Periodic dynamics in a two-stage Allee effect model are driven by tension between stage equilibria

Single species difference population models can show complex dynamics such as periodicity and chaos under certain circumstances, but usually only when rates of intrinsic population growth or other life history parameter are unrealistically high. Single species models with Allee effects (positive density dependence at low density) have also been shown to exhibit complex dynamics when combined with over-compensatory density dependence or a narrow fertility window. Here we present a simple two-stage model with Allee effects which shows large amplitude periodic fluctuations for some initial conditions, without these requirements. Periodicity arises out of a tension between the critical equilibrium of each stage, i.e. when the initial population vector is such that the adult stage is above the critical value, while the juvenile stage is below the critical value. Within this area of parameter space, the range of initial conditions giving rise to periodic dynamics is driven mainly by adult mortality rates. Periodic dynamics become more important as adult mortality increases up to a certain point, after which periodic dynamics are replaced by extinction. This model has more realistic life history parameter values than most 'chaotic' models. Conditions for periodic dynamics might arise in some marine species which are exploited (high adult mortality) leading to recruitment limitation (low juvenile density) and might be an additional source of extinction risk.     

Durable Resistance to Crop Pathogens: An Epidemiological Framework to Predict Risk under Uncertainty

Increasing the durability of crop resistance to plant pathogens is one of the key goals of virulence management. Despite the recognition of the importance of demographic and environmental stochasticity on the dynamics of an epidemic, their effects on the evolution of the pathogen and durability of resistance has not received attention. We formulated a stochastic epidemiological model, based on the Kramer-Moyal expansion of the Master Equation, to investigate how random fluctuations affect the dynamics of an epidemic and how these effects feed through to the evolution of the pathogen and durability of resistance. We focused on two hypotheses: firstly, a previous deterministic model has suggested that the effect of cropping ratio (the proportion of land area occupied by the resistant crop) on the durability of crop resistance is negligible. Increasing the cropping ratio increases the area of uninfected host, but the resistance is more rapidly broken; these two effects counteract each other. We tested the hypothesis that similar counteracting effects would occur when we take account of demographic stochasticity, but found that the durability does depend on the cropping ratio. Secondly, we tested whether a superimposed external source of stochasticity (for example due to environmental variation or to intermittent fungicide application) interacts with the intrinsic demographic fluctuations and how such interaction affects the durability of resistance. We show that in the pathosystem considered here, in general large stochastic fluctuations in epidemics enhance extinction of the pathogen. This is more likely to occur at large cropping ratios and for particular frequencies of the periodic external perturbation (stochastic resonance). The results suggest possible disease control practises by exploiting the natural sources of stochasticity.     

Extinction risk under coloured environmental noise

Positively autocorrelated red environmental noise is characterized by a strong dependence of expected sample variance on sample length. This dependence has to be taken into account when assessing extinction risk under red and white uncorrelated environmental noise. To facilitate a comparison between red and white noise, their expected variances can be scaled to be equal, but only at a chosen time scale. We show with a simple one-dimensional population dynamics model that the different but equally reasonable choices of the time scale yield qualitatively different results on the dependence of extinction risk on the colour of environmental noise: extinction risk might increase as well as decrease when the temporal correlation of noise increases.     

Mussel disturbance dynamics: signatures of oceanographic forcing from local interactions

Local interactions, biotic and abiotic, can have a strong influence on the large-scale properties of ecosystems. However, ecological models often explore the influence of local biotic interactions where physical disturbance is included as a large-scale and imposed source of variability but is not allowed to interact with biotic processes at the local scale. In marine intertidal communities dominated by mussels, wave disturbances create gaps in the mussel bed that recover through a successional sequence. We present a lattice model of mussel disturbance dynamics that allows local interactions between wave disturbance and mussel recolonization, in which each cell of the lattice can be empty, occupied by a mussel bed element, or disturbed (which corresponds to a newly disturbed cell that has unstable edges). As in natural ecosystems, wave disturbance can also spread from disturbed to adjacent occupied cells, and recolonization can also spread from occupied to adjacent empty cells. We first validate the local rules from artificial gap experiments and from natural gap monitoring along the Oregon coast. We analyze the properties of the model system as a function of different oceanographic forcings of productivity and disturbance. We show that the mussel bed can go through phase transitions characterized by a large sensitivity of mussel cover and patterns to oceanographic forcings but also that criticality (scale invariance) is observed over wide ranges of parameters, which suggests self-organization. We also show that spatial patterns in the intertidal can provide a robust signature of local processes and can inform about oceanographic regimes. We do so by comparing the large-scale patterns of the simulation (scaling exponents) with field data, which suggest that some experimental sites are close to criticality. Our results suggest that regional patterns in disturbed populations can be explained by local biotic and abiotic processes submitted to oceanographic forcing.     

