Partitioning variance in population growth for models with environmental and demographic stochasticity.

How demographic factors lead to variation or change in growth rates can be investigated using life table response experiments (LTRE) based on structured population models. Traditionally, LTREs focused on decomposing the asymptotic growth rate, but more recently decompositions of annual 'realized' growth rates using 'transient' LTREs have gained in popularity. Transient LTREs have been used particularly to understand how variation in vital rates translate into variation in growth for populations under long-term study. For these, complete population models may be constructed to investigate how temporal variation in environmental drivers affect vital rates. Such investigations have usually come down to estimating covariate coefficients for the effects of environmental variables on vital rates, but formal ways of assessing how they lead to variation in growth rates have been lacking. We extend transient LTREs to further partition the contributions from vital rates into contributions from temporally varying factors that affect them. The decomposition allows one to compare the resultant effect on the growth rate of different environmental factors, as well as density dependence, which may each act via multiple vital rates. We also show how realized growth rates can be decomposed into separate components from environmental and demographic stochasticity. The latter is typically omitted in LTRE analyses. We illustrate these extensions with an integrated population model (IPM) for data from a 26 years study on northern wheatears (Oenanthe oenanthe), a migratory passerine bird breeding in an agricultural landscape. For this population, consisting of around 50-120 breeding pairs per year, we partition variation in realized growth rates into environmental contributions from temperature, rainfall, population density and unexplained random variation via multiple vital rates, and from demographic stochasticity. The case study suggests that variation in first year survival via the unexplained random component, and adult survival via temperature are two main factors behind environmental variation in growth rates. More than half of the variation in growth rates is suggested to come from demographic stochasticity, demonstrating the importance of this factor for populations of moderate size.

Why we should care about movements: Using spatially explicit integrated population models to assess habitat source-sink dynamics.

Assessing the source-sink status of populations and habitats is of major importance for understanding population dynamics and for the management of natural populations. Sources produce a net surplus of individuals (per capita contribution to the metapopulation > 1) and will be the main contributors for self-sustaining populations, whereas sinks produce a deficit (contribution < 1). However, making these types of assessments is generally hindered by the problem of separating mortality from permanent emigration, especially when survival probabilities as well as moved distances are habitat-specific. To address this long-standing issue, we propose a spatial multi-event integrated population model (IPM) that incorporates habitat-specific dispersal distances of individuals. Using information about local movements, this IPM adjusts survival estimates for emigration outside the study area. Analysing 24 years of data on a farmland passerine (the northern wheatear Oenanthe oenanthe), we assessed habitat-specific contributions, and hence the source-sink status and temporal variation of two key breeding habitats, while accounting for habitat- and sex-specific local dispersal distances of juveniles and adults. We then examined the sensitivity of the source-sink analysis by comparing results with and without accounting for these local movements. Estimates of first-year survival, and consequently habitat-specific contributions, were higher when local movement data were included. The consequences from including movement data were sex specific, with contribution shifting from sink to likely source in one habitat for males, and previously noted habitat differences for females disappearing. Assessing the source-sink status of habitats is extremely challenging. We show that our spatial IPM accounting for local movements can reduce biases in estimates of the contribution by different habitats, and thus reduce the overestimation of the occurrence of sink habitats. This approach allows combining all available data on demographic rates and movements, which will allow better assessment of source-sink dynamics and better informed conservation interventions.

New measures for evaluation of environmental perturbations using Before-After-Control-Impact analyses.

