Population responses to perturbations: predictions and responses from laboratory mite populations

Integrating the underlying structure of stochasticity into community ecology

Stochasticity is a core component of ecology, as it underlies key processes that structure and create variability in nature. Despite its fundamental importance in ecological systems, the concept is often treated as synonymous with unpredictability in community ecology, and studies tend to focus on single forms of stochasticity rather than taking a more holistic view. This has led to multiple narratives for how stochasticity mediates community dynamics. Here, we present a framework that describes how different forms of stochasticity (notably demographic and environmental stochasticity) combine to provide underlying and predictable structure in diverse communities. This framework builds on the deep ecological understanding of stochastic processes acting at individual and population levels and in modules of a few interacting species. We support our framework with a mathematical model that we use to synthesize key literature, demonstrating that stochasticity is more than simple uncertainty. Rather, stochasticity has profound and predictable effects on community dynamics that are critical for understanding how diversity is maintained. We propose next steps that ecologists might use to explore the role of stochasticity for structuring communities in theoretical and empirical systems, and thereby enhance our understanding of community dynamics.

Trait-based predictions and responses from laboratory mite populations to harvesting in stochastic environments

Predictions on population responses to perturbations are often derived from trait-based approaches like integral projection models (IPMs), but are rarely tested. IPMs are constructed from functions that describe survival, growth and reproduction in relation to the traits of individuals and their environment. Although these functions comprise biologically non-informative statistical coefficients within standard IPMs, model parameters of the recently developed dynamic energy budget IPM (DEB-IPM) are life-history traits like "length at maturation" and "maximum reproduction rate". Testing predictions from mechanistic IPMs against empirical observations can therefore provide functional insights into the links between individual life history, the environment and population dynamics. Here, we compared the population dynamics of the bulb mite (Rhizoglyphus robini) predicted by a DEB-IPM with those observed in an experiment where populations experienced daily food rations that were either positively correlated over time (red noise), negatively (blue noise) or uncorrelated (white noise). We also selectively harvested large adults in half of these populations. The model failed to generate detailed predictions of population structure as juvenile numbers were overestimated; likely because juvenile-adult interference competition was underestimated. The model performed well at the population level as, for both harvested and unharvested populations, simulations matched the observed, long-term stochastic growth rate λ_s . We next generalised the model to investigate how stochastic change affects mite λ_s , which correlated well with the frequency f of experiencing periods of good environment, but, due to the relationship between f and noise colour ρ, did not correlate well with shifts in ρ. The sensitivity of λ_s to perturbations in life-history parameters depended on the type of stochastic change, as well as population growth. Our findings show that responses to differential mortality depend on individual life-history traits, environmental characteristics and population growth. As long-term climate change causes ever greater environmental fluctuations, trait-based approaches will be increasingly important in predicting population responses to change. We therefore conclude by illustrating what questions can be examined with mechanistic trait-based models like the DEB-IPM, the answers to which will advance our knowledge of the functional links between individual traits, the environment and population dynamics.

Harvested populations are more variable only in more variable environments

The interaction between environmental variation and population dynamics is of major importance, particularly for managed and economically important species, and especially given contemporary changes in climate variability. Recent analyses of exploited animal populations contested whether exploitation or environmental variation has the greatest influence on the stability of population dynamics, with consequences for variation in yield and extinction risk. Theoretical studies however have shown that harvesting can increase or decrease population variability depending on environmental variation, and requested controlled empirical studies to test predictions. Here, we use an invertebrate model species in experimental microcosms to explore the interaction between selective harvesting and environmental variation in food availability in affecting the variability of stage‐structured animal populations over 20 generations. In a constant food environment, harvesting adults had negligible impact on population variability or population size, but in the variable food environments, harvesting adults increased population variability and reduced its size. The impact of harvesting on population variability differed between proportional and threshold harvesting, between randomly and periodically varying environments, and at different points of the time series. Our study suggests that predicting the responses to selective harvesting is sensitive to the demographic structures and processes that emerge in environments with different patterns of environmental variation.