Simulating direct and indirect effects of climatic changes on rare perennial plant species in fragmented landscapes

Question: How does climate change influence plant species population dynamics, their time to extinction, and proportion of occupied habitats in a fragmented landscape? Location: Germany and Central European lowland. Methods: We apply a mechanistic general simulation model to test the response of plant functional types to direct and indirect effects of climate change. Three functional types were chosen to represent a set of well‐studied perennial plant species: Juncus atratus, Gentiana pneumonanthe and Primula veris. We link local population dynamics within a heterogeneous, fragmented landscape context. “Species spheres”, i.e. multi‐dimensional parameter ranges rather than single parameter realizations, based on field and literature data served as proxy for life stage transition parameters. Four climatic scenarios summarizing different cumulative weather effects on demographic rates and different local disturbance frequencies were run. The model predicts “time to extinction” (TE) and “proportion of occupied habitat” (POH) as regional indicators for species extinction risk. Results: TE decreased for all species when weather conditions worsened, and even more so when the frequency of local destructive events additionally increased. However, management towards fewer disturbance events could buffer the negative effect of climate to some extent. The magnitude of these responses varied with species type. POH declined with an increase in bad weather as well as with increasing disturbance frequency. The better the climatic conditions, the less severe were disturbances on population performance. Conclusions: The “species spheres” proved to be a valuable approach for predictive trends. As climate change usually also implies destructive events such as land‐use change, flooding or fire, our model on local and regional extinction risks can support conservation issues and management actions.     

Successful invasion of a food web in a chemostat

A food web in a chemostat is considered in which an arbitrary number of competitor populations compete for a single, essential, nonreproducing, growth-limiting substrate, and an arbitrary number of predator populations prey on some or all of the competitor populations. Although any number of predator populations may prey on the same competitor population, each predator population preys on only one competitor population. The dynamics of substrate uptake is modeled by Lotka-Volterra or Michaelis-Menten (Holling type I or II), but the dynamics of competitor uptake is restricted to Lotka-Volterra. Based on certain parameters, the model predicts the asymptotic survival or extinction of each of the different populations and suggests how competitor and/or predator populations could successfully invade the chemostat with or without causing a diverse ecosystem to crash. Similarly, it suggests how the elimination of certain populations could result in a more diverse or less diverse system.     

Estimating rates of local extinction and colonization in colonial species and an extension to the metapopulation and community levels

Coloniality has mainly been studied from an evolutionary perspective, but relatively few studies have developed methods for modelling colony dynamics. Changes in number of colonies over time provide a useful tool for predicting and evaluating the responses of colonial species to management and to environmental disturbance. Probabilistic Markov process models have been recently used to estimate colony site dynamics using presence–absence data when all colonies are detected in sampling efforts. Here, we define and develop two general approaches for the modelling and analysis of colony dynamics for sampling situations in which all colonies are, and are not, detected. For both approaches, we develop a general probabilistic model for the data and then constrain model parameters based on various hypotheses about colony dynamics. We use Akaike's Information Criterion (AIC) to assess the adequacy of the constrained models. The models are parameterised with conditional probabilities of local colony site extinction and colonization. Presence–absence data arising from Pollock's robust capture–recapture design provide the basis for obtaining unbiased estimates of extinction, colonization, and detection probabilities when not all colonies are detected. This second approach should be particularly useful in situations where detection probabilities are heterogeneous among colony sites. The general methodology is illustrated using presence–absence data on two species of herons. Estimates of the extinction and colonization rates showed interspecific differences and strong temporal and spatial variations. We were also able to test specific predictions about colony dynamics based on ideas about habitat change and metapopulation dynamics. We recommend estimators based on probabilistic modelling for future work on colony dynamics. We also believe that this methodological framework has wide application to problems in animal ecology concerning metapopulation and community dynamics.     

