An updated perspective on the role of environmental autocorrelation in animal populations

Ecological theory predicts that the presence of temporal autocorrelation in environments can considerably affect population extinction risk. However, empirical estimates of autocorrelation values in animal populations have not decoupled intrinsic growth and density feedback processes from environmental autocorrelation. In this study, we first discuss how the autocorrelation present in environmental covariates can be reduced through nonlinear interactions or by interactions with multiple limiting resources. We then estimated the degree of environmental autocorrelation present in the Global Population Dynamics Database using a robust, model-based approach. Our empirical results indicate that time series of animal populations are affected by low levels of environmental autocorrelation, a result consistent with predictions from our theoretical models. Claims supporting the importance of autocorrelated environments have been largely based on indirect empirical measures and theoretical models seldom anchored in realistic assumptions. It is likely that a more nuanced understanding of the effects of autocorrelated environments is necessary to reconcile our conclusions with previous theory. We anticipate that our findings and other recent results will lead to improvements in understanding how to incorporate fluctuating environments into population risk assessments.     

Estimating environmental effects on population dynamics: consequences of observation error

Within the paradigm of population dynamics a central task is to identify environmental factors affecting population change and to estimate the strength of these effects. We here investigate the impact of observation errors in measurements of population densities on estimates of environmental effects. Adding observation errors may change the autocorrelation of a population time series with potential consequences for estimates of effects of autocorrelated environmental covariates. Using Monte Carlo simulations, we compare the performance of maximum likelihood estimates from three stochastic versions of the Gompertz model (log–linear first order autoregressive model), assuming 1) process error only, 2) observation error only, and 3) both process and observation error (the linear state–space model on log‐scale). We also simulated population dynamics using the Ricker model, and evaluated the corresponding maximum likelihood estimates for process error models. When there is observation error in the data and the considered environmental variable is strongly autocorrelated, its estimated effect is likely to be biased when using process error models. The environmental effect is overestimated when the sign of the autocorrelations of the intrinsic dynamics and the environment are the same and underestimated when the signs differ. With non‐autocorrelated environmental covariates, process error models produce fairly exact point estimates as well as reliable confidence intervals for environmental effects. In all scenarios, observation error models produce unbiased estimates with reasonable precision, but confidence intervals derived from the likelihood profiles are far too optimistic if there is process error present. The safest approach is to use state–space models in presence of observation error. These are factors worthwhile to consider when interpreting earlier empirical results on population time series, and in future studies, we recommend choosing carefully the modelling approach with respect to intrinsic population dynamics and covariate autocorrelation.     

Effects on population persistence: the interaction between environmental noise colour,intraspecific competition and space

It is accepted that accurate estimation of risk of population extinction, or persistence time, requires prediction of the effect of fluctuations in the environment on population dynamics. Generally, the greater the magnitude, or variance, of environmental stochasticity, the greater the risk of population extinction. Another characteristic of environmental stochasticity, its colour, has been found to affect population persistence. This is important because real environmental variables, such as temperature, are reddened or positively temporally autocorrelated. However, recent work has disagreed about the effect of reddening environmental stochasticity. Ripa and Lundberg (1996) found increasing temporal autocorrelation (reddening) decreased the risk of extinction, whereas a simple and powerful intuitive argument (Lawton 1988) predicts increased risk of extinction with reddening. This study resolves the apparent contradiction, in two ways, first, by altering the dynamic behaviour of the population models. Overcompensatory dynamics result in persistence times increasing with increased temporal autocorrelation; undercompensatory dynamics result in persistence times decreasing with increased temporal autocorrelation. Secondly, in a spatially subdivided population, with a reasonable degree of spatial heterogeneity in patch quality, increasing temporal autocorrelation in the environment results in decreasing persistence time for both types of competition. Thus, the inclusion of coloured noise into ecological models can have subtle interactions with population dynamics.     