Before-After-Control-Impact (BACI) designs are powerful tools to derive inferences about environmental perturbations (e.g., hurricanes, restoration programs) when controlled experimental designs are unfeasible. Applications of BACI designs mostly rely on testing for a significant interaction between periods and treatments (so-called BACI contrast) to demonstrate the effects of the perturbation. However, significant interactions can emerge for several reasons, including when changes are larger in control sites, such that additional diagnostics must be performed to determine the full complexity of system changes. We propose two measures that detail the nature of change implied by BACI contrasts, along with its uncertainty. CI-divergence (Control-Impact divergence) quantifies to what extent control and impact sites have diverged between the after and the before period, whereas CI-contribution (Control-Impact contribution) quantifies to what extent the change between periods is stronger in impact sites relative to control sites. To illustrate how these two CI measures can be combined with BACI contrast to gain insights about effects of environmental perturbations, we used count data from the Swedish Breeding Bird Survey to investigate how hurricane Gudrun affected the long-term abundances of four bird species in forested areas of southern Sweden. Before-After-Control-Impact contrasts suggested the hurricane affected all four species. However, the values of the two CI measures strongly differed, even among species showing similar BACI contrasts. Those differences highlight qualitatively distinct population trajectories between periods and treatments requiring different ecological explanations. Overall, we show that BACI contrasts do not provide the full story in assessing the effects of environmental perturbations. The two CI measures can be used to assist ecological interpretations, or to specify detailed hypotheses about effects of restoration actions to allow stronger confirmatory inference about their outcomes. By providing a framework to develop more detailed explanations and hypotheses about ecological changes, the two CI measures can improve conclusions and strengthen evidence of effects of conservation actions and impact assessments under BACI designs.

Seed production and predation in a changing climate: new roles for resource and seed predator feedback?

Climate change may cause changes in the dynamics of populations beyond comparatively simple directional effects. To better understand complex effects on dynamics requires long-term studies of populations that experience changes in climatic conditions. We study the dynamics of a seed-production-seed-predation system, consisting of a perennial herb and its two seed predatory insects, over a 40-yr period during which climate change has caused the annual growing season to increase by 20 d. During this period, plant patches have increased almost threefold in size and seed production has slipped into a pattern of alternate high and low years with a higher variance than in the beginning of the period. We find that seed production is associated with precipitation of the present summer and a non-linear feedback from seed production of the previous year. When previous year's seed production is low, weather forcing and unexplained noise determine the extent of seed production. When previous seed production is high, depleted resources limit seed production. Resource depletion happened frequently in the latter parts of the study but rarely in the beginning. The changing patterns of seed production in turn affect the dynamics of seed predation, which is dominated by one of the seed predators. Its dynamics are strongly linked to seed density fluctuations, but its population growth rate is satiated when resource fluctuations become too large. In the latter part of the study period, when seed fluctuations were alternating between years of high and low density, satiation was common and there was a large increase in surviving seeds in good years. Our study illustrates that a changing climate can fundamentally influence patterns of long-term dynamics at multiple trophic levels.

Disentangling the effects of date, individual, and territory quality on the seasonal decline in fitness.

The seasonal timing of reproduction is a major fitness factor in many organisms. Commonly, individual fitness declines with time in the breeding season. We investigated three suggested but rarely tested hypotheses for this seasonal fitness decline: (1) time per se (date hypothesis), (2) late breeders are of lower quality than early ones (individual quality hypothesis), and (3) late breeders are breeding at poorer territories than early breeders (territory quality hypothesis). We used Bayesian variance component analyses to examine reproductive output (breeding success, number fledged, and number of recruits) from repeated observations of female Northern Wheatears (Oenanthe oenanthe) and individual territories from a 20-yr population study. The major part of the observed seasonal decline in reproductive output seemed to be driven by date-related effects, whereas female age and territory type (i.e., known indicators of temporary quality) contributed to a smaller degree. Other, persistent effects linked to individual and territory identity did not show any clear patterns on the seasonal decline in reproductive output. To better disentangle the quality effects (persistent and temporary) of individual and territory from effects caused by the deterioration of the environment we suggest a protocol combining experimental manipulation of breeding time with a variance-covariance partitioning method used here.

Monte Carlo estimation of stage structured development from cohort data.