Taking the plunge: California Grunion embryos emerge rapidly with environmentally cued hatching

The process of hatching has been well studied in some model species of teleosts: the medaka Oryzias latipes, the mummichog Fundulus heteroclitus, and the zebrafish Danio rerio. These models are compared to the California Grunion, Leuresthes tenuis that has some unique features of reproduction related to tidal synchrony of spawning and environmentally cued hatching (ECH). During oviposition at spring tides, this marine teleost spawns out of water to bury its clutches on sandy beaches in the high intertidal zone. After embryos of L. tenuis reach hatching competence, hatching can be triggered at any time. Incubation above the water line inhibits hatching until ECH is triggered by rising tides during the following lunar phase, and hatching occurs within a few seconds. We review the embryo's response to environmental cues at hatching and the effects of the surrounding medium on the chorionase and chorion for this form of ECH. Leuresthes tenuis shares some similarities as well as some important differences with the model species. Comparison of hatching across teleostean taxa indicates great variability in stage at hatching and in duration of incubation that suggest hatching plasticity in response to environmental cues may be more widespread than currently appreciated.     

Dominance, biomass and extinction resistance determine the consequences of biodiversity loss for multiple coastal ecosystem processes

Key ecosystem processes such as carbon and nutrient cycling could be deteriorating as a result of biodiversity loss. However, currently we lack the ability to predict the consequences of realistic species loss on ecosystem processes. The aim of this study was to test whether species contributions to community biomass can be used as surrogate measures of their contribution to ecosystem processes. These were gross community productivity in a salt marsh plant assemblage and an intertidal macroalgae assemblage; community clearance of microalgae in sessile suspension feeding invertebrate assemblage; and nutrient uptake in an intertidal macroalgae assemblage. We conducted a series of biodiversity manipulations that represented realistic species extinction sequences in each of the three contrasting assemblages. Species were removed in a subtractive fashion so that biomass was allowed to vary with each species removal, and key ecosystem processes were measured at each stage of community disassembly. The functional contribution of species was directly proportional to their contribution to community biomass in a 1:1 ratio, a relationship that was consistent across three contrasting marine ecosystems and three ecosystem processes. This suggests that the biomass contributed by a species to an assemblage can be used to approximately predict the proportional decline in an ecosystem process when that species is lost. Such predictions represent "worst case scenarios" because, over time, extinction resilient species can offset the loss of biomass associated with the extinction of competitors. We also modelled a "best case scenario" that accounts for compensatory responses by the extant species with the highest per capita contribution to ecosystem processes. These worst and best case scenarios could be used to predict the minimum and maximum species required to sustain threshold values of ecosystem processes in the future.     

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

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

Intermediate disturbance and its relationship to within- and between-patch dynamics

The intermediate disturbance hypothesis has been the focus of considerable analysis in terrestrial and aquatic systems. This model predicts that species diversity will be highest at intermediate frequencies of disturbance. Despite numerous theoretical and empirical analyses, the utility of the model is still the subject of intense debate. Rather than developing restrictive time and space constraints on application, we suggest that the model may best be used as a generalizable framework for testing hypotheses in both aquatic and terrestrial systems, In addition, we believe that the model may be applied to both within- and between-patch scales. Finally, we propose an empirical model in which disturbance is an extinction causing event, and post-disturbance succession is modeled based on the dynamics of immigration and extinction. Such a model can incorporate a variety of patterns in species diversity in response to disturbance.     

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.     

