Overcompensatory population dynamic responses to environmental stochasticity

1. To quantify the interactions between density-dependent, population regulation and density-independent limitation, we studied the time-series dynamics of an experimental laboratory insect microcosm system in which both environmental noise and resource limitation were manipulated. 2. A hierarchical Bayesian state-space approach is presented through which it is feasible to capture all sources of uncertainty, including observation error to accurately quantify the density dependence operating on the dynamics. 3. The regulatory processes underpinning the dynamics of two different bruchid beetles (Callosobruchus maculatus and Callosobruchus chinensis) are principally determined by environmental conditions, with fluctuations in abundance explained in terms of changes in overcompensatory dynamics and stochastic processes. 4. A general, stochastic population model is developed to explore the link between abundance fluctuations and the interaction between density dependence and noise. Taking account of time-lags in population regulation can substantially increase predicted population fluctuations resulting from underlying noise processes.     

Census error and the detection of density dependence

1. Studies aiming to identify the prevalence and nature of density dependence in ecological populations have often used statistical analysis of ecological time-series of population counts. Such time-series are also being used increasingly to parameterize models that may be used in population management. 2. If time-series contain measurement errors, tests that rely on detecting a negative relationship between log population change and population size are biased and prone to spuriously detecting density dependence (Type I error). This is because the measurement error in density for a given year appears in the corresponding change in population density, with equal magnitude but opposite sign. 3. This effect introduces bias that may invalidate comparisons of ecological data with density-independent time-series. Unless census error can be accounted for, time-series may appear to show strongly density-dependent dynamics, even though the density-dependent signal may in reality be weak or absent. 4. We distinguish two forms of census error, both of which have serious consequences for detecting density dependence. 5. First, estimates of population density are based rarely on exact counts, but on samples. Hence there exists sampling error, with the level of error depending on the method employed and the number of replicates on which the population estimate is based. 6. Secondly, the group of organisms measured is often not a truly self-contained population, but part of a wider ecological population, defined in terms of location or behaviour. Consequently, the subpopulation studied may effectively be a sample of the population and spurious density dependence may be detected in the dynamics of a single subpopulation. In this case, density dependence is detected erroneously, even if numbers within the subpopulation are censused without sampling error. 7. In order to illustrate how process variation and measurement error may be distinguished we review data sets (counts of numbers of birds by single observers) for which both census error and long-term variance in population density can be estimated. 8. Tests for density dependence need to obviate the problem that measured population sizes are typically estimates rather than exact counts. It is possible that in some cases it may be possible to test for density dependence in the presence of unknown levels of census error, for example by uncovering nonlinearities in the density response. However, it seems likely that these may lack power compared with analyses that are able to explicitly include census error and we review some recently developed methods.     

Spatio-Temporal Environmental Correlation and Population Variability in Simple Metacommunities

Natural populations experience environmental conditions that vary across space and over time. This variation is often correlated between localities depending on the geographical separation between them, and different species can respond to local environmental fluctuations similarly or differently, depending on their adaptation. How this emerging structure in environmental correlation (between-patches and between-species) affects spatial community dynamics is an open question. This paper aims at a general understanding of the interactions between the environmental correlation structure and population dynamics in spatial networks of local communities (metacommunities), by studying simple two-patch, two-species systems. Three different pairs of interspecific interactions are considered: competition, consumer–resource interaction, and host–parasitoid interaction. While the results paint a relatively complex picture of the effect of environmental correlation, the interaction between environmental forcing, dispersal, and local interactions can be understood via two mechanisms. While increasing between-patch environmental correlation couples immigration and local densities (destabilising effect), the coupling between local populations under increased between-species environmental correlation can either amplify or dampen population fluctuations, depending on the patterns in density dependence. This work provides a unifying framework for modelling stochastic metacommunities, and forms a foundation for a better understanding of population responses to environmental fluctuations in natural systems.     

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.     

