Large-body impact and extinction in the Phanerozoic

The kill curve for Phanerozoic marine species is used to investigate large-body impact as a cause of species extinction. Current estimates of Phanerozoic impact rates are combined with the kill curve to produce an impact-kill curve, which predicts extinction levels from crater diameter, on the working assumption that impacts are responsible for all "pulsed" extinctions. By definition, pulsed extinction includes the approximately 60% of Phanerozoic extinctions that occurred in short-lived events having extinction rates greater than 5%. The resulting impact-kill curve is credible, thus justifying more thorough testing of the impact-extinction hypothesis. Such testing is possible but requires an exhaustive analysis of radiometric dating of Phanerozoic impact events.     

Metapopulation extinction risk: Dispersal’s duplicity

Metapopulation extinction risk is the probability that all local populations are simultaneously extinct during a fixed time frame. Dispersal may reduce a metapopulation’s extinction risk by raising its average per-capita growth rate. By contrast, dispersal may raise a metapopulation’s extinction risk by reducing its average population density. Which effect prevails is controlled by habitat fragmentation. Dispersal in mildly fragmented habitat reduces a metapopulation’s extinction risk by raising its average per-capita growth rate without causing any appreciable drop in its average population density. By contrast, dispersal in severely fragmented habitat raises a metapopulation’s extinction risk because the rise in its average per-capita growth rate is more than offset by the decline in its average population density. The metapopulation model used here shows several other interesting phenomena. Dispersal in sufficiently fragmented habitat reduces a metapopulation’s extinction risk to that of a constant environment. Dispersal between habitat fragments reduces a metapopulation’s extinction risk insofar as local environments are asynchronous. Grouped dispersal raises the effective habitat fragmentation level. Dispersal search barriers raise metapopulation extinction risk. Nonuniform dispersal may reduce the effective fraction of suitable habitat fragments below the extinction threshold. Nonuniform dispersal may make demographic stochasticity a more potent metapopulation extinction force than environmental stochasticity.     

How is extinction risk related to population-size variability over time? A family of models for species with repeated extinction and immigration

It is well known that for an isolated population, the probability of extinction is positively related to population size variation: more variation is associated with more extinction. What, then, is the relation of extinction to population size variation for a population embedded in a metapopulation and subjected to repeated extinction and recolonization? In this case, the extinction risk can be measured by the extinction rate, the frequency at which local extinction occurs. Using several population dynamics models with immigration, we find, in general, a negative correlation between extinction and variation. More precisely, with increasing length of the time series, an initially negative regression coefficient first becomes more negative, then becomes less negative, and eventually attains positive values before decreasing again to 0. This pattern holds under substantial variation in values of parameters representing species and environmental properties. It is also rather robust to census interval length and the fraction of missed individuals but fails to hold for high thresholds (population size values below which extinction is deemed to occur) when quasi extinction rather than true extinction is represented. The few departures from the initial negative correlation correspond to populations at risk: low growth rate or frequent catastrophes.     

Non-linear biological responses to environmental noise affect population extinction risk

Non-linearities are commonly observed in the responses of organisms to environment. They potentially modify the qualitative and quantitative properties of population dynamics. We studied how non-linear responses to environment, or "noise filters", influence population variability and extinction risk by introducing coloured noise to the growth rate in the Hassell single-species model. The consequences of noise filtering were analysed by comparing the model dynamics with linearly filtered and non-linearly filtered noise that have the same mean. Three biologically plausible filters we used: saturating, unimodal optimum type, and sigmoid responses.
Filtering can either decrease or increase population variability when compared to linear noise response. The effect of noise filtering on variability is most pronounced with stable population dynamics and the outcome depends on the filter type, population growth rate, and noise colour.
Non-linear noise filtering predominantly increases extinction risks when population growth rate is low (R<5). As an exception, saturating filter has a window of decreased risk at very low growth rate and reddened environment. In the unstable range of the dynamics (15These results suggest that accounting for the non-linear responses to environment should be considered when estimating extinction risks and population variability. Moreover, the non-linear responses make noise colour a more important factor in these analyses.     

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.     