Direct effects of physical stress can be counteracted by indirect benefits: oyster growth on a tidal elevation gradient

The paradigmatic gradient for intertidal marine organisms of increasing physical stress from low to high elevation has long served as the basis for using direct effects of duration of water coverage to predict many biological patterns. Accordingly, changes in potential feeding time may predict the direction and magnitude of differences between elevations in individual growth rates of sessile marine invertebrates. Oysters (triploid Crassostrea ariakensis) experimentally introduced at intertidal (MLW+0.05 m) and subtidal (MLW–0.25 m) elevations in racks provided a test of the ability to use duration of water coverage to predict changes in growth. During early-to-mid winter, a depression of 38–47% in shell growth of intertidal oysters matched the 36% reduction in available feeding time relative to subtidal oysters. In late winter as solar heating of exposed oysters increased, growth differences of 52–55% departed only slightly from the predicted 39%. In spring, however, duration of water coverage failed to predict even the correct direction of growth change with elevation as intertidal oysters grew 34% faster despite 39% less feeding time. Intense seasonal development of shell fouling by other suspension feeders like ascidians, mussels, and barnacles on subtidal (94% incidence) but not on aerially exposed intertidal (21–38% incidence) oysters may explain why duration of water cover failed to predict spring growth differences. Less intense fouling develops on intertidal oysters due to the physiological stress of aerial exposure on settlers, especially during higher temperatures and longer solar exposures of spring. Fouling by suspension feeders is known to reduce growth of the host through localized competition for food and added energetic costs. Thus, in springtime, indirect effects of aerial exposure providing a partial refuge from biological enemies overwhelmed direct effects of reduced duration of water coverage to reverse the expected pattern of slower intertidal growth of a marine invertebrate.     

种群统计随机性和环境随机性对种群绝灭的影响

影响种群绝灭的随机干扰可分为种群统计随机性、环境随机性和随机灾害三大类。在相对稳定的环境条件下和相对较短的时间内,以前两类随机干扰对种群绝灭的影响为生态学家关注的焦点。但是,由于自然种群动态及其影响因子的复杂特征,进一步深入研究随机干扰对种群绝灭的作用在理论上和实践上都必须发展新的技术手段。本文回顾了种群统计随机性与环境随机性的概念起源与发展,系统阐述了其分析方法。归纳了两类随机性在种群绝灭研究中的应用范围、作用方式和特点的异同和区别方法。各类随机作用与种群动态之间关系的理论研究与对种群绝灭机理的实践研究紧密相关。根据理论模型模拟和自然种群实际分析两方面的研究现状,作者提出了进一步深入研究随机作用与种群非线性动态方法的策略。指出了随机干扰影响种群绝灭过程的研究的方向：更多的研究将从单纯的定性分析随机干扰对种群动力学简单性质的作用,转向结合特定的种群非线性动态特征和各类随机力作用特点具体分析绝灭极端动态的成因,以期做出精确的预测。     

Stochastic density dependence in population size of a benthic clonal invertebrate: the regulating role of fission

The influence of environmental variation on the demography of clonal organisms has been poorly studied. I utilise a matrix model of the population dynamics of the intertidal zoanthid Palythoa caesia to examine how density dependence and temporal variation in demographic rates interact in regulating population size. The model produces realistic simulations of population size, with erratic fluctuations between soft lower and upper boundaries of approximately 55 and 90% cover. Cover never exceeds the maximum possible of 100%, and the population never goes to extinction. A sensitivity analysis indicates that the model’s behaviour is driven by density dependence in the fission of large colonies to produce intermediate sized colonies. Importantly, there is no density-dependent mortality in the model, and density dependence in recruitment, while present, is unimportant. Thus it appears that the main demographic processes which are considered to regulate population size in aclonal organisms may not be important for clonal species. Received: 18 August 1999 / Accepted: 29 October 1999     

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.     