Species synchrony and its drivers: neutral and nonneutral community dynamics in fluctuating environments

Independent species fluctuations are commonly used as a null hypothesis to test the role of competition and niche differences between species in community stability. This hypothesis, however, is unrealistic because it ignores the forces that contribute to synchronization of population dynamics. Here we present a mechanistic neutral model that describes the dynamics of a community of equivalent species under the joint influence of density dependence, environmental forcing, and demographic stochasticity. We also introduce a new standardized measure of species synchrony in multispecies communities. We show that the per capita population growth rates of equivalent species are strongly synchronized, especially when endogenous population dynamics are cyclic or chaotic, while their long-term fluctuations in population sizes are desynchronized by ecological drift. We then generalize our model to nonneutral dynamics by incorporating temporal and nontemporal forms of niche differentiation. Niche differentiation consistently decreases the synchrony of species per capita population growth rates, while its effects on the synchrony of population sizes are more complex. Comparing the observed synchrony of species per capita population growth rates with that predicted by the neutral model potentially provides a simple test of deterministic asynchrony in a community.     

A perfect storm: the combined effects on population fluctuations of autocorrelated environmental noise, age structure, and density dependence

While it is widely appreciated that climate can affect the population dynamics of various species, a mechanistic understanding of how climate interacts with life-history traits to influence population fluctuations requires development. Here we build a general density-dependent age-structured model that accounts for differential responses in life-history traits to increasing population density. We show that as the temporal frequency of favorable environmental conditions increases, population fluctuations also increase provided that unfavorable environmental conditions still occur. As good years accumulate and the number of individuals in a population increases, successive life-history traits become vulnerable to density dependence once a return to unfavorable conditions prevails. The stronger this ratcheting of density dependence in life-history traits by autocorrelated climatic conditions, the larger the population fluctuations become. Highly fecund species, and those in which density dependence occurs in juvenile and adult vital rates at similar densities, are most sensitive to increases in the frequency of favorable conditions. Understanding the influence of global warming on temporal correlation in regional environmental conditions will be important in identifying those species liable to exhibit increased population fluctuations that could lead to their extinction.     

Climate and spatio-temporal variation in the population dynamics of a long distance migrant, the white stork

1. A central question in ecology is to separate the relative contribution of density dependence and stochastic influences to annual fluctuations in population size. Here we estimate the deterministic and stochastic components of the dynamics of different European populations of white stork Ciconia ciconia. We then examined whether annual changes in population size was related to the climate during the breeding period (the 'tap hypothesis' sensu Saether, Sutherland & Engen (2004, Advances in Ecological Research, 35, 185 209) or during the nonbreeding period, especially in the winter areas in Africa (the 'tube hypothesis'). 2. A general characteristic of the population dynamics of this long-distance migrant is small environmental stochasticity and strong density regulation around the carrying capacity with short return times to equilibrium. 3. Annual changes in the size of the eastern European populations were correlated by rainfall in the wintering areas in Africa as well as local weather in the breeding areas just before arrival and in the later part of the breeding season and regional climate variation (North Atlantic Oscillation). This indicates that weather influences the population fluctuations of white storks through losses of sexually mature individuals as well as through an effect on the number of individuals that manages to establish themselves in the breeding population. Thus, both the tap and tube hypothesis explains climate influences on white stork population dynamics. 4. The spatial scale of environmental noise after accounting for the local dynamics was 67 km, suggesting that the strong density dependence reduces the synchronizing effects of climate variation on the population dynamics of white stork. 5. Several climate variables reduced the synchrony of the residual variation in population size after accounting for density dependence and demographic stochasticity, indicating that these climate variables had a synchronizing effect on the population fluctuations. In contrast, other climatic variables acted as desynchronizing agents. 6. Our results illustrate that evaluating the effects of common environmental variables on the spatio-temporal variation in population dynamics require estimates and modelling of their influence on the local dynamics.     

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.     

