Environmental Uncertainty and Variable Diapause

We analyze a stage-structured model of a population that displays variable diapause in a randomly varying environment. The ruggedness of the environment is measured by the extent of random variation in per-capita reproductive success. We show how variable diapause and environmental characteristics affect the population′s stochastic growth rate. In rugged unpredictable environments, phenotypes that show some tendency to diapause are found to have a higher growth rate than nondiapausing phenotypes. In harsh rugged environments, some tendency to diapause may be all that permits population persistence. Positive serial autocorrelation causes the optimal diapause fraction to decrease, while negative autocorrelation causes that fraction to increase. The structured model behaves very differently from a scalar model for large diapause fractions even in uncorrelated environments, and in many cases predicts a broad optimum. The difference between models is due to the extreme variability of stage structure in populations subject to even small variability when diapause tendency is high.     

Environmental variability and population dynamics: do European and North American ducks play by the same rules?

Density dependence, population regulation, and variability in population size are fundamental population processes, the manifestation and interrelationships of which are affected by environmental variability. However, there are surprisingly few empirical studies that distinguish the effect of environmental variability from the effects of population processes. We took advantage of a unique system, in which populations of the same duck species or close ecological counterparts live in highly variable (north American prairies) and in stable (north European lakes) environments, to distinguish the relative contributions of environmental variability (measured as between‐year fluctuations in wetland numbers) and intraspecific interactions (density dependence) in driving population dynamics. We tested whether populations living in stable environments (in northern Europe) were more strongly governed by density dependence than populations living in variable environments (in North America). We also addressed whether relative population dynamical responses to environmental variability versus density corresponded to differences in life history strategies between dabbling (relatively “fast species” and governed by environmental variability) and diving (relatively “slow species” and governed by density) ducks. As expected, the variance component of population fluctuations caused by changes in breeding environments was greater in North America than in Europe. Contrary to expectations, however, populations in more stable environments were not less variable nor clearly more strongly density dependent than populations in highly variable environments. Also, contrary to expectations, populations of diving ducks were neither more stable nor stronger density dependent than populations of dabbling ducks, and the effect of environmental variability on population dynamics was greater in diving than in dabbling ducks. In general, irrespective of continent and species life history, environmental variability contributed more to variation in species abundances than did density. Our findings underscore the need for more studies on populations of the same species in different environments to verify the generality of current explanations about population dynamics and its association with species life history.     

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.     

Persistence of plague outbreaks among great gerbils in Kazakhstan: effects of host population dynamics

Outbreaks of plague (Yersinia pestis) among great gerbils (Rhombomys opimus) generally require a high host abundance to be initiated. The duration of an outbreak is expected to depend on the subsequent development of this abundance; however, prediction is nontrivial due to the complexity of the gerbil–plague system. The aim of this study was to investigate how the duration of outbreaks depends on different types of host population dynamics generated from: a cyclic model; an autoregressive model giving irregular fluctuations; and a simple model with uncorrelated fluctuations. For each model, outbreak duration was studied under various levels of mean and variability of host abundance. Its focus on the effect of different gerbil dynamics sets this study apart from the few published studies on diseases in dynamic host populations. Plague outbreaks were simulated in a cellular automaton model based on statistical analysis of archived records of plague and host abundance. Temporal autocorrelation was found to make outbreak duration less sensitive to changes in mean abundance than uncorrelated fluctuations. Cyclicity had little effect on the mean duration of outbreaks, but resulted in a multimodal distribution. For all three types of gerbil dynamics, increased variability in gerbil abundance reduced the duration of outbreaks when the mean abundance was high (paralleling results on the risk of species extinction in fluctuating environments), but increased their duration when the mean abundance was lower. Spatial heterogeneity was briefly tested and produced longer outbreaks than the homogenous case. The results are relevant to predicting plague activity in populations of great gerbils.     

Prolonged diapause: a trait increasing invasion speed?

Invasive species are considered to be the second cause of biodiversity erosion, and one challenge is to determine the life history traits that cause an increased invasion capacity. Prolonged diapause is a major trait in evolution and insect population dynamics, but its effects on invasion speed remain unknown. From a recently developed mathematical approach (integro-difference equations) applied to the insect dormancy, we show that despite a dispersal cost, bet-hedging diapause strategies with low (0.1-0.2) prolonged diapause frequency (emergence after 1 or 2 years) can have a higher invasion speed than a simple diapause strategy (emergence after 1 year) when the environmental stochasticity is sufficiently high. In such conditions, prolonged diapause is a trait supporting invasion capacity by increasing population stochastic growth rate. This conclusion, which applies to a large range of demographic parameters, is in opposition to the usual view that prolonged dormancy is an alternative strategy to dispersal. However, prolonged diapause does not support invasion if the level of environmental stochasticity is low. Therefore, conclusion about its influence on invasion ability needs a good knowledge of environmental stochasticity in the introduction area of considered species.     

