Extinctions in competitive communities forced by coloured environmental variation

Understanding the relationships between environmental fluctuations, population dynamics and species interactions in natural communities is of vital theoretical and practical importance. This knowledge is essential in assessing extinction risks in communities that are, for example, pressed by changing environmental conditions and increasing exploitation. We developed a model of density dependent population renewal, in a Lotka–Volterra competitive community context, to explore the significance of interspecific interactions, demographic stochasticity, population growth rate and species abundance on extinction risk in populations under various autocorrelation (colour) regimes of environmental forcing. These factors were evaluated in two cases, where either a single species or the whole community was affected by the external forcing. Species' susceptibility to environmental noise with different autocorrelation structure depended markedly on population dynamics, species' position in the abundance hierarchy and how similarly community members responded to external forcing. We also found interactions between demographic stochasticity and environmental noise leading to a reversal in extinction probabilities from under- to overcompensatory dynamics. We compare our results with studies of single species populations and contrast possible mechanisms leading to extinctions. Our findings indicate that abundance rank, the form of population dynamics, and the colour of environmental variation interact in affecting species extinction risk. These interactions are further modified by interspecific interactions within competitive communities as the interactions filter and modulate the environmental noise.     

Biological hierarchies and the nature of extinction

Hierarchy theory recognises that ecological and evolutionary units occur in a nested and interconnected hierarchical system, with cascading effects occurring between hierarchical levels. Different biological disciplines have routinely come into conflict over the primacy of different forcing mechanisms behind evolutionary and ecological change. These disconnects arise partly from differences in perspective (with some researchers favouring ecological forcing mechanisms while others favour developmental/historical mechanisms), as well as differences in the temporal framework in which workers operate. In particular, long‐term palaeontological data often show that large‐scale (macro) patterns of evolution are predominantly dictated by shifts in the abiotic environment, while short‐term (micro) modern biological studies stress the importance of biotic interactions. We propose that thinking about ecological and evolutionary interactions in a hierarchical framework is a fruitful way to resolve these conflicts. Hierarchy theory suggests that changes occurring at lower hierarchical levels can have unexpected, complex effects at higher scales due to emergent interactions between simple systems. In this way, patterns occurring on short‐ and long‐term time scales are equally valid, as changes that are driven from lower levels will manifest in different forms at higher levels. We propose that the dual hierarchy framework fits well with our current understanding of evolutionary and ecological theory. Furthermore, we describe how this framework can be used to understand major extinction events better. Multi‐generational attritional loss of reproductive fitness (MALF) has recently been proposed as the primary mechanism behind extinction events, whereby extinction is explainable solely through processes that result in extirpation of populations through a shutdown of reproduction. While not necessarily explicit, the push to explain extinction through solely population‐level dynamics could be used to suggest that environmentally mediated patterns of extinction or slowed speciation across geological time are largely artefacts of poor preservation or a coarse temporal scale. We demonstrate how MALF fits into a hierarchical framework, showing that MALF can be a primary forcing mechanism at lower scales that still results in differential survivorship patterns at the species and clade level which vary depending upon the initial environmental forcing mechanism. Thus, even if MALF is the primary mechanism of extinction across all mass extinction events, the primary environmental cause of these events will still affect the system and result in differential responses. Therefore, patterns at both temporal scales are relevant.     

Plant population dynamics, pollinator foraging, and the selection of self-fertilization

Many flowering plants rely on pollinators, self-fertilization, or both for reproduction. We model the consequences of these features for plant population dynamics and mating system evolution. Our mating systems-based population dynamics model includes an Allee effect. This often leads to an extinction threshold, defined as a density below which population densities decrease. Reliance on generalist pollinators who primarily visit higher density plant species increases the extinction threshold, whereas autonomous modes of selfing decrease and can eliminate the threshold. Generalist pollinators visiting higher density plant species coupled with autonomous selfing may introduce an effect where populations decreasing in density below the extinction threshold may nonetheless persist through selfing. The extinction threshold and selfing at low density result in populations where individuals adopting a single reproductive strategy exhibit mating systems that depend on population density. The ecological and evolutionary analyses provide a mechanism where prior selfing evolves even though inbreeding depression is greater than one-half. Simultaneous consideration of ecological and evolutionary dynamics confirms unusual features (e.g., evolution into extinction or abrupt increases in population density) implicit in our separate consideration of ecological and evolutionary scenarios. Our analysis has consequences for understanding pollen limitation, reproductive assurance, and the evolution of mating systems.     