Intrinsically generated coloured noise in laboratory insect populations

What are the mechanisms responsible for generating the erratic fluctuations observed in natural populations? This question has been at the centre of a long debate in contemporary ecology. The irregularities in the patterns of population abundance were initially mostly attributed to environmental factors. In the mid-1970s, however, it was proposed that these fluctuations may be generated intrinsically, by the underlying nonlinearities inherent in population processes. More recently, the focus of this argument has turned increasingly towards the statistical properties of population fluctuations, with many studies showing that ecological systems tend to be dominated by low-frequency or long-term dynamics, termed ''red'' noise. Currently, the source of the ''redness'' in ecological time-series is hotly debated, with the general consensus being that environmental variables are the major driving force. Here we show that three classic laboratory populations known to display irregular fluctuations also have reddened spectra. Furthermore, the dynamics of these populations show very well-defined generic scaling properties in the form of power laws. These results imply that long-term influences in ecological systems can be the product of intrinsic dynamics.     

Modelling non-additive and nonlinear signals from climatic noise in ecological time series: Soay sheep as an example

Understanding how climate can interact with other factors in determining patterns of species abundance is a persistent challenge in ecology. Recent research has suggested that the dynamics exhibited by some populations may be a non-additive function of climate, with climate affecting population growth more strongly at high density than at low density. However, we lack methodologies to adequately explain patterns in population growth generated as a result of interactions between intrinsic factors and extrinsic climatic variation in non-linear systems. We present a novel method (the Functional Coefficient Threshold Auto-Regressive (FCTAR) method) that can identify interacting influences of climate and density on population dynamics from time-series data. We demonstrate its use on count data on the size of the Soay sheep population, which is known to exhibit dynamics generated by nonlinear and non-additive interactions between density and climate, living on Hirta in the St Kilda archipelago. The FCTAR method suggests that climate fluctuations can drive the Soay sheep population between different dynamical regimes--from stable population size through limit cycles and non-periodic fluctuations.     

Demographic response to perturbations: the role of compensatory density dependence in a North American duck under variable harvest regulations and changing habitat

1. Most wild animal populations are subjected to many perturbations, including environmental forcing and anthropogenic mortality. How population size varies in response to these perturbations largely depends on life-history strategy and density regulation. 2. Using the mid-continent population of redhead Aythya americana (a North American diving duck), we investigated the population response to two major perturbations, changes in breeding habitat availability (number of ponds in the study landscape) and changes in harvest regulations directed at managing mortality patterns (bag limit). We used three types of data collected at the continental scale (capture-recovery, population surveys and age- and sex ratios in the harvest) and combined them into integrated population models to assess the interaction between density dependence and the effect of perturbations. 3. We observed a two-way interaction between the effects on fecundity of pond number and population density. Hatch-year female survival was also density dependent. Matrix modelling showed that population booms could occur after especially wet years. However, the effect of moderate variation in pond number was generally offset by density dependence the following year. 4. Mortality patterns were insensitive to changes in harvest regulations and, in males at least, insensitive to density dependence as well. We discuss potential mechanisms for compensation of hunting mortality as well as possible confounding factors. 5. Our results illustrate the interplay of density dependence and environmental variation both shaping population dynamics in a harvested species, which could be generalized to help guide the dual management of habitat and harvest regulations.     

Estimating partial observability and nonlinear climate effects on stochastic community dynamics of migratory waterfowl

1. Understanding the impact of environmental variability on migrating species requires the estimation of sequential abiotic effects in different geographic areas across the life cycle. For instance, waterfowl (ducks, geese and swans) usually breed widely dispersed throughout their breeding range and gather in large numbers in their wintering headquarters, but there is a lack of knowledge on the effects of the sequential environmental conditions experienced by migrating birds on the long-term community dynamics at their wintering sites. 2. Here, we analyse multidecadal time-series data of 10 waterfowl species wintering in the Guadalquivir Marshes (SW Spain), the single most important wintering site for waterfowl breeding in Europe. We use a multivariate state-space approach to estimate the effects of biotic interactions, local environmental forcing during winter and large-scale climate during breeding and migration on wintering multispecies abundance fluctuations, while accounting for partial observability (observation error and missing data) in both population and environmental data. 3. The joint effect of local weather and large-scale climate explained 31·6% of variance at the community level, while the variability explained by interspecific interactions was negligible (<5%). In general, abiotic conditions during winter prevailed over conditions experienced during breeding and migration. Across species, a pervasive and coherent nonlinear signal of environmental variability on population dynamics suggests weaker forcing at extreme values of abiotic variables. 4. Modelling missing observations through data augmentation increased the estimated magnitude of environmental forcing by an average 30·1% and reduced the impact of stochasticity by 39·3% when accounting for observation error. Interestingly however, the impact of environmental forcing on community dynamics was underestimated by an average 15·3% and environmental stochasticity overestimated by 14·1% when ignoring both observation error and data augmentation. 5. These results provide a salient example of sequential multiscale environmental forcing in a major migratory bird community, which suggests a demographic link between the breeding and wintering grounds operating through nonlinear environmental effects. Remarkably, this study highlights that modelling observation error in the environmental covariates of an ecological model can be proportionally more important than modelling this source of variance in the population data.     