Environmental noise and population dynamics of the ciliated protozoa Tetrahymena thermophila in aquatic microcosms

Population theory predicts that the reddened environmental noise, especially in combination with high population growth rate, reddens population dynamics, increases population variability and strengthens environment–population correlation. We tested these predictions with axenic populations of ciliated protozoa Tetrahymena thermophila. Populations with low and high growth rate were cultured in a stable environment, and in environments with sublethal temperature fluctuations that had blue, white and red spectra (i.e. negatively autocorrelated, uncorrelated, or positively autocorrelated, respectively). Population size and biomass of individuals were determined at 3-h intervals for 18 days.
Dynamics of all populations were reddened, suggesting that internal mechanisms can redden the population spectra. However, population dynamics were reddest, variability highest, and environment–population correlation strongest in the red environment as predicted. Contrary to theoretical predictions and previous empirical findings, population growth rate (r_max being equal to 0.05 and 0.3 h⁻¹) had no effect on population dynamics.
Mean cell size and variability of cell size were affected by the presence and type of environmental noise suggesting that the physiological consequences of variability depend on colour. Environmental variability decreased mean population size and biomass and the decrease was strongest in rapidly fluctuating blue and white environments. The latter finding implies that rapid fluctuations are physiologically stressful, an effect that is not accounted for in the basic population models.     

A stochastic model for extinction and recurrence of epidemics: estimation and inference for measles outbreaks

Epidemic dynamics pose a great challenge to stochastic modelling because chance events are major determinants of the size and the timing of the outbreak. Reintroduction of the disease through contact with infected individuals from other areas is an important latent stochastic variable. In this study we model these stochastic processes to explain extinction and recurrence of epidemics observed in measles. We develop estimating functions for such a model and apply the methodology to temporal case counts of measles in 60 cities in England and Wales. In order to estimate the unobserved spatial contact process we suggest a method based on stochastic simulation and marginal densities. The estimation results show that it is possible to consider a unified model for the UK cities where the parameters depend on the city size. Stochastic realizations from the dynamic model realistically capture the transitions from an endemic cyclic pattern in large populations to irregular epidemic outbreaks in small human host populations.     

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.     

Temporal Population Genetics of Time Travelling Insects: A Long Term Study in a Seed-Specialized Wasp

Many animal species experiencing spatial or interannual fluctuations of their environment are capable of prolonged diapause, a kind of dormancy that extends over more than one year. Such a prolonged diapause is commonly perceived as a temporal demographic refuge in stochastic environments, but empirical evidence is still lacking of its consequences on temporal population genetic structures. In this long-term study, we investigated how a particular pattern of prolonged diapause may influence the temporal population genetics of the invasive seed-specialized wasp Megastigmus schimitscheki (Hymenoptera: Torymidae) in southeastern France. We characterized the diapause strategy of M. schimitscheki using records of emergence from diapause in 97 larval cohorts, and we conducted a temporal population genetic study on a natural invasive wasp population sampled during ten consecutive years (1999–2008) using polymorphic microsatellite markers. We found that M. schimitscheki can undergo a prolonged diapause of up to five years and displays two main adult emergence peaks after two and four years of diapause. Such a bimodal and atypical pattern did not disrupt temporal gene flow between cohorts produced in even and in odd years during the period of the study. Unexpectedly, we found that this wasp population consisted of two distinct genetic sub-populations that strongly diverged in their diapause strategies, with very few admixed individuals. One of the sub-populations displayed both short and prolonged diapause (2 and 4 years respectively) in equal proportions, whereas the other sub-population displayed mainly short diapause. This study provided empirical evidence that prolonged diapause phenotypes can substantially contribute to reproduction and impact temporal genetic structures. Prolonged diapause is likely to act as both demographic and genetic refuges for insect populations living in fluctuating environments.     