Cohort data are frequently collected to study stage-structured development and mortalities of many organisms, particularly arthropods. Such data can provide information on mean stage durations, among-individual variation in stage durations, and on mortality rates. Current statistical methods for cohort data lack flexibility in the specification of stage duration distributions and mortality rates. In this paper, we present a new method for fitting models of stage-duration distributions and mortality to cohort data. The method is based on a Monte Carlo within MCMC algorithm and provides Bayesian estimates of parameters of stage-structured cohort models. The algorithm is computationally demanding but allows for flexible specifications of stage-duration distributions and mortality rates. We illustrate the algorithm with an application to data from a previously published experiment on the development of brine shrimp from Mono Lake, California, through nine successive stages. In the experiment, three different food supply and temperature combination treatments were studied. We compare the mean duration of the stages among the treatments while simultaneously estimating mortality rates and among-individual variance of stage durations. The method promises to enable more detailed studies of development of both natural and experimental cohorts. An R package implementing the method and which allows flexible specification of stage duration distributions is provided.

The importance of individual developmental variation in stage-structured population models.

Population stage structure is fundamental to ecology, and models of this structure have proven useful in many different systems. Many ecological variables other than stage, such as habitat type, site occupancy and metapopulation status are also modelled using transitions among discrete states. Transitions among life stages can be characterised by the distribution of time spent in each stage, including the mean and variance of each stage duration and within-individual correlations among multiple stage durations. Three modelling traditions represent stage durations differently. Matrix models can be derived as a long-run approximation from any distribution of stage durations, but they are often interpreted directly as a Markov model for stage transitions. Statistical stage-duration distribution models accommodate the variation typical of cohort development data, but such realism has rarely been incorporated in population theory or statistical population models. Delay-differential equation models include lags but no variation, except in limited cases. We synthesise these models in one framework and illustrate how individual variation and correlations in development can impact population growth. Furthermore, different development models can yield the same long-term matrix transition rates but different sensitivities and elasticities. Finally, we discuss future directions for estimating realistic stage duration models from data.

An approximate Bayesian computation approach to parameter estimation in a stochastic stage-structured population model.

Complex population processes may require equally complex models, which can lead to analytically intractable estimation problems. Approximate Bayesian computation (ABC) is a computational tool for parameter estimation in situations where likelihoods cannot be computed. Instead of using likelihoods, ABC methods quantify the similarities between an observed data set and repeated simulations from a model. A practical obstacle to implementing an ABC algorithm is selecting summary statistics and distance metrics that accurately capture the main features of the data. We demonstrate the application of a sequential Monte Carlo ABC sampler (ABC SMC) to parameter estimation of a general stochastic stage-structured population model with ongoing reproduction and heterogeneity in development and mortality. Individual variation in demographic traits has considerable consequences for population dynamics in many systems, but including it in a population model by explicitly allowing stage durations to follow a realistic distribution creates a complex model. We applied the ABC SMC to fit the model to a simulated representative data set with known underlying parameters to evaluate the performance of the algorithm. We also introduced a systematic method for selecting summary statistics and distance metrics, using simulated data and receiver operating characteristic (ROC) curves from classification theory. Evaluations suggest that the approach is promising for model inference in our example of realistic stage-structured population models.

Separating direct and indirect effects of global change: a population dynamic modeling approach using readily available field data.

Two sources of complexity make predicting plant community response to global change particularly challenging. First, realistic global change scenarios involve multiple drivers of environmental change that can interact with one another to produce non-additive effects. Second, in addition to these direct effects, global change drivers can indirectly affect plants by modifying species interactions. In order to tackle both of these challenges, we propose a novel population modeling approach, requiring only measurements of abundance and climate over time. To demonstrate the applicability of this approach, we model population dynamics of eight abundant plant species in a multifactorial global change experiment in alpine tundra where we manipulated nitrogen, precipitation, and temperature over 7 years. We test whether indirect and interactive effects are important to population dynamics and whether explicitly incorporating species interactions can change predictions when models are forecast under future climate change scenarios. For three of the eight species, population dynamics were best explained by direct effect models, for one species neither direct nor indirect effects were important, and for the other four species indirect effects mattered. Overall, global change had negative effects on species population growth, although species responded to different global change drivers, and single-factor effects were slightly more common than interactive direct effects. When the fitted population dynamic models were extrapolated under changing climatic conditions to the end of the century, forecasts of community dynamics and diversity loss were largely similar using direct effect models that do not explicitly incorporate species interactions or best-fit models; however, inclusion of species interactions was important in refining the predictions for two of the species. The modeling approach proposed here is a powerful way of analyzing readily available datasets which should be added to our toolbox to tease apart complex drivers of global change.