Spatial and spatiotemporal variation in metapopulation structure affects population dynamics in a passively dispersing arthropod

The spatial and temporal variation in the availability of suitable habitat within metapopulations determines colonization-extinction events, regulates local population sizes and eventually affects local population and metapopulation stability. Insights into the impact of such a spatiotemporal variation on the local population and metapopulation dynamics are principally derived from classical metapopulation theory and have not been experimentally validated. By manipulating spatial structure in artificial metapopulations of the spider mite Tetranychus urticae, we test to which degree spatial (mainland-island metapopulations) and spatiotemporal variation (classical metapopulations) in habitat availability affects the dynamics of the metapopulations relative to systems where habitat is constantly available in time and space (patchy metapopulations). Our experiment demonstrates that (i) spatial variation in habitat availability decreases variance in metapopulation size and decreases density-dependent dispersal at the metapopulation level, while (ii) spatiotemporal variation in habitat availability increases patch extinction rates, decreases local population and metapopulation sizes and decreases density dependence in population growth rates. We found dispersal to be negatively density dependent and overall low in the spatial variable mainland-island metapopulation. This demographic variation subsequently impacts local and regional population dynamics and determines patterns of metapopulation stability. Both local and metapopulation-level variabilities are minimized in mainland-island metapopulations relative to classical and patchy ones.

Towards a general, population-level understanding of eco-evolutionary change

Most population-level studies of eco-evolutionary dynamics assume that evolutionary change occurs in response to ecological change and vice versa. However, a growing number of papers report simultaneous ecological and evolutionary change, suggesting that the eco-evolutionary consequences of environmental change for populations can only be fully understood through the simultaneous analysis of statistics used to describe both ecological and evolutionary dynamics. Here we argue that integral projection models (IPM), and matrix approximations of them, provide a powerful approach to integrate population ecology, life history theory, and evolution. We discuss key questions in population biology that can be examined using these models, the answers to which are essential for a general, population-level understanding of eco-evolutionary change.

Population responses to perturbations: the importance of trait-based analysis illustrated through a microcosm experiment

Environmental change continually perturbs populations from a stable state, leading to transient dynamics that can last multiple generations. Several long-term studies have reported changes in trait distributions along with demographic response to environmental change. Here we conducted an experimental study on soil mites and investigated the interaction between demography and an individual trait over a period of nonstationary dynamics. By following individual fates and body sizes at each life-history stage, we investigated how body size and population density influenced demographic rates. By comparing the ability of two alternative approaches, a matrix projection model and an integral projection model, we investigated whether consideration of trait-based demography enhances our ability to predict transient dynamics. By utilizing a prospective perturbation analysis, we addressed which stage-specific demographic or trait-transition rate had the greatest influence on population dynamics. Both body size and population density had important effects on most rates; however, these effects differed substantially among life-history stages. Considering the observed trait-demography relationships resulted in better predictions of a population's response to perturbations, which highlights the role of phenotypic plasticity in transient dynamics. Although the perturbation analyses provided comparable predictions of stage-specific elasticities between the matrix and integral projection models, the order of importance of the life-history stages differed between the two analyses. In conclusion, we demonstrate how a trait-based demographic approach provides further insight into transient population dynamics.

Individual variation and population dynamics: lessons from a simple system

The mapping of environment, through variation in individuals' life histories, to dynamics can be complex and often poorly known. Consequently, it is not clear how important it is dynamically. To explore this, I incorporated lessons from an empirical system, a soil mite, into an individual-based model. Individuals compete for resource and allocate this according to eight 'genetic' rules that specify investment in growth or reserves (which influences survival or fecundity), size at maturation and reproductive allocation. Density dependence, therefore, emerges from competition for food, limiting individual's growth and fecundity. We use this model to examine the role that genetic and phenotypically plastic variation plays in dynamics, by fixing phenotypes, by allowing phenotypes to vary plastically and by creating genetic variation between individuals. Variation, and how it arises, influences short- and long-run dynamics in a way comparable in magnitude with halving food supply. In particular, by switching variation on and off, it is possible to identify a range of processes necessary to capture the dynamics of the 'full model'. Exercises like this can help identify key processes and parameters, but a concerted effort is needed across many different systems to search for shared understanding of both process and modelling.

Is hunting mortality additive or compensatory to natural mortality? Effects of experimental harvest on the survival and cause-specific mortality of willow ptarmigan

