Population Dynamics in a Noisy World: Lessons From a Mite Experimental System

Anthelmintic Treatment and the Stability of Parasite Distribution in Ruminants

Parasites are generally overdispersed among their hosts, with far-reaching implications for their population dynamics and control. The factors determining parasite overdispersion have long been debated. In particular, stochastic parasite acquisition and individual host variation in density-dependent regulation through acquired host immunity have been identified as key factors, but their relative roles and possible interactions have seen little empirical exploration in parasite populations. Here, Taylor's power law is applied to test the hypothesis that periodic parasite removal destabilises the host-parasite relationship and increases variance in parasite burden around the mean. The slope of the power relationship was compared by analysis of covariance among 325 nematode populations in wild and domestic ruminants, exploiting that domestic ruminants are often routinely treated against parasite infections. In Haemonchus spp. and Trichostrongylus axei in domestic livestock, the slope increased with the frequency of anthelmintic treatment, supporting this hypothesis. In Nematodirus spp., against which acquired immunity is known to be strong, the slope was significantly greater in post-mortem worm burden data than in faecal egg counts, while this relationship did not hold for the less immunogenic genus Marshallagia. Considered together, these findings suggest that immunity acting through an exposure-dependent reduction in parasite fecundity stabilises variance in faecal egg counts, reducing overdispersion, and that periodic anthelmintic treatment interferes with this process and increases overdispersion. The results have implications for the diagnosis and control of parasitic infections in domestic animals, which are complicated by overdispersion, and for our understanding of parasite distribution in free-living wildlife. Parasite-host systems, in which treatment and immunity effectively mimic metapopulation processes of patch extinction and density dependence, could also yield general insights into the spatio-temporal stability of animal distributions.

Plasticity is a locally adapted trait with consequences for ecological dynamics in novel environments

Phenotypic plasticity is predicted to evolve in more variable environments, conferring an advantage on individual lifetime fitness. It is less clear what the potential consequences of that plasticity will have on ecological population dynamics. Here, we use an invertebrate model system to examine the effects of environmental variation (resource availability) on the evolution of phenotypic plasticity in two life history traits-age and size at maturation-in long-running, experimental density-dependent environments. Specifically, we then explore the feedback from evolution of life history plasticity to subsequent ecological dynamics in novel conditions. Plasticity in both traits initially declined in all microcosm environments, but then evolved increased plasticity for age-at-maturation, significantly so in more environmentally variable environments. We also demonstrate how plasticity affects ecological dynamics by creating founder populations of different plastic phenotypes into new microcosms that had either familiar or novel environments. Populations originating from periodically variable environments that had evolved greatest plasticity had lowest variability in population size when introduced to novel environments than those from constant or random environments. This suggests that while plasticity may be costly it can confer benefits by reducing the likelihood that offspring will experience low survival through competitive bottlenecks in variable environments. In this study, we demonstrate how plasticity evolves in response to environmental variation and can alter population dynamics-demonstrating an eco-evolutionary feedback loop in a complex animal moderated by plasticity in growth.

Spatial variance-mass allometry of population density in felids from camera-trapping studies worldwide

Power laws are cornerstone relationships in ecology and evolutionary biology. The density-mass allometry (DMA), which predicts an allometric scaling of population abundance, and Taylor’s law (TL), which predicts a decrease in the population abundance variation along with a decrease in population density, have enhanced our knowledge of inter- and intra-specific variation in population abundance. When combined, these two power laws led to the variance-mass allometry (VMA), which states that larger species have lower spatial variation in population density than smaller species. The VMA has been predicted through theoretical models, however few studies have investigated if this law is also supported by empirical data. Here, to formally test the VMA, we have used the population density estimates obtained through worldwide camera trapping studies for an emblematic and ecologically important carnivorous taxa, the Felidae family. Our results showed that the VMA law hold in felids, as well as the TL and the DMA laws; bigger cat species showed less variation for the population density than smaller species. These results have important implications for the conservation of wildlife population and confirm the validity of important ecological concepts, like the allometric scaling of population growth rate and the slow-fast continuum of life history strategies.

Life-history evolution under fluctuating density-dependent selection and the adaptive alignment of pace-of-life syndromes

We present a novel perspective on life-history evolution that combines recent theoretical advances in fluctuating density-dependent selection with the notion of pace-of-life syndromes (POLSs) in behavioural ecology. These ideas posit phenotypic co-variation in life-history, physiological, morphological and behavioural traits as a continuum from the highly fecund, short-lived, bold, aggressive and highly dispersive 'fast' types at one end of the POLS to the less fecund, long-lived, cautious, shy, plastic and socially responsive 'slow' types at the other. We propose that such variation in life histories and the associated individual differences in behaviour can be explained through their eco-evolutionary dynamics with population density - a single and ubiquitous selective factor that is present in all biological systems. Contrasting regimes of environmental stochasticity are expected to affect population density in time and space and create differing patterns of fluctuating density-dependent selection, which generates variation in fast versus slow life histories within and among populations. We therefore predict that a major axis of phenotypic co-variation in life-history, physiological, morphological and behavioural traits (i.e. the POLS) should align with these stochastic fluctuations in the multivariate fitness landscape created by variation in density-dependent selection. Phenotypic plasticity and/or genetic (co-)variation oriented along this major POLS axis are thus expected to facilitate rapid and adaptively integrated changes in various aspects of life histories within and among populations and/or species. The fluctuating density-dependent selection POLS framework presented here therefore provides a series of clear testable predictions, the investigation of which should further our fundamental understanding of life-history evolution and thus our ability to predict natural population dynamics.