Comparative population dynamics of large and small mammals in the Northern Hemisphere: deterministic and stochastic forces

Deterministic feedbacks within populations interact with extrinsic, stochastic processes to generate complex patterns of animal abundance over time and space. Animals inherently differ in their responses to fluctuating environments due to differences in body sizes and life history traits. However, controversy remains about the relative importance of deterministic and stochastic forces in shaping population dynamics of large and small mammals. We hypothesized that effects of environmental stochasticity and density dependence are stronger in small mammal populations relative to their effects in large mammal populations and thus differentiate the patterns of population dynamics between them. We conducted an extensive, comparative analysis of population dynamics in large and small mammals to test our hypothesis, using seven population parameters to describe general dynamic patterns for 23 (14 species) time series of observations of abundance of large mammals and 38 (21 species) time series for small mammals. We used state‐space models to estimate the strength of direct and delayed density dependence as well as the strength of environmental stochasticity. We further used phylogenetic comparative analysis to detect differences in population dynamic patterns and individual population parameters, respectively, between large and small mammals. General population dynamic patterns differed between large and small mammals. However, the strength of direct and delayed density dependence was comparable between large and small mammals. Moreover, the variances of population growth rates and environmental stochasticity were greater in small mammals than in large mammals. Therefore, differences in population response to stochastic forces and strength of environmental stochasticity are the primary factor that differentiates population dynamic patterns between large and small mammal species.     

Intrinsic and extrinsic determinants of mountain pine beetle population growth

1 Mountain pine beetle Dendroctonus ponderosae populations have large, economically significant outbreaks. Density dependence and environmental variability are expected to have important effects on their dynamics. We analysed time series data from an outbreak in the 1930s to determine the relative importance of population density and environmental variability on local population growth rates.
2 Resource depletion occurred rapidly at the scale of 0.4 ha and population growth rates were strongly density dependent. Annual environmental changes did not have detectable effects on population growth rates, leading to the conclusion that intrinsic processes influenced local population density more than extrinsic factors during this outbreak.
3 Our calculated value of r _max (1.16) does not suggest intrinsically cyclic population dynamics. Our estimate of r _max and density dependence will be useful in developing applied models of mountain pine beetle outbreaks, and the subsequent evaluation of management strategies.     

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.     

Shifting patterns: malaria dynamics and rainfall variability in an African highland

The long-term patterns of malaria in the East African highlands typically involve not only a general upward trend in cases but also a dramatic increase in the size of epidemic outbreaks. The role of climate variability in driving epidemic cycles at interannual time scales remains controversial, in part because it has been seen as conflicting with the alternative explanation of purely endogenous cycles exclusively generated by the nonlinear dynamics of the disease. We analyse a long temporal record of monthly cases from 1970 to 2003 in a highland of western Kenya with both a time-series epidemiological model (time-series susceptible-infected-recovered) and a statistical approach specifically developed for non-stationary patterns. Results show that multiyear cycles of malaria outbreaks appear in the 1980s, concomitant with the timing of a regime shift in the dynamics of cases; the cycles become more pronounced in the 1990s, when the coupling between disease and rainfall is also stronger as the variance of rainfall increased at the frequencies of coupling. Disease dynamics and climate forcing play complementary and interacting roles at different temporal scales. Thus, these mechanisms should not be viewed as alternative and their interaction needs to be integrated in the development of future predictive models.     