Environmental Variation Generates Environmental Opportunist Pathogen Outbreaks

Many socio-economically important pathogens persist and grow in the outside host environment and opportunistically invade host individuals. The environmental growth and opportunistic nature of these pathogens has received only little attention in epidemiology. Environmental reservoirs are, however, an important source of novel diseases. Thus, attempts to control these diseases require different approaches than in traditional epidemiology focusing on obligatory parasites. Conditions in the outside-host environment are prone to fluctuate over time. This variation is a potentially important driver of epidemiological dynamics and affect the evolution of novel diseases. Using a modelling approach combining the traditional SIRS models to environmental opportunist pathogens and environmental variability, we show that epidemiological dynamics of opportunist diseases are profoundly driven by the quality of environmental variability, such as the long-term predictability and magnitude of fluctuations. When comparing periodic and stochastic environmental factors, for a given variance, stochastic variation is more likely to cause outbreaks than periodic variation. This is due to the extreme values being further away from the mean. Moreover, the effects of variability depend on the underlying biology of the epidemiological system, and which part of the system is being affected. Variation in host susceptibility leads to more severe pathogen outbreaks than variation in pathogen growth rate in the environment. Positive correlation in variation on both targets can cancel the effect of variation altogether. Moreover, the severity of outbreaks is significantly reduced by increase in the duration of immunity. Uncovering these issues helps in understanding and controlling diseases caused by environmental pathogens.     

Persistence of structured populations in random environments

Environmental fluctuations often have different impacts on individuals that differ in size, age, or spatial location. To understand how population structure, environmental fluctuations, and density-dependent interactions influence population dynamics, we provide a general theory for persistence for density-dependent matrix models in random environments. For populations with compensating density dependence, exhibiting “bounded” dynamics, and living in a stationary environment, we show that persistence is determined by the stochastic growth rate (alternatively, dominant Lyapunov exponent) when the population is rare. If this stochastic growth rate is negative, then the total population abundance goes to zero with probability one. If this stochastic growth rate is positive, there is a unique positive stationary distribution. Provided there are initially some individuals in the population, the population converges in distribution to this stationary distribution and the empirical measures almost surely converge to the distribution of the stationary distribution. For models with overcompensating density-dependence, weaker results are proven. Methods to estimate stochastic growth rates are presented. To illustrate the utility of these results, applications to unstructured, spatially structured, and stage-structured population models are given. For instance, we show that diffusively coupled sink populations can persist provided that within patch fitness is sufficiently variable in time but not strongly correlated across space.     

Phenotypic plasticity and population viability: the importance of environmental predictability

Phenotypic plasticity plays a key role in modulating how environmental variation influences population dynamics, but we have only rudimentary understanding of how plasticity interacts with the magnitude and predictability of environmental variation to affect population dynamics and persistence. We developed a stochastic individual-based model, in which phenotypes could respond to a temporally fluctuating environmental cue and fitness depended on the match between the phenotype and a randomly fluctuating trait optimum, to assess the absolute fitness and population dynamic consequences of plasticity under different levels of environmental stochasticity and cue reliability. When cue and optimum were tightly correlated, plasticity buffered absolute fitness from environmental variability, and population size remained high and relatively invariant. In contrast, when this correlation weakened and environmental variability was high, strong plasticity reduced population size, and populations with excessively strong plasticity had substantially greater extinction probability. Given that environments might become more variable and unpredictable in the future owing to anthropogenic influences, reaction norms that evolved under historic selective regimes could imperil populations in novel or changing environmental contexts. We suggest that demographic models (e.g. population viability analyses) would benefit from a more explicit consideration of how phenotypic plasticity influences population responses to environmental change.     

Selective consequences of catastrophes for growth rates in a stream-dwelling salmonid

Optimal life histories in a fluctuating environment are likely to differ from those that are optimal in a constant environment, but we have little understanding of the consequences of bounded fluctuations versus episodic massive mortality events. Catastrophic disturbances, such as floods, droughts, landslides and fires, substantially alter the population dynamics of affected populations, but little has been done to investigate how catastrophes may act as a selective agent for life-history traits. We use an individual-based model of population dynamics of the stream-dwelling salmonid marble trout (Salmo marmoratus) to investigate how trade-offs between the growth and mortality of individuals and density-dependent body growth can lead to the maintenance of a wide or narrow range of individual variation in body growth rates in environments that are constant (i.e., only demographic stochasticity), variable (i.e., environmental stochasticity), or variable with catastrophic events that cause massive mortalities (e.g., flash floods). We find that occasional episodes of massive mortality can substantially reduce persistent variability in individual growth rates. Lowering the population density reduces density dependence and allows for higher fitness of more opportunistic strategies (rapid growth and early maturation) during the recovery period.     