Complex interaction of resource availability, life-history and demography determines the dynamics and stability of stage-structured populations

The dynamics of stage-structured populations facing stage-specific variability in resource availability and/or demographic factors like unequal sex-ratios, remains poorly understood. We addressed these issues using a stage-structured individual-based model that incorporates life-history parameters common to many holometabolous insects. The model was calibrated using time series data from a 49-generation experiment on laboratory populations of Drosophila melanogaster, subjected to four different combinations of larval and adult nutritional levels. The model was able to capture multiple qualitative and quantitative aspects of the empirical time series across three independent studies. We then simulated the model to explore the interaction of various life-history parameters and nutritional levels in determining population stability. In all nutritional regimes, constancy stability of the populations was reduced upon increasing egg-hatchability, critical mass, and proportion of body resource allocated to female fecundity. However, the effects of increasing sensitivity of female-fecundity to adult density on constancy stability varied across nutrition regimes. The effects of unequal sex-ratio and sex-specific culling were greatly influenced by fecundity but not by levels of juvenile nutrition. Finally, we investigated the implications of some of these insights on the efficiency of the widely-used pest control method, the Sterile Insect Technique (SIT). We show that increasing the amount of juvenile food had no effects on SIT efficiency when the density-independent fecundity is low, but reduces SIT efficiency when the density-independent fecundity is high.

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.

An automated image analysis system to measure and count organisms in laboratory microcosms

1. Because of recent technological improvements in the way computer and digital camera perform, the potential use of imaging for contributing to the study of communities, populations or individuals in laboratory microcosms has risen enormously. However its limited use is due to difficulties in the automation of image analysis. 2. We present an accurate and flexible method of image analysis for detecting, counting and measuring moving particles on a fixed but heterogeneous substrate. This method has been specifically designed to follow individuals, or entire populations, in experimental laboratory microcosms. It can be used in other applications. 3. The method consists in comparing multiple pictures of the same experimental microcosm in order to generate an image of the fixed background. This background is then used to extract, measure and count the moving organisms, leaving out the fixed background and the motionless or dead individuals. 4. We provide different examples (springtails, ants, nematodes, daphnia) to show that this non intrusive method is efficient at detecting organisms under a wide variety of conditions even on faintly contrasted and heterogeneous substrates. 5. The repeatability and reliability of this method has been assessed using experimental populations of the Collembola Folsomia candida. 6. We present an ImageJ plugin to automate the analysis of digital pictures of laboratory microcosms. The plugin automates the successive steps of the analysis and recursively analyses multiple sets of images, rapidly producing measurements from a large number of replicated microcosms.

Taylor's law and body size in exploited marine ecosystems

Taylor's law (TL), which states that variance in population density is related to mean density via a power law, and density-mass allometry, which states that mean density is related to body mass via a power law, are two of the most widely observed patterns in ecology. Combining these two laws predicts that the variance in density is related to body mass via a power law (variance-mass allometry). Marine size spectra are known to exhibit density-mass allometry, but variance-mass allometry has not been investigated. We show that variance and body mass in unexploited size spectrum models are related by a power law, and that this leads to TL with an exponent slightly <2. These simulated relationships are disrupted less by balanced harvesting, in which fishing effort is spread across a wide range of body sizes, than by size-at-entry fishing, in which only fish above a certain size may legally be caught.

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.

Taylor's Law holds in experimental bacterial populations but competition does not influence the slope

Populations vary in time and in space, and temporal variation may differ from spatial variation. Yet, in the past half century, field data have confirmed both the temporal and spatial forms of Taylor's power Law, a linear relationship between log(variance) and log(mean) of population size. Recent theory predicted that competitive species interactions should reduce the slope of the temporal version of Taylor's Law. We tested whether this prediction applied to the spatial version of Taylor's Law using simple, well-controlled laboratory populations of two species of bacteria that were cultured either separately or together for 24 h in media of widely varying nutrient richness. Experimentally, the spatial form of Taylor's Law with a slope of 2 held for these simple bacterial communities, but competitive interactions between the two species did not reduce the spatial Taylor's Law slope. These results contribute to the widespread usefulness of Taylor's Law in population ecology, epidemiology and pest control.