Environmental forcing, invasion and control of ecological and epidemiological systems

Destabilising a biological system through periodic or stochastic forcing can lead to significant changes in system behaviour. Forcing can bring about coexistence when previously there was exclusion; it can excite massive system response through resonance, it can offset the negative effect of apparent competition and it can change the conditions under which the system can be invaded. Our main focus is on the invasion properties of continuous time models under periodic forcing. We show that invasion is highly sensitive to the strength, period, phase, shape and configuration of the forcing components. This complexity can be of great advantage if some of the forcing components are anthropogenic in origin. They can be turned into instruments of control to achieve specific objectives in ecology and disease management, for example. Culling, vaccination and resource regulation are considered. A general analysis is presented, based on the leading Lyapunov exponent criterion for invasion. For unstructured invaders, a formula for this exponent can typically be written down from the model equations. Whether forcing hinders or encourages invasion depends on two factors: the covariances between invader parameters and resident populations and the shifts in average resident population levels brought about by the forcing. The invasion dynamics of a structured invader are much more complicated but an analytic solution can be obtained in quadratic approximation for moderate forcing strength. The general theory is illustrated by a range of models drawn from ecology and epidemiology. The relationship between periodic and stochastic forcing is also considered.     

Temporal autocorrelation in host density increases establishment success of parasitoids in an experimental system

Environmental variation is classically expected to affect negatively population growth and to increase extinction risk, and it has been identified as a major determinant of establishment failures in the field. Yet, recent theoretical investigations have shown that the structure of environmental variation and more precisely the presence of positive temporal autocorrelation might alter this prediction. This is particularly likely to affect the establishment dynamics of biological control agents in the field, as host–parasitoid interactions are expected to induce temporal autocorrelation in host abundance. In the case where parasitoid populations display overcompensatory dynamics, the presence of such positive temporal autocorrelation should increase their establishment success in a variable environment. We tested this prediction in laboratory microcosms by introducing parasitoids to hosts whose abundances were manipulated to simulate uncorrelated or positively autocorrelated variations in carrying capacity. We found that environmental variability decreased population size and increased parasitoid population variance, which is classically expected to extinction risk. However, although exposed to significant environmental variation, we found that parasitoid populations experiencing positive temporal autocorrelation in host abundance were more likely to persist than populations exposed to uncorrelated variation. These results confirm that environmental variation is a key determinant of extinction dynamics that can have counterintuitive effects depending on its autocorrelation structure.     

Dynamics of a physiologically structured population in a time-varying environment

Physiologically structured population models have become a valuable tool to model the dynamics of populations. In a stationary environment such models can exhibit equilibrium solutions as well as periodic solutions. However, for many organisms the environment is not stationary, but varies more or less regularly. In order to understand the interaction between an external environmental forcing and the internal dynamics in a population, we examine the response of a physiologically structured population model to a periodic variation in the food resource. We explore the addition of forcing in two cases: (A) where the population dynamics is in equilibrium in a stationary environment, and (B) where the population dynamics exhibits a periodic solution in a stationary environment. When forcing is applied in case A, the solutions are mainly periodic. In case B the forcing signal interacts with the oscillations of the unforced system, and both periodic and irregular (quasi-periodic or chaotic) solutions occur. In both cases the periodic solutions include one and multiple period cycles, and each cycle can have several reproduction pulses.     