Estimation of stage duration distributions and mortality under repeated cohort censuses.

Many processes in nature can be viewed as arising from subjects progressing through sequential stages and may be described by multistage models. Examples include disease development and the physiological development of plants and animals. We develop a multistage model for sampling designs where a small set of subjects is followed and the number of subjects in each stage is assessed repeatedly for a sequence of time points, but for which the subjects cannot be identified. The motivating problem is the laboratory study of developing arthropods through stage frequency data. Our model assumes that the same individuals are censused at each time, introducing among sample dependencies. This type of data often occur in laboratory studies of small arthropods but their detailed analysis has received little attention. The likelihood of the model is derived from a stochastic model of the development and mortality of the individuals in the cohort. We present an MCMC scheme targeting the posterior distribution of the times of development and times of death of individuals. This is a novel type of MCMC that uses customized proposals to explore a posterior with disconnected support arising from the fact that individual identities are unknown. The MCMC algorithm may be used for inference about parameters governing stage duration distributions and mortality rates. The method is demonstrated by fitting the development model to stage frequency data of a mealybug cohort placed on a grape vine.

Unclear relationships between mean survival rate and its environmental variance in vertebrates.

Current environmental changes may increase temporal variability of life history traits of species thus affecting their long-term population growth rate and extinction risk. If there is a general relationship between environmental variances (EVs) and mean annual survival rates of species, that relationship could be used as a guideline for analyses of population growth and extinction risk for populations, where data on EVs are missing. For this purpose, we present a comprehensive compilation of 252 EV estimates from 89 species belonging to five vertebrate taxa (birds, mammals, reptiles, amphibians and fish) covering mean annual survival rates from 0.01 to 0.98. Since variances of survival rates are constrained by their means, particularly for low and high mean survival rates, we assessed whether any observed relationship persisted after applying two types of commonly used variance stabilizing transformations: relativized EVs (observed/mathematical maximum) and logit-scaled EVs. With raw EVs at the arithmetic scale, mean-variance relationships of annual survival rates were hump-shaped with small EVs at low and high mean survival rates and higher (and widely variable) EVs at intermediate mean survival rates. When mean annual survival rates were related to relativized EVs the hump-shaped pattern was less distinct than for raw EVs. When transforming EVs to logit scale the relationship between mean annual survival rates and EVs largely disappeared. The within-species juvenile-adult slopes were mainly positive at low (<0.5) and negative at high (>0.5) mean survival rates for raw and relativized variances while these patterns disappeared when EVs were logit transformed. Uncertainties in how to interpret the results of relativized and logit-scaled EVs, and the observed high variation in EV's for similar mean annual survival rates illustrates that extrapolations of observed EVs and tests of life history drivers of survival-EV relationships need to also acknowledge the large variation in these parameters.

A global database of soil seed bank richness, density, and abundance.