Spatial heterogeneity in climate change effects decouples the long‐term dynamics of wild reindeer populations in the high Arctic

The ‘Moran effect’ predicts that dynamics of populations of a species are synchronized over similar distances as their environmental drivers. Strong population synchrony reduces species viability, but spatial heterogeneity in density dependence, the environment, or its ecological responses may decouple dynamics in space, preventing extinctions. How such heterogeneity buffers impacts of global change on large‐scale population dynamics is not well studied. Here, we show that spatially autocorrelated fluctuations in annual winter weather synchronize wild reindeer dynamics across high‐Arctic Svalbard, while, paradoxically, spatial variation in winter climate trends contribute to diverging local population trajectories. Warmer summers have improved the carrying capacity and apparently led to increased total reindeer abundance. However, fluctuations in population size seem mainly driven by negative effects of stochastic winter rain‐on‐snow (ROS) events causing icing, with strongest effects at high densities. Count data for 10 reindeer populations 8–324 km apart suggested that density‐dependent ROS effects contributed to synchrony in population dynamics, mainly through spatially autocorrelated mortality. By comparing one coastal and one ‘continental’ reindeer population over four decades, we show that locally contrasting abundance trends can arise from spatial differences in climate change and responses to weather. The coastal population experienced a larger increase in ROS, and a stronger density‐dependent ROS effect on population growth rates, than the continental population. In contrast, the latter experienced stronger summer warming and showed the strongest positive response to summer temperatures. Accordingly, contrasting net effects of a recent climate regime shift—with increased ROS and harsher winters, yet higher summer temperatures and improved carrying capacity—led to negative and positive abundance trends in the coastal and continental population respectively. Thus, synchronized population fluctuations by climatic drivers can be buffered by spatial heterogeneity in the same drivers, as well as in the ecological responses, averaging out climate change effects at larger spatial scales.     

Are patterns of density dependence in the Global Population Dynamics Database driven by uncertainty about population abundance?

Density dependence in population growth rates is of immense importance to ecological theory and application, but is difficult to estimate. The Global Population Dynamics Database (GPDD), one of the largest collections of population time series available, has been extensively used to study cross-taxa patterns in density dependence. A major difficulty with assessing density dependence from time series is that uncertainty in population abundance estimates can cause strong bias in both tests and estimates of strength. We analyse 627 data sets in the GPDD using Gompertz population models and account for uncertainty via the Kalman filter. Results suggest that at least 45% of the time series display density dependence, but that it is weak and difficult to detect for a large fraction. When uncertainty is ignored, magnitude of and evidence for density dependence is strong, illustrating that uncertainty in abundance estimates qualitatively changes conclusions about density dependence drawn from the GPDD.     

Estimation of a Nonlinear Density-Dependence Parameter for Wild Turkey

Abstract: Although previous research and theory has suggested that wild turkey (Meleagris gallopavo) populations may be subject to some form of density dependence, there has been no effort to estimate and incorporate a density-dependence parameter into wild turkey population models. To estimate a functional relationship for density dependence in wild turkey, we analyzed a set of harvest-index time series from 11 state wildlife agencies. We tested for lagged correlations between annual harvest indices using partial autocorrelation analysis. We assessed the ability of the density-dependent theta-Ricker model to explain harvest indices over time relative to exponential or random walk growth models. We tested the homogeneity of the density-dependence parameter estimates (θ) from 3 different harvest indices (spring harvest no. reported harvest/effort, survey harvest/effort) and calculated a weighted average based on each estimate's variance and its estimated covariance with the other indices. To estimate the potential bias in parameter estimates from measurement error, we conducted a simulation study using the theta-Ricker with known values and lognormally distributed measurement error. Partial autocorrelation function analysis indicated that harvest indices were significantly correlated only with their value at the previous time step. The theta-Ricker model performed better than the exponential growth or random walk models for all 3 indices. Simulation of known parameters and measurement error indicated a strong positive upward bias in the density-dependent parameter estimate, with increasing measurement error. The average density-dependence estimate, corrected for measurement error ranged 0.25 ≤ θC ≤ 0.49, depending on the amount of measurement error and assumed spring harvest rate. We infer that density dependence is nonlinear in wild turkey, where growth rates are maximized at 39-42% of carrying capacity. The annual yield produced by density-dependent population growth will tend to be less than that caused by extrinsic environmental factors. This study indicates that both density-dependent and density-independent processes are important to wild turkey population growth, and we make initial suggestions on incorporating both into harvest management strategies.     