The evolution of parental care in stochastic environments

Parental care is of fundamental importance to understanding reproductive strategies and allocation decisions. Here, we explore how parental care strategies evolve in variable environments. Using a set of life-history trait trade-offs, we explore the relative costs and benefits of parental care in stochastic environments. Specifically, we consider the cases in which environmental variability results in varying adult death rates, egg death rates, reproductive rate and carrying capacity. Using a measure of fitness appropriate for stochastic environments, we find that parental care has the potential to evolve over a wide range of life-history characteristics when the environment is variable. A variable environment that affects adult or egg death rates can either increase or decrease the fitness of care relative to that in a constant environment, depending on the specific costs of care. Variability that affects carrying capacity or adult reproductive rate has negligible effects on the fitness associated with care. Increasing parental care across different life-history stages can increase fitness gains in variable environments. Costly investment in care is expected to affect the overall fitness benefits, the fitness optimum and rate of evolution of parental care. In general, we find that environmental variability, the life-history traits affected by such variability and the specific costs of care interact to determine whether care will be favoured in a variable environment and what levels of care will be selected.     

Impact of temperature shifts on the joint evolution of seed dormancy and size

Seed dormancy and size are two important life‐history traits that interplay as adaptation to varying environmental settings. As evolution of both traits involves correlated selective pressures, it is of interest to comparatively investigate the evolution of the two traits jointly as well as independently. We explore evolutionary trajectories of seed dormancy and size using adaptive dynamics in scenarios of deterministic or stochastic temperature variations. Ecological dynamics usually result in unbalanced population structures, and temperature shifts or fluctuations of high magnitude give rise to more balanced ecological structures. When only seed dormancy evolves, it is counter‐selected and temperature shifts hasten this evolution. Evolution of seed size results in the fixation of a given strategy and evolved seed size decreases when seed dormancy is lowered. When coevolution is allowed, evolutionary variations are reduced while the speed of evolution becomes faster given temperature shifts. Such coevolution scenarios systematically result in reduced seed dormancy and size and similar unbalanced population structures. We discuss how this may be linked to the system stability. Dormancy is counter‐selected because population dynamics lead to stable equilibrium, while small seeds are selected as the outcome of size‐number trade‐offs. Our results suggest that unlike random temperature variation between generations, temperature shifts with high magnitude can considerably alter population structures and accelerate life‐history evolution. This study increases our understanding of plant evolution and persistence in the context of climate changes.     

Facilitation and competition interact with seed dormancy to affect population dynamics in annual plants

Seed dormancy increases population size via bet-hedging and by limiting negative interactions (e.g., competition) among individuals. On the other hand, individuals also interact positively (e.g., facilitation), and in some systems, facilitation among juveniles precedes competition among adults in the same generation. Nevertheless, studies of the benefits of seed dormancy typically ignore facilitation. Using a population growth model, we ask how the facilitation–competition balance interacts with seed dormancy rate to affect population dynamics in constant and variable environments. Facilitation increases the growth rate and equilibrium size (in both constant and variable environments) and reduces the extinction rate of populations (in a variable environment), and a higher rate of seed dormancy allows populations with facilitation to reach larger sizes. However, the combined benefits of facilitation and a high dormancy rate only occur in large populations. In small populations, weak facilitation does not affect the growth rate, but does induce a weak demographic Allee effect (where population growth decreases with decreasing population size). Our results suggest that facilitation within populations can interact with bet-hedging traits (such as dormancy) or other traits that mediate density to affect population dynamics. Further, by ensuring survival but limiting reproduction, ontogenetic switches from facilitation to competition may enable populations to persist but limit their maximum size in variable environments. Such intrinsic regulation of populations could then contribute to the maintenance of similar species within communities.     

Impacts of dispersal on rapid adaptation and dynamic stability of Daphnia in fluctuating environments

Prior ecological research has shown that spatial processes can enhance the temporal stability of populations in fluctuating environments. Less explored is the effect of dispersal on rapid adaptation and its concomitant impact on population dynamics. For asexually reproducing populations, theory predicts that dispersal in fluctuating environments can facilitate asynchrony among clones and enhance stability by reducing temporal variability of total population abundance. This effect is predicted when clones exhibit heritable variation in environmental optima and when fluctuations occur asynchronously among patches. We tested this in the field using artificial ponds and metapopulations composed of a diverse assemblage of Daphnia pulex clones. We directly manipulated dispersal presence/absence and environmental fluctuations in the form of nutrient pulses. Consistent with predictions, dispersal enhanced temporal asynchrony among clones in the presence of nutrient pulses; this in turn stabilized population dynamics. This effect only emerged when patches experienced spatially asynchronous nutrient pulses (dispersal had no effect when patches were synchronously pulsed). Clonal asynchrony was driven by strong positive selection for a single clone that exhibited a performance advantage under conditions of low resource availability. Our work highlights the importance of dispersal as a driver of eco-evolutionary dynamics and population stability in variable environments.     

