When can environmental variability benefit population growth? Counterintuitive effects of nonlinearities in vital rates

Stochastic resonance in climate reddening increases the risk of cyclic ecosystem extinction via phase-tipping

Human activity is leading to changes in the mean and variability of climatic parameters in most locations around the world. The changing mean has received considerable attention from scientists and climate policy makers. However, recent work indicates that the changing variability, that is, the amplitude and the temporal autocorrelation of deviations from the mean, may have greater and more imminent impact on ecosystems. In this paper, we demonstrate that changes in climate variability alone could drive cyclic predator-prey ecosystems to extinction via so-called phase-tipping (P-tipping), a new type of instability that occurs only from certain phases of the predator-prey cycle. We construct a mathematical model of a variable climate and couple it to two self-oscillating paradigmatic predator-prey models. Most importantly, we combine realistic parameter values for the Canada lynx and snowshoe hare with actual climate data from the boreal forest. In this way, we demonstrate that critically important species in the boreal forest have increased likelihood of P-tipping to extinction under predicted changes in climate variability, and are most vulnerable during stages of the cycle when the predator population is near its maximum. Furthermore, our analysis reveals that stochastic resonance is the underlying mechanism for the increased likelihood of P-tipping to extinction.

Logistic-growth models measuring density feedback are sensitive to population declines, but not fluctuating carrying capacity

Analysis of long-term trends in abundance of animal populations provides insights into population dynamics. Population growth rates are the emergent interplay of inter alia fertility, survival, and dispersal. However, the density feedbacks operating on some vital rates ("component feedback") can be decoupled from density feedbacks on population growth rates estimated using abundance time series ("ensemble feedback"). Many of the mechanisms responsible for this decoupling are poorly understood, thereby questioning the validity of using logistic-growth models versus vital rates to infer long-term population trends. To examine which conditions lead to decoupling, we simulated age-structured populations of long-lived vertebrates experiencing component density feedbacks on survival. We then quantified how imposed stochasticity in survival rates, density-independent mortality (catastrophes, harvest-like removal of individuals) and variation in carrying capacity modified the ensemble feedback in abundance time series simulated from age-structured populations. The statistical detection of ensemble density feedback from census data was largely unaffected by density-independent processes. Long-term population decline caused from density-independent mortality was the main mechanism decoupling the strength of component versus ensemble density feedbacks. Our study supports the use of simple logistic-growth models to capture long-term population trends, mediated by changes in population abundance, when survival rates are stochastic, carrying capacity fluctuates, and populations experience moderate catastrophic mortality over time.

Life history adaptations to fluctuating environments: Combined effects of demographic buffering and lability

Demographic buffering and lability have been identified as adaptive strategies to optimise fitness in a fluctuating environment. These are not mutually exclusive, however, we lack efficient methods to measure their relative importance for a given life history. Here, we decompose the stochastic growth rate (fitness) into components arising from nonlinear responses and variance-covariance of demographic parameters to an environmental driver, which allows studying joint effects of buffering and lability. We apply this decomposition for 154 animal matrix population models under different scenarios to explore how these main fitness components vary across life histories. Faster-living species appear more responsive to environmental fluctuations, either positively or negatively. They have the highest potential for strong adaptive demographic lability, while demographic buffering is a main strategy in slow-living species. Our decomposition provides a comprehensive framework to study how organisms adapt to variability through buffering and lability, and to predict species responses to climate change.

Detecting climate signals in populations across life histories

Climate impacts are not always easily discerned in wild populations as detecting climate change signals in populations is challenged by stochastic noise associated with natural climate variability, variability in biotic and abiotic processes, and observation error in demographic rates. Detection of the impact of climate change on populations requires making a formal distinction between signals in the population associated with long-term climate trends from those generated by stochastic noise. The time of emergence (ToE) identifies when the signal of anthropogenic climate change can be quantitatively distinguished from natural climate variability. This concept has been applied extensively in the climate sciences, but has not been explored in the context of population dynamics. Here, we outline an approach to detecting climate-driven signals in populations based on an assessment of when climate change drives population dynamics beyond the envelope characteristic of stochastic variations in an unperturbed state. Specifically, we present a theoretical assessment of the time of emergence of climate-driven signals in population dynamics ( ToE pop ). We identify the dependence of ToE pop on the magnitude of both trends and variability in climate and also explore the effect of intrinsic demographic controls on ToE pop . We demonstrate that different life histories (fast species vs. slow species), demographic processes (survival, reproduction), and the relationships between climate and demographic rates yield population dynamics that filter climate trends and variability differently. We illustrate empirically how to detect the point in time when anthropogenic signals in populations emerge from stochastic noise for a species threatened by climate change: the emperor penguin. Finally, we propose six testable hypotheses and a road map for future research.

The Demographic Buffering Hypothesis: Evidence and Challenges

In (st)age-structured populations, the long-run population growth rate is negatively affected by temporal variation in vital rates. In most cases, natural selection should minimize temporal variation in the vital rates to which the long-run population growth is most sensitive, resulting in demographic buffering. By reviewing empirical studies on demographic buffering in wild populations, we found overall support for this hypothesis. However, we also identified issues when testing for demographic buffering. In particular, solving scaling problems for decomposing, measuring, and comparing stochastic variation in vital rates and accounting for density dependence are required in future tests of demographic buffering. In the current context of climate change, demographic buffering may mitigate the negative impact of environmental variation and help populations to persist in an increasingly variable environment.