Spatial synchrony in red grouse population dynamics

Red grouse Lagopus lagopus scoticus populations exhibit unstable dynamics that are often characterised by regular periodic fluctuations in abundance. Time-series' of grouse harvesting records collected from 287 management units (moors) across Scotland, England and Wales were analysed to investigate the broad scale patterns of synchrony in these fluctuations. Estimation of the spatial autocorrelation of grouse population dynamics across moors indicates relatively high levels of synchrony between populations on adjacent moors, but that this synchrony declines sharply with increasing inter-moor distance. At distances of greater than 100  km, grouse population time-series exhibit only weakly positive cross-correlation coefficients. Twenty-eight geographical, environmental and other candidate variables were examined to construct a general linear model to explain variation in local synchrony. Grouse moor productivity (average size of shooting bag), distance from the Atlantic coast moving in a north-easterly direction, April and June temperatures, and June rainfall significantly increased the explanatory power of this model. An understanding of the processes underlying synchrony in red grouse population dynamics is a prerequisite to anticipating the effects of large-scale environmental change on regional patterns of grouse distribution and abundance.     

Temporal stability of European rocky shore assemblages: variation across a latitudinal gradient and the role of habitat‐formers

Compensatory dynamics, overyielding and statistical averaging are mechanisms promoting the temporal stability of natural communities. Using the model of European intertidal rocky shore assemblages and collating 17 datasets, we investigated how the strength of these stability‐enhancing mechanisms varies with latitude and how it can be altered by the loss of habitat‐formers (e.g. canopy‐forming macroalgae). Community stability decreased with increasing latitude, mostly as a consequence of a greater synchronization of species fluctuations. Statistical averaging and overyielding (i.e. richness effect) promoted stability, but their strength did not vary with latitude. An experimental removal of macroalgal canopies caused a strengthening of the statistical averaging effect that was consistent across the latitudinal gradient investigated. Nonetheless, the loss of canopies depressed stability by enhancing the synchronization of species fluctuations on southernmost shores, while it had weak effects on shores at higher latitudes. Variation in life‐history traits among canopy‐forming species and/or in prevailing environmental conditions across a gradient of latitude could underlie variable effects of habitat‐formers on species fluctuations. Our study shows 1) that the stability of intertidal assemblages and strength of compensatory dynamics varies with latitude, 2) that canopy‐forming macroalgae, exerting a strong control on understorey species, can influence the strength of compensatory dynamics and 3) that biological forcing (i.e. facilitation) can be as important as environmental forcing in enhancing the synchronization of species fluctuations.     

Population fluctuations and regulation in great snipe: a time-series analysis

1. During the last centuries, the breeding range of the great snipe Gallinago media has declined dramatically in the western part of its distribution. To examine present population dynamics in the Scandinavian mountains, we collected and analysed a 19-year time series of counts of great snipe males at leks in central Norway, 1987-2005. 2. The population showed large annual fluctuations in the number of males displaying at lek sites (range 45-90 males at the peak of the mating season), but no overall trend. 3. We detected presence of direct density-dependent mechanisms regulating this population. Inclusion of the density-dependent term in a Ricker-type model significantly improved the fit with observed data (evaluated with Parametric Bootstrap Likelihood Ratio tests and Akaike's Information Criterion for small sample size). 4. An analysis of (a number of a priori likely) environmental covariates suggests that the population dynamics were affected by conditions influencing reproduction and survival of offspring during the summer, but not by conditions influencing survival at the wintering grounds in Africa. This is in contrast to many altricial birds breeding in the northern hemisphere, and supports the idea that population dynamics of migratory nidifugous birds are more influenced by conditions during reproduction. 5. Inclusion of these external factors into our model improved the detectability of density dependence. This illustrates that allowing for external effects may increase statistical power of density dependence tests and thus be of particular importance in relatively short time series. 6. In our best model of the population dynamics, two likely density-independent offspring survival covariates explained 47.3% of the variance in great snipe numbers (predation pressure estimated by willow grouse reproductive success and food availability estimated by the amount of precipitation in June), whereas density dependence explained 35.5%. Demographic stochasticity and unidentified environmental stochasticity may account for the remaining 17.2%.