Variability in primary productivity determines metapopulation dynamics

Temporal variability in primary productivity can change habitat quality for consumer species by affecting the energy levels available as food resources. However, it remains unclear how habitat-quality fluctuations may determine the dynamics of spatially structured populations, where the effects of habitat size, quality and isolation have been customarily assessed assuming static habitats. We present the first empirical evaluation on the effects of stochastic fluctuations in primary productivity—a major outcome of ecosystem functions—on the metapopulation dynamics of a primary consumer. A unique 13-year dataset from an herbivore rodent was used to test the hypothesis that inter-annual variations in primary productivity determine spatiotemporal habitat occupancy patterns and colonization and extinction processes. Inter-annual variability in productivity and in the growing season phenology significantly influenced habitat colonization patterns and occupancy dynamics. These effects lead to changes in connectivity to other potentially occupied habitat patches, which then feed back into occupancy dynamics. According to the results, the dynamics of primary productivity accounted for more than 50% of the variation in occupancy probability, depending on patch size and landscape configuration. Evidence connecting primary productivity dynamics and spatiotemporal population processes has broad implications for metapopulation persistence in fluctuating and changing environments.     

Can hyperparasitoids cause large‐scale outbreaks of insect herbivores?

Synchronous population fluctuations occur in many species and have large economic impacts, but remain poorly understood. Dispersal, climate and natural enemies have been hypothesized to cause synchronous population fluctuations across large areas. For example, insect herbivores cause extensive forest defoliation and have many natural enemies, such as parasitoids, that may cause landscape‐scale changes in density. Between outbreaks, parasitoid‐caused mortality of hosts/herbivores is high, but it drops substantially during outbreak episodes. Because of their essential role in regulating herbivore populations, we need to include parasitoids in spatial modelling approaches to more effectively manage insect defoliation. However, classic host‐parasitoid population models predict parasitoid density, and parasitoid density is difficult to relate to host‐level observations of parasitoid‐caused mortality. We constructed a novel model to study how parasitoids affect insect outbreaks at the landscape scale. The model represents metacommunity dynamics, in which herbivore regulation, colonisation and extinction are driven by interactions with the forest, primary parasitoids and hyperparasitoids. The model suggests that parasitoid spatial dynamics can produce landscape‐scale outbreaks. Our results propose the testable prediction that hyperparasitoid prevalence should increase just before the onset of an outbreak because of hyperparasitoid overexploitation. If verified empirically, hyperparasitoid distribution could provide a biotic indicator that an outbreak will occur.     

Geographical gradients in the population dynamics of North American prairie ducks

1. Geographic gradients in population dynamics may occur because of spatial variation in resources that affect the deterministic components of the dynamics (i.e. carrying capacity, the specific growth rate at small densities or the strength of density regulation) or because of spatial variation in the effects of environmental stochasticity. To evaluate these, we used a hierarchical Bayesian approach to estimate parameters characterizing deterministic components and stochastic influences on population dynamics of eight species of ducks (mallard, northern pintail, blue-winged teal, gadwall, northern shoveler, American wigeon, canvasback and redhead (Anas platyrhynchos, A. acuta, A. discors, A. strepera, A. clypeata, A. americana, Aythya valisineria and Ay. americana, respectively) breeding in the North American prairies, and then tested whether these parameters varied latitudinally. 2. We also examined the influence of temporal variation in the availability of wetlands, spring temperature and winter precipitation on population dynamics to determine whether geographical gradients in population dynamics were related to large-scale variation in environmental effects. Population variability, as measured by the variance of the population fluctuations around the carrying capacity K, decreased with latitude for all species except canvasback. This decrease in population variability was caused by a combination of latitudinal gradients in the strength of density dependence, carrying capacity and process variance, for which details varied by species. 3. The effects of environmental covariates on population dynamics also varied latitudinally, particularly for mallard, northern pintail and northern shoveler. However, the proportion of the process variance explained by environmental covariates, with the exception of mallard, tended to be small. 4. Thus, geographical gradients in population dynamics of prairie ducks resulted from latitudinal gradients in both deterministic and stochastic components, and were likely influenced by spatial differences in the distribution of wetland types and shapes, agricultural practices and dispersal processes. 5. These results suggest that future management of these species could be improved by implementing harvest models that account explicitly for spatial variation in density effects and environmental stochasticity on population abundance.