Colonization and extinction dynamics of an annual plant metapopulation in an urban environment

The metapopulation framework considers that the spatiotemporal distribution of organisms results from a balance between the colonization and extinction of populations in a suitable and discrete habitat network. Recent spatially realistic metapopulation models have allowed patch dynamics to be investigated in natural populations but such models have rarely been applied to plants. Using a simple urban fragmented population system in which favourable habitat can be easily mapped, we studied patch dynamics in the annual plant Crepis sancta (Asteraceae). Using stochastic patch occupancy models (SPOMs) and multi‐year occupancy data we dissected extinction and colonization patterns in our system. Overall, our data were consistent with two distinct metapopulation scenarios. A metapopulation (sensu stricto) dynamic in which colonization occurs over a short distance and extinction is lowered by nearby occupied patches (rescue effect) was found in a set of patches close to the city centre, while a propagule rain model in which colonization occurs from a large external population was most consistent with data from other networks. Overall, the study highlights the importance of external seed sources in urban patch dynamics. Our analysis emphasizes the fact that plant distributions are governed not only by habitat properties but also by the intrinsic properties of colonization and dispersal of species. The metapopulation approach provides a valuable tool for understanding how colonization and extinction shape occupancy patterns in highly fragmented plant populations. Finally, this study points to the potential utility of more complex plant metapopulation models than traditionally used for analysing ecological and evolutionary processes in natural metapopulations.     

Spatial dynamics of specialist seed predators on synchronized and intermittent seed production of host plants

Masting, the synchronized and intermittent seed production by plant populations, provides highly variable food resources for specialist seed predators. Such a reproductive mode helps minimize seed losses through predator satiation and extinction of seed predator populations. The seed predators can buffer the resource variation through dispersal or extended diapause. We developed a spatially explicit resource-consumer model to understand the effect of masting on specialist seed predators. The masting dynamics were assumed to follow a resource-based model for plant reproduction, and the population dynamics of the predator were represented by a spatially extended Nicholson-Bailey model. The resultant model demonstrated that when host plants reproduce intermittently, seed predator populations go locally extinct, but global persistence of the predator is facilitated by dispersal or extended diapause. Global extinction of the predator resulted when the intermittent reproduction is highly synchronized among plants. An approximate invasion criterion for the predators showed that negative lag-1 autocorrelation in seeding reduces invasibility, and positive lag-1 cross-correlation enhances invasibility. Spatial synchronization in seeding at local scale caused by pollen coupling (or climate forcing) further prevented invasion of the predators. If the predators employed extended diapause, extremely high temporal variability in reproduction was required for plants to evade the predators.     

Scaling the extinction vortex: Body size as a predictor of population dynamics close to extinction events

1. Mutual reinforcement between abiotic and biotic factors can drive small populations into a catastrophic downward spiral to extinction—a process known as the “extinction vortex.” However, empirical studies investigating extinction dynamics in relation to species'' traits have been lacking.
2. We assembled a database of 35 vertebrate populations monitored to extirpation over a period of at least ten years, represented by 32 different species, including 25 birds, five mammals, and two reptiles. We supplemented these population time series with species‐specific mean adult body size to investigate whether this key intrinsic trait affects the dynamics of populations declining toward extinction.
3. We performed three analyses to quantify the effects of adult body size on three characteristics of population dynamics: time to extinction, population growth rate, and residual variability in population growth rate.
4. Our results provide support for the existence of extinction vortex dynamics in extirpated populations. We show that populations typically decline nonlinearly to extinction, while both the rate of population decline and variability in population growth rate increase as extinction is approached. Our results also suggest that smaller‐bodied species are particularly prone to the extinction vortex, with larger increases in rates of population decline and population growth rate variability when compared to larger‐bodied species.
5. Our results reaffirm and extend our understanding of extinction dynamics in real‐life extirpated populations. In particular, we suggest that smaller‐bodied species may be at greater risk of rapid collapse to extinction than larger‐bodied species, and thus, management of smaller‐bodied species should focus on maintaining higher population abundances as a priority.