Biological correlates of extinction risk in bats

We investigated patterns and processes of extinction and threat in bats using a multivariate phylogenetic comparative approach. Of nearly 1,000 species worldwide, 239 are considered threatened by the International Union for Conservation of Nature and Natural Resources (IUCN) and 12 are extinct. Small geographic ranges and low wing aspect ratios are independently found to predict extinction risk in bats, which explains 48% of the total variance in IUCN assessments of threat. The pattern and correlates of extinction risk in the two bat suborders are significantly different. A higher proportion (4%) of megachiropteran species have gone extinct in the last 500 years than microchiropteran bats (0.3%), and a higher proportion is currently at risk of extinction (Megachiroptera: 34%; Microchiroptera: 22%). While correlates of microchiropteran extinction risk are the same as in the order as a whole, megachiropteran extinction is correlated more with reproductive rate and less with wing morphology. Bat extinction risk is not randomly distributed phylogenetically: closely related species have more similar levels of threat than would be expected if extinction risk were random. Given the unbalanced nature of the evolutionary diversification of bats, it is probable that the amount of phylogenetic diversity lost if currently threatened taxa disappear may be greater than in other clades with numerically more threatened species.     

Survival of small populations under demographic stochasticity.

We estimate the mean time to extinction of small populations in an environment with constant carrying capacity but under stochastic demography. In particular, we investigate the interaction of stochastic variation in fecundity and sex ratio under several different schemes of density dependent population growth regimes. The methods used include Markov chain theory, Monte Carlo simulations, and numerical simulations based on Markov chain theory. We find a strongly enhanced extinction risk if stochasticity in sex ratio and fluctuating population size act simultaneously as compared to the case where each mechanism acts alone. The distribution of extinction times deviates slightly from a geometric one, in particular for short extinction times. We also find that whether maximization of intrinsic growth rate decreases the risk of extinction or not depends strongly on the population regulation mechanism. If the population growth regime reduces populations above the carrying capacity to a size below the carrying capacity for large r (overshooting) then the extinction risk increases if the growth rate deviates from an optimal r-value.     

Are certain life histories particularly prone to local extinction?

Using stochastic simulations and elasticity analysis, we show that there are inherent differences in the risk of extinction between life histories with different demographies. Which life history is the most vulnerable depends on which vital rate varies. When juvenile survival varies semelparous organisms with delayed reproduction are the most vulnerable ones, while a varying developmental rate puts a greater threat to semelparous organisms with rapid development. Iteroparous organisms are the most vulnerable ones when adult survival varies. Generally, we do not expect to observe organisms in nature having variation in vital rates that produce a high risk of extinction. Given the results here we therefore predict that iteroparous organisms should show low variation in adult survival. Moreover, we predict that semelparous organisms should show low variation in juvenile survival and low variation in developmental rate. The effect of temporal correlation on extinction risk is most pronounced in organisms with semelparous life histories.     

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

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

Predicting patterns of long‐term adaptation and extinction with population genetics

Population genetics struggles to model extinction; standard models track the relative rather than absolute fitness of genotypes, while the exceptions describe only the short‐term transition from imminent doom to evolutionary rescue. But extinction can result from failure to adapt not only to catastrophes, but also to a backlog of environmental challenges. We model long‐term adaptation to long series of small challenges, where fitter populations reach higher population sizes. The population's long‐term fitness dynamic is well approximated by a simple stochastic Markov chain model. Long‐term persistence occurs when the rate of adaptation exceeds the rate of environmental deterioration for some genotypes. Long‐term persistence times are consistent with typical fossil species persistence times of several million years. Immediately preceding extinction, fitness declines rapidly, appearing as though a catastrophe disrupted a stably established population, even though gradual evolutionary processes are responsible. New populations go through an establishment phase where, despite being demographically viable, their extinction risk is elevated. Should the population survive long enough, extinction risk later becomes constant over time.     

The importance of habitat and life history to extinction risk in sharks, skates, rays and chimaeras

We compared life-history traits and extinction risk of chondrichthyans (sharks, rays and chimaeras), a group of high conservation concern, from the three major marine habitats (continental shelves, open ocean and deep sea), controlling for phylogenetic correlation. Deep-water chondrichthyans had a higher age at maturity and longevity, and a lower growth completion rate than shallow-water species. The average fishing mortality needed to drive a deep-water chondrichthyan species to extinction (Fextinct) was 38-58% of that estimated for oceanic and continental shelf species, respectively. Mean values of Fextinct were 0.149, 0.250 and 0.368 for deep-water, oceanic and continental shelf species, respectively. Reproductive mode was an important determinant of extinction risk, while body size had a weak effect on extinction risk. As extinction risk was highly correlated with phylogeny, the loss of species will be accompanied by a loss of phylogenetic diversity. Conservation priority should not be restricted to large species, as is usually suggested, since many small species, like those inhabiting the deep ocean, are also highly vulnerable to extinction. Fishing mortality of deep-water chondrichthyans already exploited should be minimized, and new deep-water fisheries affecting chondrichthyans should be prevented.     