Intraspecific variation in the strength of density dependence in aphid populations

Abstract.  1. Experimental evidence is presented for positive, negative, and no density dependence from 32 independent density manipulations of milkweed aphids ( Aphis nerii ) in laboratory and field experiments. This substantial variation in intraspecific density dependence is associated with temperature and host-plant species.
2. It is reported that as population growth rate increases, density dependence becomes more strongly negative, suggesting that the monotonic definition of density dependence used in many common population models is appropriate for these aphids, and that population growth rate and carrying capacity are not directly proportional.
3. For populations that conform to these assumptions, population growth rate may be widely applicable as a predictor of the strength of density dependence.     

Evaluating the current condition of a threatened marine mammal population: Estimating northern sea otter (Enhydra lutris kenyoni) abundance in southwest Alaska

We estimated density and abundance of the threatened southwest Alaska distinct population segment of northern sea otters (Enhydra lutris kenyoni) in two management units. We conducted aerial surveys in Bristol Bay and South Alaska Peninsula management units in 2016, and modeled sea otter density and abundance with Bayesian hierarchical distance sampling models and spatial environmental covariates (depth, distance to shore, depth × distance to shore). Spatial environmental covariates substantially impacted sea otter group density in both management units, but effects sizes differed between the two management units. Abundance (9,733 otters, 95% CrI 6,412–17,819) and density (0.82 otters/km², 95% CrI 0.54–1.49) estimates for Bristol Bay indicated a moderate population size. In contrast, abundance (546 otters, 95% CrI 322–879) and density (0.06 otters/km², 95% CrI 0.03–0.09) estimates indicated a relatively low population size in South Alaska Peninsula. Overall, our results highlight the importance of accounting for the detection process in monitoring at-risk species to reduce the uncertainty associated with making conclusions about population declines.     

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.     

The effects of climate change on density‐dependent population dynamics of aquatic invertebrates

Global climate change has the potential to alter aquatic communities through changes in evapotranspiration and increased variability in precipitation. We used aquatic mesocosms to test the impacts of variable precipitation on population dynamics of common mosquito (Culicidae) and midge (Chironomidae) larvae that inhabit vernal pools. In a mixed deciduous forest in northern Vermont, USA, we orthogonally crossed seven levels of mean water level (increased rainfall) with seven levels of water level coefficient of variation (more variable rainfall) to simulate a broad array of climate change scenarios in 49 experimental mesocosms. The average abundance of Culicidae was highest at low water levels, whereas the average abundance of Chironomidae was highest at higher water levels and low variability in water level. Treatments and environmental and spatial covariates collectively explained 49% of the variance in mean abundance. For both taxa, we fit hierarchical Bayesian models to each 16‐week time series to estimate the parameters in a Gompertz logistic equation of population growth with density dependence. We found that Culicidae population growth rate increased with decreasing water levels and that 87% of the variance in Chironomidae density dependence could be explained by treatment. Collectively, these results suggest that climate change can alter abundances aquatic invertebrate taxa but not necessarily through the same mechanism on all populations. In the case of Culicidae the abundance is affected by changes in growth rate, and in Chironomidae by changes in the strength of density dependence.     

Detecting and estimating density dependence in wildlife populations

We review methods for detecting and assessing the strength of density dependence based on 2 types of approaches: surveys of population size and studies of life history traits, in particular demographic parameters. For the first type of studies, methods neglecting uncertainty in population size should definitely be abandoned. Bayesian approaches to simple state-space models accounting for uncertainty in population size are recommended, with some caution because of numerical difficulties and risks of model misspecification. Realistic state-space models incorporating features such as environmental covariates, age structure, etc., may lack power because of the shortness of the time series and the simultaneous presence of process and sampling variability. In all cases, complementing the population survey data with some external information, with priority on the intrinsic growth rate, is highly recommended. Methods for detecting density dependence in life history traits are generally conservative (i.e., tend to underestimate the strength of density dependence). Among approaches to correct for this effect, the state-space formulation of capture–recapture models is again the most promising. Foreseeable developments will exploit integrated monitoring combining population size surveys and individual longitudinal data in refined state-space models, for which a Bayesian approach is the most straightforward statistical treatment. One may thus expect an integration of various types of models that will make it possible to look at density dependence as a complex biological process interacting with other processes rather than in terms of a simple equation; modern statistical and modeling tools make such a synthesis within reach. © 2012 The Wildlife Society.     