A soil seed bank is the collective name for viable seeds that are stored naturally in the soil. At the species or population level, the ability to form a seed bank represents a strategy for (re)colonization following a disturbance or other change in the local environmental conditions. At the community level, seed banks are thought to buffer local diversity during periods of environmental change and are often studied in relation to the potential for passive habitat restoration. The role that seed banks play in plant population and community dynamics, as well as their importance in the agricultural sector, means that they have been widely studied in ecological research. This database is the result of a comprehensive literature search, including all seed bank studies from the Web of Science from which data could be extracted, as well as an additional search of the Russian language literature. The database contains information on the species richness, seed density, and/or seed abundance in 3096 records from at least 1929 locations across the world's seven continents, extracted from 1442 studies published between 1940 and 2020. Records are grouped into five broad habitat categories (aquatic, arable, forest, grassland-including shrubland-and wetland), including information relating to habitat degradation from, or restoration to other habitats (total 14 combinations). Sampling protocols were also extracted for each record, and the database was extensively checked for errors. The location of each record was then used to extract summary climate data and biome classification from external published databases. The database has several potential uses. The large geographical spread relative to many other global biodiversity datasets is relevant for investigating patterns of diversity in biogeographical or macroecological contexts. Habitat type and status (intact, degraded, and restored) can be used to provide insights for biodiversity conservation, while the potential effects of sampling method and effort can be used to inform optimized data collection for future seed bank studies. This database is released under the CC-BY license.

Using uncertainty estimates in analyses of population time series.

Recording and monitoring wildlife is crucial for the conservation of wild species and the protection of their environment. The most common type of information reported from a monitoring scheme is a time series of population abundance estimates, but the potential of such data for analyzing population dynamics is limited due to lack of information on sampling error. Recent work has shown that replicating the sampling process and analyzing replicates jointly in a dynamical model can considerably increase estimation efficiency compared to analyzing population estimates alone. This method requires that independent replicates are available, and model fitting can be complex in general. Often, however, population estimates are accompanied by standard errors, or standard errors may be estimated from raw data using a sampling model. We evaluate a method where standard errors are used in combination with population estimates to account for sampling variability in state-space models of population dynamics. The method is simple and lends itself readily to data derived from many sampling procedures but ignores uncertainty in the standard errors themselves. We simulate data from a Gaussian state-space model where several observations, which may come from different sites, are available for the population at each time. Fitting the simulated data, we show that the method yields similar or even better results than a method utilizing all observations, even when there are few observations at each time. This holds under a range of simulation settings involving heteroscedastic observation error, site effects, and correlation among observations. We illustrate the approach on real data from the North American Breeding Bird Survey and show that it performs well in comparison to a more difficult maximum-likelihood analysis of the full data under non-Gaussian sampling error.

Estimating tree growth from complex forest monitoring data.

Understanding tree growth as a function of tree size is important for a multitude of ecological and management applications. Determining what limits growth is of central interest, and forest inventory permanent plots are an abundant source of long-term information but are highly complex. Observation error and multiple sources of shared variation (spatial plot effects, temporal repeated measures, and a mosaic of sampling intervals) make these data challenging to use for growth estimation. We account for these complexities and incorporate potential limiting factors (tree size, competition, and resource supply) into a hierarchical state-space model. We estimate the diameter growth of white fir (Abies concolor) in the Sierra Nevada of California from forest inventory data, showing that estimating such a model is feasible in a Bayesian framework using readily available modeling tools. In this forest, white fir growth depends strongly on tree size, total plot basal area, and unexplained variation between individual trees. Plot-level resource supply variables (representing light, water, and nutrient availability) do not have a strong impact on inventory-size trees. This approach can be applied to other networks of permanent forest plots, leading to greater ecological insights on tree growth.

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.

Fitting complex population models by combining particle filters with Markov chain Monte Carlo.

We show how a recent framework combining Markov chain Monte Carlo (MCMC) with particle filters (PFMCMC) may be used to estimate population state-space models. With the purpose of utilizing the strengths of each method, PFMCMC explores hidden states by particle filters, while process and observation parameters are estimated using an MCMC algorithm. PFMCMC is exemplified by analyzing time series data on a red kangaroo (Macropus rufus) population in New South Wales, Australia, using MCMC over model parameters based on an adaptive Metropolis-Hastings algorithm. We fit three population models to these data; a density-dependent logistic diffusion model with environmental variance, an unregulated stochastic exponential growth model, and a random-walk model. Bayes factors and posterior model probabilities show that there is little support for density dependence and that the random-walk model is the most parsimonious model. The particle filter Metropolis-Hastings algorithm is a brute-force method that may be used to fit a range of complex population models. Implementation is straightforward and less involved than standard MCMC for many models, and marginal densities for model selection can be obtained with little additional effort. The cost is mainly computational, resulting in long running times that may be improved by parallelizing the algorithm.