     

Metapopulation dynamics and the quality of the matrix

In both strictly theoretical and more applied contexts it has been historically assumed that metapopulations exist within a featureless, uninhabitable matrix and that dynamics within the matrix are unimportant. In this article, we explore the range of theoretical consequences that result from relaxing this assumption. We show, with a variety of modeling techniques, that matrix quality can be extremely important in determining metapopulation dynamics. A higher-quality matrix generally buffers against extinction. However, in some situations, an increase in matrix quality can generate chaotic subpopulation dynamics, where stability had been the rule in a lower-quality matrix. Furthermore, subpopulations acting as source populations in a low-quality matrix may develop metapopulation dynamics as the quality of the matrix increases. By forcing metapopulation dynamics on a formerly heterogeneous (but stable within subpopulations) population, the probability of simultaneous extinction of all subpopulations actually increases. Thus, it cannot be automatically assumed that increasing matrix quality will lower the probability of global extinction of a population.     

Stochastic resonance in a single neuron model: theory and analog simulation.

Here, we consider a noisy, bistable, single neuron model in the presence of periodic external modulation. The modulation induces a correlated switching between states driven by the noise. The information flow through the system, from the modulation, or signal, to the output switching events, leads to a succession of strong peaks in the power spectrum. The signal-to-noise ratio (SNR) obtained from this power spectrum is a measure of the information content in the neuron response. With increasing noise intensity, the SNR passes through a maximum: an effect which has been called stochastic resonance, and which was first advanced as a possible explanation of the observed periodicity in the recurrences of the Earth's ice ages. We treat the problem within the framework of a recently developed approximate theory, valid in the limits of weak noise intensity, weak periodic forcing and low forcing frequency, for both additive and multiplicative noise. Moreover, we have constructed an analog simulator of the neuron which demonstrates the stochastic resonance effect, and with which we have measured the SNRs for comparison with the theoretical results. Our model should be of interest in situations where a single inherently noisy neuron is the receptor of a periodic signal, which is itself noisy, either from the network or from an external source.     

Dispersal and population structure of the rufous bettong,Aepyprymnus rufescens (Marsupialia: Potoroidae)

Abstract Many species of herbivorous mammals declined to extinction following European settlement of inland Australia. The rufous bettong, Aepyprymnus rufescens (a macropodoid marsupial), is ecologically similar to many of these species. We used analysis of microsatellite markers to determine dispersal patterns and mating system characteristics in a cluster of local populations of A. rufescens, with the aim of gaining a better understanding of regional population dynamics in such species. Particularly, we asked whether the rufous bettong showed source‐sink dynamics, as Morton (1990) hypothesized that many mammals may have been made vulnerable to extinction through such processes. We compared populations separated by distances of up to 12 km, and detected significant genetic differentiation among local populations (F_ST = 0.016). Females displayed greater genetic structuring than males, suggesting that females dispersed over shorter distances or less frequently than males. Geographic distance was weakly related to genetic distance between populations suggesting some gene flow at this scale, and paternity assignment indicated that dispersal can occur over distances of up to 6.5 km. Our study populations varied widely in density, but density did not explain the pattern of genetic differentiation observed. These findings of significant structure among populations, some influence of distance on genetic divergence and that density explains little of the divergence among populations, suggested that source‐sink dynamics did not play a large role among these populations. Variance in male mating success was low (maximum assigned paternity for an individual male was 14% of offspring). While data on multiple maternity were limited, roughly half of repeat maternity was assigned to the same male, suggesting that the mating system of the rufous bettong is not purely promiscuous.     