The 2002 European seal plague: epidemiology and population consequences

We present the first epidemiological data on the 2002 outbreak of phocine distemper virus (PDV) in European harbour seals (Phoca vitulina). The epizootic curve to date supports a mortality rate and probability of infection identical to that of the 1988 outbreak, which killed 58% of the population. Thus immunity is playing no significant role in the dynamics of the current outbreak. Because the timing of the outbreak is important in determining local mortality rates, we predict higher mortality rates on the European continent than in Great Britain or Ireland. A stochastic model is used to quantify how recurrent epizootics affect the long‐term growth, fluctuation, and persistence of the population. Recurrent PDV epizootics with the observed frequency and severity would reduce the long‐term stochastic growth rate of the harbour seal population by half, and significantly increase the risk of quasi‐extinction.     

Viability in a pink environment: why "white noise" models can be dangerous

Analysis of long time series suggests that environmental fluctuations may be accurately represented by 1/ f   noise (pink noise), where temporal correlation is found at several scales, and the range of fluctuations increases over time. Previous studies on the effects of coloured noise on population dynamics used first or second order autoregressive noise. I examined the importance of coloured noise for extinction risk using true 1/ f   noise. I also considered the problem of estimating extinction risk with a limited sample of environmental variation. Pink noise environments increased extinction risk in random walk models where environmental variation affected the growth rate. However, pink noise environments decreased extinction risk in the Ricker model where environmental variation modified the carrying capacity. Underestimation of environmental variance almost always yielded underestimation of extinction risk. For either population viability analysis or management, we should carefully consider the long-term behaviour of the environment as well as how we include environmental noise in population models.     

Separating spatial search and efficiency rates as components of predation risk

Predation risk is an important driver of ecosystems, and local spatial variation in risk can have population-level consequences by affecting multiple components of the predation process. I use resource selection and proportional hazard time-to-event modelling to assess the spatial drivers of two key components of risk—the search rate (i.e. aggregative response) and predation efficiency rate (i.e. functional response)—imposed by wolves (Canis lupus) in a multi-prey system. In my study area, both components of risk increased according to topographic variation, but anthropogenic features affected only the search rate. Predicted models of the cumulative hazard, or risk of a kill, underlying wolf search paths validated well with broad-scale variation in kill rates, suggesting that spatial hazard models provide a means of scaling up from local heterogeneity in predation risk to population-level dynamics in predator–prey systems. Additionally, I estimated an integrated model of relative spatial predation risk as the product of the search and efficiency rates, combining the distinct contributions of spatial heterogeneity to each component of risk.     

Environment,but not migration rate,influences extinction risk in experimental metapopulations

Ecological theory suggests that several demographic factors influence metapopulation extinction risk, including synchrony in population size between subpopulations, metapopulation size and the magnitude of fluctuations in population size. Theoretically, each of these is influenced by the rate of migration between subpopulations. Here we report on an experiment where we manipulated migration rate within metapopulations of the freshwater zooplankton Daphnia magna to examine how migration influenced each of these demographic variables, and subsequent effects on metapopulation extinction. In addition, our experimental procedures introduced unplanned but controlled differences between metapopulations in light intensity, enabling us to examine the relative influences of environmental and demographic factors. We found that increasing migration rate increased subpopulation synchrony. We failed to detect effects of migration on population size and fluctuations in population size at the metapopulation or subpopulation level, however. In contrast, light intensity did not influence synchrony, but was positively correlated with population size and negatively correlated with population fluctuation. Finally, synchrony did not influence time to extinction, while population size and the magnitude of fluctuations did. We conclude that environmental factors had a greater influence on extinction risk than demographic factors, and that metapopulation size and fluctuation were more important to extinction risk than metapopulation synchrony.     