1. The effects of harvest on the annual and seasonal survival of willow ptarmigan Lagopus lagopus L. were tested in a large-scale harvest experiment. Management units were randomly assigned to one of three experimental treatments: 0%, 15% or 30% harvest. Seasonal quotas were based on the experimental treatment and estimates of bird density before the hunting season. Survival rates and hazard functions for radio-marked ptarmigan were then estimated under the competing risks of harvest and natural mortality. 2. The partially compensatory mortality hypothesis was supported: annual survival of ptarmigan was 0·54 ± 0·08 SE under 0% harvest, 0·47 ± 0·06 under 15% harvest, and was reduced to 0·30 ± 0·05 under 30% harvest. Harvest mortality increased linearly from 0·08 ± 0·05, 0·27 ± 0·05 and 0·42 ± 0·06 from 0% to 30% harvest, whereas natural mortality was 0·38 ± 0·08, 0·25 ± 0·05 and 0·28 ± 0·06 under the same treatments. 3. Realized risk of harvest mortality was 0·08-0·12 points higher than our set harvest treatments of 0-30% because birds were exposed to risk if they moved out of protected areas. The superadditive hypothesis was supported because birds in the 30% harvest treatment had higher natural mortality during winter after the hunting season. 4. Natural mortality was mainly because of raptor predation, with two seasonal peaks in fall and spring. Natural and harvest mortality coincided during early autumn with little potential for compensation during winter months. Peak risk of harvest mortality was 5× higher than natural mortality. Low natural mortality during winter suggests that most late season harvest would be additive mortality. 5. Environmental correlates of natural mortality of ptarmigan included seasonal changes in snow cover, onset of juvenile dispersal, and periods of territorial activity. Natural mortality of ptarmigan was highest during autumn movements and nesting by gyrfalcons Falco rusticolus L. Mortality was low when gyrfalcons had departed for coastal wintering sites, and during summer when ptarmigan were attending nests and broods. 6. Our experimental results have important implications for harvest management of upland gamebirds. Seasonal quotas based on proportional harvest were effective and should be set at ≤ 15% of August populations for regional management plans. Under threshold harvest of a reproductive surplus, 15% harvest would be sustainable at productivity rates ≥ 2·5 young per pair. Impacts of winter harvest could be minimized by closing the hunting season in early November or by reducing late season quotas.

When can efforts to control nuisance and invasive species backfire?

Population control through harvest has the potential to reduce the abundance of nuisance and invasive species. However, demographic structure and density-dependent processes can confound removal efforts and lead to undesirable consequences, such as overcompensation (an increase in abundance in response to harvest) and instability (population cycling or chaos). Recent empirical studies have demonstrated the potential for increased mortality (such as that caused by harvest) to lead to overcompensation and instability in plant, insect, and fish populations. We developed a general population model with juvenile and adult stages to help determine the conditions under which control harvest efforts can produce unintended outcomes. Analytical and simulation analyses of the model demonstrated that the potential for overcompensation as a result of harvest was significant for species with high fecundity, even when annual stage-specific survivorship values were fairly low. Population instability as a result of harvest occurred less frequently and was only possible with harvest strategies that targeted adults when both fecundity and adult survivorship were high. We considered these results in conjunction with current literature on nuisance and invasive species to propose general guidelines for assessing the risks associated with control harvest based on life history characteristics of target populations. Our results suggest that species with high per capita fecundity (over discrete breeding periods), short juvenile stages, and fairly constant survivorship rates are most likely to respond undesirably to harvest. It is difficult to determine the extent to which overcompensation and instability could occur during real-world removal efforts, and more empirical removal studies should be undertaken to evaluate population-level responses to control harvests. Nevertheless, our results identify key issues that have been seldom acknowledged and are potentially generic across taxa.

Unifying Ecological and Evolutionary Dynamics Through Experimental Stochastic Demography

Ecological and evolutionary dynamics depend upon variation in birth and death rates. Consequently characterizing birth and death rates, and identifying factors that explain variation in these rates, should be the foundation of population and evolutionary ecology. Given the central role of birth and death, it is perhaps surprising that relatively few population biologists apply the most recent demographic approaches to their research. This may be because demography is seen as little more than accounting, and therefore dull, or because stochastic demography is seen as mathematically challenging. It is our belief that ecologists and evolutionary biologists have much to gain through increased mastery of stochastic demography. Its applications could push forward our understanding of eco-evolutionary dynamics in stochastic environments, and the outcome could further the unification of ecology and evolution. In this essay we briefly explain why mastering demographic approaches should be a desirable objective for any evolutionary ecologist. We start by describing some aspects and insights gained through application of demographic methods, before suggesting an area where we believe application could prove insightful.