RISK OF EXTIRPATION OF STELLER SEA LIONS IN THE GULF OF ALASKA AND ALEUTIAN ISLANDS: A POPULATION VIABILITY ANALYSIS BASED ON ALTERNATIVE HYPOTHESES FOR WHY SEA LIONS DECLINED IN WESTERN ALASKA

We estimated the risk that the Steller sea lion will be extirpated in western Alaska using a population viability analysis (PVA) that combined simulations with statistically fitted models of historical population dynamics. Our analysis considered the roles that density‐dependent and density‐independent factors may have played in the past, and how they might influence future population dynamics. It also established functional relationships between population size, population growth rate and the risk of extinction under alternative hypotheses about population regulation and environmental variability. These functional relationships can be used to develop recovery criteria and guide research and management decisions. Life table parameters (e.g., birth and survival rates) operating during the population decline (1978–2002) were estimated by fitting simple age‐structured models to time‐series of pup and non‐pup counts from 33 rookeries (subpopulations). The PVA was carried out by projecting all 33 subpopulations into the future using these estimated site‐specific life tables (with associated uncertainties) and different assumptions about carrying capacities and the presence or absence of density‐dependent population regulation. Results suggest that the overall predicted risk of extirpation of Steller sea lions as a species in western Alaska was low in the next 100 yr under all scenarios explored. However, most subpopulations of Steller sea lions had high probabilities of going extinct within the next 100 yr if trends observed during the 1990s were to continue. Two clusters of contiguous subpopulations occurring in the Unimak Pass area in the western Gulf of Alaska/eastern Aleutian Islands and the Seguam–Adak region in the central Aleutian Islands had relatively lower risks of extinction. Risks of extinction for a number of subpopulations in the Gulf of Alaska were reduced if the increases observed since the late 1990s continue into the future. The risks of subpopulations going extinct were small when density‐dependent compensation in birth and survival rates was assumed, even when random stochasticity in these vital rates was introduced.     

Estimating selection on neonatal traits in red deer using elasticity path analysis

Van Tienderen recently published a method that links selection gradients between a phenotypic trait and multiple fitness components with the effects of these fitness components on the population growth rate (mean absolute fitness). The method allows selection to be simultaneously estimated across multiple fitness components in a population dynamic framework. In this paper we apply the method to a population of red deer living in the North Block of the Isle of Rum, Scotland. We show that (1) selection on birth date and birth weight can operate through multiple fitness components simultaneously; (2) our estimates of the response to selection are consistent with the observed change in trait values that we cannot explain with environmental and phenotypic covariates; (3) selection on both traits has fluctuated over the course of the study; (4) selection operates through different fitness components in different years; and (5) no environmental covariates correlate with selection because different fitness components respond to density and climatic variation in contrasting ways.     

Modeling spatiotemporal abundance of mobile wildlife in highly variable environments using boosted GAMLSS hurdle models

Modeling organism distributions from survey data involves numerous statistical challenges, including accounting for zero‐inflation, overdispersion, and selection and incorporation of environmental covariates. In environments with high spatial and temporal variability, addressing these challenges often requires numerous assumptions regarding organism distributions and their relationships to biophysical features. These assumptions may limit the resolution or accuracy of predictions resulting from survey‐based distribution models. We propose an iterative modeling approach that incorporates a negative binomial hurdle, followed by modeling of the relationship of organism distribution and abundance to environmental covariates using generalized additive models (GAM) and generalized additive models for location, scale, and shape (GAMLSS). Our approach accounts for key features of survey data by separating binary (presence‐absence) from count (abundance) data, separately modeling the mean and dispersion of count data, and incorporating selection of appropriate covariates and response functions from a suite of potential covariates while avoiding overfitting. We apply our modeling approach to surveys of sea duck abundance and distribution in Nantucket Sound (Massachusetts, USA), which has been proposed as a location for offshore wind energy development. Our model results highlight the importance of spatiotemporal variation in this system, as well as identifying key habitat features including distance to shore, sediment grain size, and seafloor topographic variation. Our work provides a powerful, flexible, and highly repeatable modeling framework with minimal assumptions that can be broadly applied to the modeling of survey data with high spatiotemporal variability. Applying GAMLSS models to the count portion of survey data allows us to incorporate potential overdispersion, which can dramatically affect model results in highly dynamic systems. Our approach is particularly relevant to systems in which little a priori knowledge is available regarding relationships between organism distributions and biophysical features, since it incorporates simultaneous selection of covariates and their functional relationships with organism responses.     