ADAPTATION AND MALADAPTATION IN SELFING AND OUTCROSSING SPECIES: NEW MUTATIONS VERSUS STANDING VARIATION

Evolution of selfing from outcrossing recurrently occurred in many lineages, especially in flowering plants. Evolution of selfing induces dramatic changes in the population genetics functioning but its consequences on the dynamics of adaptation have been overlooked. We studied a simple one‐locus model of adaptation where a population experiences an environmental change at a given time. We first determined the effect of the mating system on the genetic bases and the speed of adaptation, focusing on the dominance of beneficial mutations and the respective part of standing variation and new mutations. Then, we assumed that the environmental change is associated with population decline to determine the effect of the mating system on the probability of population extinction. Extending previous results, we found that adaptation is more efficient and extinction less likely in outcrossers when beneficial mutations are dominant and codominant and when standing variation plays a significant role in adaptation. However, given adaptation does occur, it is usually more rapid in selfers than in outcrossers. Our results bear implications for the evolution of the selfing syndrome, the dynamics of the domestication process, and the dead‐end hypothesis that posits that selfing lineages are doomed to extinction on the long run.     

When Did Carcharocles megalodon Become Extinct? A New Analysis of the Fossil Record

Carcharocles megalodon (“Megalodon”) is the largest shark that ever lived. Based on its distribution, dental morphology, and associated fauna, it has been suggested that this species was a cosmopolitan apex predator that fed on marine mammals from the middle Miocene to the Pliocene (15.9–2.6 Ma). Prevailing theory suggests that the extinction of apex predators affects ecosystem dynamics. Accordingly, knowing the time of extinction of C. megalodon is a fundamental step towards understanding the effects of such an event in ancient communities. However, the time of extinction of this important species has never been quantitatively assessed. Here, we synthesize the most recent records of C. megalodon from the literature and scientific collections and infer the date of its extinction by making a novel use of the Optimal Linear Estimation (OLE) model. Our results suggest that C. megalodon went extinct around 2.6 Ma. Furthermore, when contrasting our results with known ecological and macroevolutionary trends in marine mammals, it became evident that the modern composition and function of modern gigantic filter-feeding whales was established after the extinction of C. megalodon. Consequently, the study of the time of extinction of C. megalodon provides the basis to improve our understanding of the responses of marine species to the removal of apex predators, presenting a deep-time perspective for the conservation of modern ecosystems.     

Recurrent habitat disturbance and species diversity in a multiple-competitive species system

To address how species interactions, dispersal and environmental disturbances interplay to affect the spatial distribution and diversity of species, we present a compartment model in which multiple species undergo competitive interaction of Lotka-Volterra type in a patchy environment arranged in a square lattice. Dispersal of species occurs between adjacent patches. Disturbances are periodically imposed on a central part of the environment in a belt-like block or an island-like block of various sizes where each species is killed for a certain time interval and then allowed to recover for the rest of a disturbance cycle. We deal with a case in which the local population dynamics within each patch is analytically determinable and has multiple locally stable equilibrium states in the absence of environmental disturbance. We further assume a trade-off between the reproductive rate of species and its dispersal ability. With these settings, we numerically examine how the spatio-temporal distributions of species are affected by changes in the pattern, size and duration of disturbances. The results demonstrate that: (1) in the undisturbed area, environmental disturbances could generate spatially segregated distributions of species; (2) in the disturbed area, species with higher dispersal abilities quickly invade and preferentially recover their population during the post-disturbance period, being temporarily relieved of competition from other species. These mechanisms collectively lead to increased species diversity in the whole habitat, functioning best when both the size and duration of disturbances are intermediate. In particular, the belt-like disturbance is more effective than the island-like disturbance in sustaining spatial heterogeneity for a wider range of duration of disturbance.     

34 Pieces of a puzzle: biogeography of southeast farallon Island,California

Rocky intertidal communities in cold waters on open shores tend to have a stable, predictable makeup worldwide. The structure of the environment, the morphology and life history of species, the economics of species behavior and the dynamics of population changes all contribute to the distribution of species in a given habitat. South East Farallon Island, in the Pacific Ocean off the northern California coast, hosts an intertidal community typical in many ways of other rocky intertidal communities. However, two orders of marine algae one might expect to be there, the Fucales and Laminariales, are unexpectedly uncommon on this island. In this paper some of the possible environmental, morphological and life history factors contributing to and restricting the distribution of marine algae in the intertidal zone on South East Farallon Island are considered.