Demographic analysis of continuous-time life-history models

I present a computational approach to calculate the population growth rate, its sensitivity to life-history parameters and associated statistics like the stable population distribution and the reproductive value for exponentially growing populations, in which individual life history is described as a continuous development through time. The method is generally applicable to analyse population growth and performance for a wide range of individual life-history models, including cases in which the population consists of different types of individuals or in which the environment is fluctuating periodically. It complements comparable methods developed for discrete-time dynamics modelled with matrix or integral projection models. The basic idea behind the method is to use Lotka's integral equation for the population growth rate and compute the integral occurring in that equation by integrating an ordinary differential equation, analogous to recently derived methods to compute steady-states of physiologically structured population models. I illustrate application of the method using a number of published life-history models.

Robustness: Predicting the effects of life history perturbations on stage-structured population dynamics

Matrix-based models lie at the core of many applications across the physical, engineering and life sciences. In ecology, matrix models arise naturally via population projection matrices (PPM). The eigendata of PPMs provide detailed quantitative and qualitative information on the dynamic behaviour of model populations, especially their asymptotic rates of growth or decline. A fundamental task in modern ecology is to assess the effect that perturbations to life-cycle transition rates of individuals have on such eigendata. The prevailing assessment tools in ecological applications of PPMs are direct matrix simulations of eigendata and linearised extrapolations to the typically non-linear relationship between perturbation magnitude and the resulting matrix eigenvalues. In recent years, mathematical systems theory has developed an analytical framework, called 'Robustness Analysis and Robust Control', encompassing also algorithms and numerical tools. This framework provides a systematic and precise approach to studying perturbations and uncertainty in systems represented by matrices. Here we lay down the foundations and concepts for a 'robustness' inspired approach to predictive analyses in population ecology. We treat a number of application-specific perturbation problems and show how they can be formulated and analysed using these robustness methodologies.

Harvest reserves reduce extinction risk in an experimental microcosm

Overharvesting by humans threatens a substantial fraction of endangered species. Reserves have recently received enormous attention as a means of better conserving harvested resources, despite limited empirical evidence of their efficacy. We used manipulated microcosms to test whether reserves reduce extinction risk in mobile populations of harvested Tetrahymena thermophila, a ciliate. Here we show that patterns of population distribution inside and outside reserves can be accurately predicted on the basis of simple models of diffusion coupled with logistic controls on local population growth. No extinctions occurred in eight experimental trials with reserves, whereas extinction occurred in seven of eight trials without reserves, as predicted by population viability models based on stochastic population processes. These results suggest that marine reserves may be an effective means of improving long-term viability in heavily harvested fish species.

Complex population dynamics and complex causation: devils, details and demography

Population dynamics result from the interplay of density-independent and density-dependent processes. Understanding this interplay is important, especially for being able to predict near-term population trajectories for management. In recent years, the study of model systems-experimental, observational and theoretical-has shed considerable light on the way that the both density-dependent and -independent aspects of the environment affect population dynamics via impacting on the organism's life history and therefore demography. These model-based approaches suggest that (i) individuals in different states differ in their demographic performance, (ii) these differences generate structure that can fluctuate independently of current total population size and so can influence the dynamics in important ways, (iii) individuals are strongly affected by both current and past environments, even when the past environments may be in previous generations and (iv) dynamics are typically complex and transient due to environmental noise perturbing complex population structures. For understanding population dynamics of any given system, we suggest that 'the devil is in the detail'. Experimental dissection of empirical systems is providing important insights into the details of the drivers of demographic responses and therefore dynamics and should also stimulate theory that incorporates relevant biological mechanism.

Integral projection models for species with complex demography

Matrix projection models occupy a central role in population and conservation biology. Matrix models divide a population into discrete classes, even if the structuring trait exhibits continuous variation (e.g., body size). The integral projection model (IPM) avoids discrete classes and potential artifacts from arbitrary class divisions, facilitates parsimonious modeling based on smooth relationships between individual state and demographic performance, and can be implemented with standard matrix software. Here, we extend the IPM to species with complex demographic attributes, including dormant and active life stages, cross-classification by several attributes (e.g., size, age, and condition), and changes between discrete and continuous structure over the life cycle. We present a general model encompassing these cases, numerical methods, and theoretical results, including stable population growth and sensitivity/elasticity analysis for density-independent models, local stability analysis in density-dependent models, and optimal/evolutionarily stable strategy life-history analysis. Our presentation centers on an IPM for the thistle Onopordum illyricum based on a 6-year field study. Flowering and death probabilities are size and age dependent, and individuals also vary in a latent attribute affecting survival, but a predictively accurate IPM is completely parameterized by fitting a few regression equations. The online edition of the American Naturalist includes a zip archive of R scripts illustrating our suggested methods.A zip archive of R scripts illustrating our suggested methods is also provided.