Indirect effects of primary prey population dynamics on alternative prey

We develop a theory of generalist predation showing how alternative prey species are affected by changes in both mean abundance and variability (coefficient of variation) of their predator's primary prey. The theory is motivated by the indirect effects of cyclic rodent populations on ground-breeding birds, and developed through progressive analytic simplifications of an empirically-based model. It applies nonetheless to many other systems where primary prey have fast life-histories and can become superabundant, thus facilitating impact on alternative prey species and generating highly asymmetric interactions. Our results suggest that predator effects on alternative prey should generally decrease with mean primary prey abundance, and increase with primary prey variability (low to high CV)-unless predators have strong aggregative responses, in which case these results can be reversed. Approximations of models including predator dynamics (general numerical response with possible delays) confirm these results but further suggest that negative temporal correlation between predator and primary prey is harmful to alternative prey. Finally, we find that measurements of predator numerical responses are crucial to predict-even qualitatively-the response of ecosystems to changes in the dynamics of outbreaking prey species.

Environmental variation and population responses to global change

Species' responses to environmental changes such as global warming are affected not only by trends in mean conditions, but also by natural and human-induced environmental fluctuations. Methods are needed to predict how such environmental variation affects ecological and evolutionary processes, in order to design effective strategies to conserve biodiversity under global change. Here, we review recent theoretical and empirical studies to assess: (1) how populations respond to changes in environmental variance, and (2) how environmental variance affects population responses to changes in mean conditions. Contrary to frequent claims, empirical studies show that increases in environmental variance can increase as well as decrease long-term population growth rates. Moreover, environmental variance can alter and even reverse the effects of changes in the mean environment, such that even if environmental variance remains constant, omitting it from population models compromises their ability to predict species' responses to changes in mean conditions. Drawing on theory relating these effects of environmental variance to the curvatures of population growth responses to the environment, we outline how species' traits such as phylogenetic history and body mass could be used to predict their responses to global change under future environmental variability.

Dampening prey cycle overrides the impact of climate change on predator population dynamics: a long-term demographic study on tawny owls

Predicting the dynamics of animal populations with different life histories requires careful understanding of demographic responses to multifaceted aspects of global changes, such as climate and trophic interactions. Continent-scale dampening of vole population cycles, keystone herbivores in many ecosystems, has been recently documented across Europe. However, its impact on guilds of vole-eating predators remains unknown. To quantify this impact, we used a 27-year study of an avian predator (tawny owl) and its main prey (field vole) collected in Kielder Forest (UK) where vole dynamics shifted from a high- to a low-amplitude fluctuation regime in the mid-1990s. We measured the functional responses of four demographic rates to changes in prey dynamics and winter climate, characterized by wintertime North Atlantic Oscillation (wNAO). First-year and adult survival were positively affected by vole density in autumn but relatively insensitive to wNAO. The probability of breeding and number of fledglings were higher in years with high spring vole densities and negative wNAO (i.e. colder and drier winters). These functional responses were incorporated into a stochastic population model. The size of the predator population was projected under scenarios combining prey dynamics and winter climate to test whether climate buffers or alternatively magnifies the impact of changes in prey dynamics. We found the observed dampening vole cycles, characterized by low spring densities, drastically reduced the breeding probability of predators. Our results illustrate that (i) change in trophic interactions can override direct climate change effect; and (ii) the demographic resilience entailed by longevity and the occurrence of a floater stage may be insufficient to buffer hypothesized environmental changes. Ultimately, dampened prey cycles would drive our owl local population towards extinction, with winter climate regimes only altering persistence time. These results suggest that other vole-eating predators are likely to be threatened by dampening vole cycles throughout Europe.

Demographic responses of a site-faithful and territorial predator to its fluctuating prey: long-tailed skuas and arctic lemmings

Environmental variability, through interannual variation in food availability or climatic variables, is usually detrimental to population growth. It can even select for constancy in key life-history traits, though some exceptions are known. Changes in the level of environmental variability are therefore important to predict population growth or life-history evolution. Recently, several cyclic vole and lemming populations have shown large dynamical changes that might affect the demography or life-histories of rodent predators. Skuas constitute an important case study among rodent predators, because of their strongly saturating breeding productivity (they lay only two eggs) and high degree of site fidelity, in which they differ from nomadic predators raising large broods in good rodent years. This suggests that they cannot capitalize on lemming peaks to the same extent as nomadic predators and might be more vulnerable to collapses of rodent cycles. We develop a model for the population dynamics of long-tailed skuas feeding on lemmings to assess the demographic consequences of such variable and non-stationary prey dynamics, based on data collected in NE Greenland. The model shows that populations of long-tailed skua sustain well changes in lemming dynamics, including temporary collapses (e.g. 10 years). A high floater-to-breeder ratio emerges from rigid territorial behaviour and a long-life expectancy, which buffers the impact of adult abundance's decrease on the population reproductive output. The size of the floater compartment is affected by changes in both mean and coefficient of variation of lemming densities (but not cycle amplitude and periodicity per se). In Greenland, the average lemming density is below the threshold density required for successful breeding (including during normally cyclic periods). Due to Jensen's inequality, skuas therefore benefit from lemming variability; a positive effect of environmental variation. Long-tailed skua populations are strongly adapted to fluctuating lemming populations, an instance of demographic lability in the reproduction rate. They are also little affected by poor lemming periods, if there are enough floaters, or juveniles disperse to neighbouring populations. The status of Greenland skua populations therefore strongly depends upon floater numbers and juvenile movements, which are not known. This reveals a need to intensify colour-ringing efforts on the long-tailed skua at a circumpolar scale.