The role of density-dependent dispersal in source-sink dynamics

I investigate two aspects of source-sink theory that have hitherto received little attention: density-dependent dispersal and the cost of dispersal to sources. The cost arises because emigration reduces the per capita growth rate of sources, thus predisposing them to extinction. I show that source-sink persistence depends critically on the interplay between these two factors. When the emigration rate increases with abundance at an accelerating rate, dispersal costs to sources is the lowest and risk of source-sink extinction the least. When the emigration rate increases with abundance at a decelerating rate, dispersal costs to sources is the highest and the risk of source-sink extinction the greatest. Density-independent emigration has an intermediate effect. Thus, density-dependent dispersal per se does not increase or decrease source-sink persistence relative to density-independent dispersal. The exact mode of dispersal is crucial. A key point to appreciate is that these effects of dispersal on source-sink extinction arise from the temporal density-dependence that dispersal induces in the per capita growth rates of source and sink populations. Temporal density-dependence due to dispersal is beneficial at low abundances because it rescues sinks from extinction, and detrimental at high abundances because it drives otherwise viable sources to extinction. These results are robust to the nature of population dynamics in the sink, whether exponential or logistic. They provide a means of assessing the relative costs and benefits of preserving sink habitats given three biological parameters.     

Climate change in metacommunities: dispersal gives double-sided effects on persistence

Climate change is increasingly affecting the structure and dynamics of ecological communities both at local and at regional scales, and this can be expected to have important consequences for their robustness and long-term persistence. The aim of the present work is to analyse how the spatial structure of the landscape and dispersal patterns of species (dispersal rate and average dispersal distance) affects metacommunity response to two disturbances: (i) increased mortality during dispersal and (ii) local species extinction. We analyse the disturbances both in isolation and in combination. Using a spatially and dynamically explicit metacommunity model, we find that the effect of dispersal on metacommunity persistence is two-sided: on the one hand, high dispersal significantly reduces the risk of bottom-up extinction cascades following the local removal of a species; on the other hand, when dispersal imposes a risk to the dispersing individuals, high dispersal increases extinction risks, especially when dispersal is global. Large-bodied species with long generation times at the highest trophic level are particularly vulnerable to extinction when dispersal involves a risk. This suggests that decreasing the mortality risk of dispersing individuals by improving the quality of the habitat matrix may greatly increase the robustness of metacommunities.     

Dynamics of Intraguild Predation Systems with Intraspecific Competition

This paper considers intraguild predation (IGP) systems where species in the same community kill and eat each other and there is intraspecific competition in each species. The IGP systems are characterized by a lattice gas model, in which reaction between sites on the lattice occurs in a random and independent way. Global dynamics of the model with two species demonstrate mechanisms by which IGP leads to survival/extinction of species. It is shown that an intermediary level of predation promotes survival of species, while over-predation or under-predation could result in species extinction. An interesting result is that increasing intraspecific competition of one species can lead to extinction of one or both species, while increasing intraspecific competitions of both species would result in coexistence of species in facultative predation. Initial population densities of the species are also shown to play a role in persistence of the system. Then the analysis is extended to IGP systems with one species. Numerical simulations confirm and extend our results.     

Phylogenetically clustered extinction risks do not substantially prune the Tree of Life

Anthropogenic activities have increased the rate of biological extinction many-fold. Recent empirical studies suggest that projected extinction may lead to extensive loss to the Tree of Life, much more than if extinction were random. One suggested cause is that extinction risk is heritable (phylogenetically patterned), such that entire higher groups will be lost. We show here with simulation that phylogenetically clustered extinction risks are necessary but not sufficient for the extensive loss of phylogenetic diversity (PD) compared to random extinction. We simulated Yule trees and evolved extinction risks at various levels of heritability (measured using Pagel's λ). At most levels of heritability (λ in range of 0 to 10), mean values of extinction risk (range 0.25 to 0.75), tree sizes (64 to 128 tips), tree balance and temporal heterogeneity of diversification rates (Yule and coalescent trees), extinction risks do not substantially increase the loss of PD in these trees when compared to random extinction. The maximum loss of PD (20% above random) was only associated with the combination of extremely excessive values of phylogenetic signal, high mean species' extinction probabilities, and extreme (coalescent) tree shapes. Interestingly, we also observed a decline in the rate of increase in the loss of PD at high phylogenetic clustering (λ → 10) of extinction risks. Our results suggest that the interplay between various aspects of tree shape and a predisposition of higher extinction risks in species-poor clades is required to explain the substantial pruning of the Tree of Life.