The carrying capacity of ecosystems

We analyse the concept of carrying capacity (CC), from populations to the biosphere, and offer a definition suitable for any level. For communities and ecosystems, the CC evokes density‐dependence assumptions analogous to those of population dynamics. At the biosphere level, human CC is uncertain and dynamic, leading to apprehensive rather than practical conclusions. The term CC is widely used among ecological disciplines but remains vague and elusive. We propose the following definition: the CC is ‘the limit of growth or development of each and all hierarchical levels of biological integration, beginning with the population, and shaped by processes and interdependent relationships between finite resources and the consumers of those resources’. The restrictions of the concept relate to the hierarchical approach. Emergent properties arise at each level, and environmental heterogeneity restrains the measurement and application of the CC. Because the CC entails a myriad of interrelated, ever‐changing biotic and abiotic factors, it must not be assumed constant, if we are to derive more effective and realistic management schemes. At the ecosystem level, stability and resilience are dynamic components of the CC. Historical processes that help shape global biodiversity (e.g. continental drift, glaciations) are likely drivers of large‐scale changes in the earth's CC. Finally, world population growth and consumption of resources by humanity will necessitate modifications to the paradigm of sustainable development, and demand a clear and fundamental understanding of how CC operates across all biological levels.     

The impact of mortality on predator population size and stability in systems with stage-structured prey

The relationships between a predator population's mortality rate and its population size and stability are investigated for several simple predator-prey models with stage-structured prey populations. Several alternative models are considered; these differ in their assumptions about the nature of density dependence in the prey's population growth; the nature of stage-transitions; and the stage-selectivity of the predator. Instability occurs at high, rather than low predator mortality rates in most models with highly stage-selective predation; this is the opposite of the effect of mortality on stability in models with homogeneous prey populations. Stage-selective predation also increases the range of parameters that lead to a stable equilibrium. The results suggest that it may be common for a stable predator population to increase in abundance as its own mortality rate increases in stable systems, provided that the predator has a saturating functional response. Sufficiently strong density dependence in the prey generally reverses this outcome, and results in a decrease in predator population size with increasing predator mortality rate. Stability is decreased when the juvenile stage has a fixed duration, but population increases with increasing mortality are still observed in large areas of stable parameter space. This raises two coupled questions which are as yet unanswered; (1) do such increases in population size with higher mortality actually occur in nature; and (2) if not, what prevents them from occurring? Stage-structured prey and stage-related predation can also reverse the 'paradox of enrichment', leading to stability rather than instability when prey growth is increased.     

Incorporating capture heterogeneity in the estimation of autoregressive coefficients of animal population dynamics using capture–recapture data

Population dynamic models combine density dependence and environmental effects. Ignoring sampling uncertainty might lead to biased estimation of the strength of density dependence. This is typically addressed using state‐space model approaches, which integrate sampling error and population process estimates. Such models seldom include an explicit link between the sampling procedures and the true abundance, which is common in capture–recapture settings. However, many of the models proposed to estimate abundance in the presence of capture heterogeneity lead to incomplete likelihood functions and cannot be straightforwardly included in state‐space models. We assessed the importance of estimating sampling error explicitly by taking an intermediate approach between ignoring uncertainty in abundance estimates and fully specified state‐space models for density‐dependence estimation based on autoregressive processes. First, we estimated individual capture probabilities based on a heterogeneity model for a closed population, using a conditional multinomial likelihood, followed by a Horvitz–Thompson estimate for abundance. Second, we estimated coefficients of autoregressive models for the log abundance. Inference was performed using the methodology of integrated nested Laplace approximation (INLA). We performed an extensive simulation study to compare our approach with estimates disregarding capture history information, and using R‐package VGAM, for different parameter specifications. The methods were then applied to a real data set of gray‐sided voles Myodes rufocanus from Northern Norway. We found that density‐dependence estimation was improved when explicitly modeling sampling error in scenarios with low process variances, in which differences in coverage reached up to 8% in estimating the coefficients of the autoregressive processes. In this case, the bias also increased assuming a Poisson distribution in the observational model. For high process variances, the differences between methods were small and it appeared less important to model heterogeneity.     