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。     

Spatially structured population dynamics in feral oilseed rape

We studied the population dynamics of feral oilseed rape (Brassica napus) for 10 years (1993-2002) in 3658 adjacent permanent 100 m quadrats in the verges of the M25 motorway around London, UK. The aim was to determine the relative importance of different factors affecting the observed temporal patterns of population dynamics and their spatial correlations. A wide range of population dynamics was observed (downward or upward trends, cycles, local extinctions and recolonizations), but overall the populations were not self-replacing (lambda < 1). Many quadrats remained unoccupied throughout the study period, but a few were occupied at high densities for all 10 years. Most quadrats showed transient oilseed rape populations, lasting 1-4 years. There were strong spatial patterns in mean population density, associated with soil conditions and the successional age of the plant community dominating the verge, and these large-scale spatial patterns were highly consistent from year to year. The importance of seed spilled from trucks in transit to the processing plant at Erith in Kent was confirmed: rape populations were significantly higher on the 'to Erith' verge than the 'from Erith' verge (overall mean 2.83-fold greater stem density). Quadrats in which lambda > 1 were much more frequent in the 'to Erith' verge, indicating that seed immigration can give the spurious impression of self-replacing population dynamics in time-series analysis. There was little evidence of a pervasive Moran effect, and climatic forcing did not produce widespread large-scale synchrony in population dynamics for the motorway as a whole; just 23% of quadrats had significant rank correlations with the mean time-series. There was, however, significant local spatial synchrony of population dynamics, apparently associated with soil disturbance and seed input. This study draws attention to the possibility that different processes may impose population synchrony at different scales. We hypothesize that synchrony in this system is driven by at least three processes: small-scale, local forcing caused by soil disturbance, intermediate-scale forcing as a result of seed input, and large-scale climatic forcing (e.g. winter rainfall) that affects the motorway as a whole.     

Incorporating the temporal autocorrelation of demographic rates into structured population models

Population dynamics are typically temporally autocorrelated: population sizes are positively or negatively correlated with past population sizes. Previous studies have found that positive temporal autocorrelation increases the risk of extinction due to ‘inertia’ that prolongs downward fluctuations in population size. However, temporal autocorrelation has not yet been analyzed at the level of life cycle transitions. We developed an R package, colorednoise, which creates stochastic matrix population projections with distinct temporal autocorrelation values for each matrix element. We used it to analyze long-term demographic data on 25 populations from the COMADRE and COMPADRE databases and simulate their stochastic dynamics. We found a broad range of temporal autocorrelation across species, populations and life cycle stages. The number of stage-classes in the matrix strongly affected the temporal autocorrelation of the growth rate. In the plant populations, reproduction transitions had more negative temporal autocorrelation than survival transitions, and matrices dominated by positive temporal autocorrelation had higher extinction risk, while in animal populations transition type was not associated with noise color. Our results indicate that temporal autocorrelation varies across life cycle transitions, even among populations of the same species. We present the colorednoise package for researchers to analyze the temporal autocorrelation of structured demographic rates.     

State‐dependent dynamics of cycles in red grouse abundance

Fluctuating populations are frequently demonstrated to co‐vary in abundance over space, but the dynamics of coupling between populations that gives rise to this synchrony are poorly understood. Synchrony may arise through coupling that is weak and continuous, but in populations that cycle with a characteristic period, synchrony can be maintained through stronger coupling that acts only intermittently. Here, we apply a discrete Markov model that describes the state of a population trajectory to be in one of four possible states. The Markov model reveals the nature of the coupling that gives rise to the weakly synchronous cycles of red grouse abundance. Using time‐series data from 287 populations across the species range in the UK, we show that grouse populations appear mostly uncoupled through time, but that approximately one year in six, “collective forcing events” occur, where populations in a region are forced into synchrony to a significantly greater degree than would be expected if their dynamics proceeded independently. In the absence of these events, synchrony between populations dissipates within ~3 yr. Smaller, low abundance populations tend to make the less probable phase shifts required to synchronize with nearby high abundance populations, suggesting that these low abundance populations are more susceptible to the perturbations responsible for phase shifts than larger populations.     

