as did PR-trained Ss. An hypothesis is offered, along the lines of the Frustration theory.