Global asymptotic stability of plant-seed bank models

Many plant populations have persistent seed banks, which consist of viable seeds that remain dormant in the soil for many years. Seed banks are important for plant population dynamics because they buffer against environmental perturbations and reduce the probability of extinction. Viability of the seeds in the seed bank can depend on the seed’s age, hence it is important to keep track of the age distribution of seeds in the seed bank. In this paper we construct a general density-dependent plant-seed bank model where the seed bank is age-structured. We consider density dependence in both seedling establishment and seed production, since previous work has highlighted that overcrowding can suppress both of these processes. Under certain assumptions on the density dependence, we prove that there is a globally stable equilibrium population vector which is independent of the initial state. We derive an analytical formula for the equilibrium population using methods from feedback control theory. We apply these results to a model for the plant species Cirsium palustre and its seed bank.     

Quantile regression estimates of animal population trends

Ecologists often estimate population trends of animals in time series of counts using linear regression to estimate parameters in a linear transformation of multiplicative growth models, where logarithms of rates of change in counts in time intervals are used as response variables. We present quantile regression estimates for the median (0.50) and interquartile (0.25, 0.75) relationships as an alternative to mean regression estimates for common density-dependent and density-independent population growth models. We demonstrate that the quantile regression estimates are more robust to outliers and require fewer distributional assumptions than conventional mean regression estimates and can provide information on heterogeneous rates of change ignored by mean regression. We provide quantile regression trend estimates for 2 populations of greater sage-grouse (Centrocercus urophasianus) in Wyoming, USA, and for the Crawford population of Gunnison sage-grouse (Centrocercus minimus) in southwestern Colorado, USA. Our selected Gompertz models of density dependence for both populations of greater sage-grouse had smaller negative estimates of density-dependence terms and less variation in corresponding predicted growth rates (λ) for quantile than mean regression models. In contrast, our selected Gompertz models of density dependence with piecewise linear effects of years for the Crawford population of Gunnison sage-grouse had predicted changes in λ across years from quantile regressions that varied more than those from mean regression because of heterogeneity in estimated λs that were both less and greater than mean estimates. Our results add to literature establishing that quantile regression provides better behaved estimates than mean regression when there are outlying growth rates, including those induced by adjustments for zeros in the time series of counts. The 0.25 and 0.75 quantiles bracketing the median provide robust estimates of population changes (λ) for the central 50% of time series data and provide a 50% prediction interval for a single new prediction without making parametric distributional assumptions or assuming homogeneous λs. Compared to mean estimates, our quantile regression trend estimates for greater sage-grouse indicated less variation in density-dependent λs by minimizing sensitivity to outlying values, and for Gunnison sage-grouse indicated greater variation in density-dependent λs associated with heterogeneity among quantiles.     

Direct negative density‐dependence in a pond‐breeding frog population

Understanding population dynamics is critical for the management of animal populations. Comparatively little is known about the relative importance of endogenous (i.e. density‐dependent) and exogenous (i.e. density‐independent) factors on the population dynamics of amphibians with complex life cycles. We examined the potential effects of density‐dependent and ‐independent (i.e. climatic) factors on population dynamics by analyzing a 15‐yr time series data of the agile frog Rana dalmatina population from Târnava Mare Valley, Romania. We used two statistical models: 1) the partial rate correlation function to identify the feedback structure and the potential time lags in the time series data and 2) a Gompertz state‐space model to simultaneously investigate direct and delayed density dependence as well as climatic effects on population growth rate. We found evidence for direct negative density dependence, whereas delayed density dependence and climate did not show a strong influence on population growth rate. Here we demonstrated that direct density dependence rather than delayed density dependence or climate determined the dynamics of our study population. Our results confirm the findings of many experimental studies and suggest that density dependence may buffer amphibian populations against environmental stress. Consequently, it may not be easy to scale up from individual‐level effects to population‐level effects.