The stability of host-pathogen interactions of plant disease in relation to biological weed control

A theoretical analysis was conducted to investigate the dynamics of plant-pathogen interactions for biological weed control. Computer simulation showed that the dynamics of plant-pathogen interactions can be determined by the properties of the pathogen. Pathogens with high levels of virulence may exist in nature in low frequencies due to high extinction rates. Pathogens of this type are suitable for the mycoherbicide strategy. Pathogens with a low level of virulence are frequent and may coexist stably with their host. Good candidates for the classical strategy may be the pathogens with intermediate pathogenicity, which maintain a stable interaction and a high control efficiency. The probability of extinction of a pathogen increases when pathogenicity is greater than a critical value at the intermediate range. The regulation of plant populations through reducing host reproductivity and increasing host mortality has similar results.     

Evolutionary regime shifts in simulated ecosystems

Catastrophic regime shifts in ecosystems occur when the system is tipped into a new attractor state under some external forcing. Here we consider whether evolutionary adaptations within ecosystems can trigger similar transitions. We use an individual‐based, evolutionary model of interconnected ecosystems to analyze nonlinear changes in global state resulting from local adaptations. Transitions between periods of stability occur when new traits arise that allow exploitation of under‐utilized resources. Subsequent rapid growth of the population carrying the new trait causes abrupt environmental change that drives incumbent species extinct. We call these transitions ‘evolutionary regime shifts’. These internally generated perturbations can result in ecosystem collapse, followed by recovery to an alternate stable state, or occasionally system‐wide extinction. While these disruptions may have a negative impact on ecosystem productivity in individual simulation runs, mean results over many simulations show a trend for increasing ecosystem productivity and stability over time. Feedback between life and the abiotic environment in the model creates a ‘long‐tailed’ distribution of extinction sizes without any external trigger for large extinction events.     

Chaos and the (un)predictability of evolution in a changing environment

Among the factors that may reduce the predictability of evolution, chaos, characterized by a strong dependence on initial conditions, has received much less attention than randomness due to genetic drift or environmental stochasticity. It was recently shown that chaos in phenotypic evolution arises commonly under frequency‐dependent selection caused by competitive interactions mediated by many traits. This result has been used to argue that chaos should often make evolutionary dynamics unpredictable. However, populations also evolve largely in response to external changing environments, and such environmental forcing is likely to influence the outcome of evolution in systems prone to chaos. We investigate how a changing environment causing oscillations of an optimal phenotype interacts with the internal dynamics of an eco‐evolutionary system that would be chaotic in a constant environment. We show that strong environmental forcing can improve the predictability of evolution by reducing the probability of chaos arising, and by dampening the magnitude of chaotic oscillations. In contrast, weak forcing can increase the probability of chaos, but it also causes evolutionary trajectories to track the environment more closely. Overall, our results indicate that, although chaos may occur in evolution, it does not necessarily undermine its predictability.     

Density dependent dispersal decisions and the Allee effect

The decision to move between patches in the environment is among the most important life history choices an organism can make. I derive a new density dependent dispersal rule, and examine how dispersal decisions based on avoiding fitness loss associated with an Allee effect or competitive effects impact upon population dynamics in spatially structured populations with qualitatively different dynamics. I also investigate the effects of the number of patches in the system and a limit to the patch sampling time available to dispersers. Dispersing to avoid competitive pressures can destabilise otherwise stable population dynamics, and stabilise chaotic dynamics. Dispersing to avoid an Allee effect does not qualitatively change local population dynamics until eventually driving unstable populations to global extinction with a sufficiently high fitness threshold. A time limit for sampling can stabilise dynamics if dispersal is based on escaping the Allee effect, and rescue populations from global extinction. The results are sensitive to the number of patches available in the environment and suggest that dispersal to avoid an Allee effect will only arise under biologically plausible conditions, i.e. where there is a limit to the number of dispersal attempts that can be made between generations.