The dynamics of a quantitative trait in an age-structured population living in a variable environment

Time series of rapid phenotypic change have been documented in age-structured populations living in the wild. Researchers are often interested in identifying the processes responsible for such change. We derive an equation to exactly decompose change in the mean value of a phenotypic trait into contributions from fluctuations in the demographic structure and age-specific viability selection, fertility selection, phenotypic plasticity, and differences between offspring and parental trait values. We treat fitness as a sum of its components rather than as a scalar and explicitly consider age structure by focusing on short time steps, which are appropriate for describing phenotypic change in species with overlapping generations. We apply the method to examine stasis in birth weight in a well-characterized population of red deer. Stasis is achieved because positive viability selection for an increase in birth weight is countered by parents producing offspring that are, on average, smaller than they were at birth. This is one of many ways in which equilibria in the mean value of a phenotypic trait can be maintained. The age-structured Price equation we derive has the potential to provide considerable insight into the processes generating now frequently reported cases of rapid phenotypic change.

Colour of environmental noise affects the nonlinear dynamics of cycling, stage-structured populations

Populations fluctuate because of their internal dynamics, which can be nonlinear and stochastic, and in response to environmental variation. Theory predicts how the colour of environmental stochasticity affects population means, variances and correlations with the environment over time. The theory has not been tested for cycling populations, commonly observed in field systems. We applied noise of different colours to cycling laboratory beetle populations, holding other statistical properties of the noise fixed. Theory was largely validated, but failed to predict observations in sufficient detail. The main period of population cycling was shifted up to 33% by the colour of environmental stochasticity. Noise colour affected population means, variances and dominant periodicities differently for populations that cycled in different ways without noise. Our results show that changes in the colour of climatic variability, partly caused by humans, may affect the main periodicity of cycling populations, possibly impacting industry, pest management and conservation.

Individual differences, density dependence and offspring birth traits in a population of red deer

Variation between individuals is an essential component of natural selection and evolutionary change, but it is only recently that the consequences of persistent differences between individuals on population dynamics have been considered. In particular, few authors have addressed whether interactions exist between individual quality and environmental variation. In part, this is due to the difficulties of collecting sufficient data, but also the challenge of defining individual quality. Using a long-established study population of red deer, Cervus elaphus, inhabiting the North Block of the Isle of Rum, and three quality measures, this paper investigates how differences in maternal quality affect variation in birth body mass and date, as population density varies, and how this differs depending on the sex of the offspring and the maternal quality measure used. Significant interactions between maternal quality, measured as a hind's total contribution to population growth, and population density are reported for birth mass, but only for male calves. Analyses using dominance or age at primiparity to define maternal quality showed no significant interactions with population density, highlighting the difficulties of defining a consistent measure of individual quality.

Microcosm experiments can inform global ecological problems

Global-scale environmental problems are rarely regarded as amenable to traditional scientific experiment. We argue here that small-scale experiments using 'model organisms' in microcosms or mesocosms can be a useful approach for apparently intractable global problems, such as ecosystem responses to climate change or managing biodiversity through the design of nature reserves. An experimental, small-scale research programme can easily be coupled with the development of theory and act as a stimulus to further research, thereby hastening both understanding of the issues and development of practical solutions. This process--from microcosm experiment to the development of practical application--has previously been influential but also has a long time lag. We suggest short-cuts in an attempt to stimulate the use of small-scale experiments to address globally urgent issues with meaningful policy implications.

The extended Moran effect and large-scale synchronous fluctuations in the size of great tit and blue tit populations

1. Synchronous fluctuations of geographically separated populations are in general explained by the Moran effect, i.e. a common influence on the local population dynamics of environmental variables that are correlated in space. Empirical support for such a Moran effect has been difficult to provide, mainly due to problems separating out effects of local population dynamics, demographic stochasticity and dispersal that also influence the spatial scaling of population processes. Here we generalize the Moran effect by decomposing the spatial autocorrelation function for fluctuations in the size of great tit Parus major and blue tit Cyanistes caeruleus populations into components due to spatial correlations in the environmental noise, local differences in the strength of density regulation and the effects of demographic stochasticity. 2. Differences between localities in the strength of density dependence and nonlinearity in the density regulation had a small effect on population synchrony, whereas demographic stochasticity reduced the effects of the spatial correlation in environmental noise on the spatial correlations in population size by 21.7% and 23.3% in the great tit and blue tit, respectively. 3. Different environmental variables, such as beech mast and climate, induce a common environmental forcing on the dynamics of central European great and blue tit populations. This generates synchronous fluctuations in the size of populations located several hundred kilometres apart. 4. Although these environmental variables were autocorrelated over large areas, their contribution to the spatial synchrony in the population fluctuations differed, dependent on the spatial scaling of their effects on the local population dynamics. We also demonstrate that this effect can lead to the paradoxical result that a common environmental variable can induce spatial desynchronization of the population fluctuations. 5. This demonstrates that a proper understanding of the ecological consequences of environmental changes, especially those that occur simultaneously over large areas, will require information about the spatial scaling of their effects on local population dynamics.

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.