Role of weather and other factors in the dynamics of a low-density insect population.

Insect population dynamics are the result of an interplay between intrinsic factors such as density dependence, trophic web interactions, and external forces such as weather conditions. We investigate potential mechanisms of population dynamics in a natural, low-density insect population. Eggs and larvae of the noctuid moth, Abrostola asclepiadis, develop on its host plant during summer. The population density, and mortality, was closely monitored throughout this period during 15 years. Densities fluctuated between one and two orders of magnitude. Egg-larval developmental time varied substantially among years, with lower survival in cool summers with slower development. This was presumably due to the prolonged exposure to a large guild of polyphagous arthropod enemies. We also found a density-dependent component during this period that could be a result of intraspecific competition for food among the last larval instars. Dynamics during the long period from pupation in late summer through winter survival in the ground to adult emergence and oviposition the next year displayed few clear patterns and more unexplained variability, thus giving a more random appearance. The population hence shows more unexplained or unpredictable variation during the long wintering period, but seems more predictable over the summer egg-larval period. Our study illustrates how weather-via a window of exposure to enemies and in combination with density-dependent processes-can determine the course of population change through the insect life cycle.

Temporal trends in opportunistic citizen science reports across multiple taxa.

Opportunistic reporting of species observations to online platforms provide one of the most extensive sources of information about the distribution and status of organisms in the wild. The lack of a clear sampling design, and changes in reporting over time, leads to challenges when analysing these data for temporal change in organisms. To better understand temporal changes in reporting, we use records submitted to an online platform in Sweden (Artportalen), currently containing 80 million records. Focussing on five taxonomic groups, fungi, plants, beetles, butterflies and birds, we decompose change in reporting into long-term and seasonal trends, and effects of weekdays, holidays and weather variables. The large surge in number of records since the launch of the, initially taxa-specific, portals is accompanied by non-trivial long-term and seasonal changes that differ between the taxonomic groups and are likely due to changes in, and differences between, the user communities and observer behaviour.

Effects of weather and climate on the dynamics of animal population time series.

Weather is one of the most basic factors impacting animal populations, but the typical strength of such impacts on population dynamics is unknown. We incorporate weather and climate index data into analysis of 492 time series of mammals, birds and insects from the global population dynamics database. A conundrum is that a multitude of weather data may a priori be considered potentially important and hence present a risk of statistical over-fitting. We find that model selection or averaging alone could spuriously indicate that weather provides strong improvements to short-term population prediction accuracy. However, a block randomization test reveals that most improvements result from over-fitting. Weather and climate variables do, in general, improve predictions, but improvements were barely detectable despite the large number of datasets considered. Climate indices such as North Atlantic Oscillation are not better predictors of population change than local weather variables. Insect time series are typically less predictable than bird or mammal time series, although all taxonomic classes display low predictability. Our results are in line with the view that population dynamics is often too complex to allow resolving mechanisms from time series, but we argue that time series analysis can still be useful for estimating net environmental effects.

Individual heterogeneity and senescence in silvereyes on Heron Island.

Individual heterogeneity and correlations between life history traits play a fundamental role in life history evolution and population dynamics. Unobserved individual heterogeneity in survival can be a nuisance for estimation of age effects at the individual level by causing bias due to mortality selection. We jointly analyze survival and breeding output from successful breeding attempts in an island population of Silvereyes (Zosterops lateralis chlorocephalus) by fitting models that incorporate age effects and individual heterogeneity via random effects. The number of offspring produced increased with age of parents in their first years of life but then eventually declined with age. A similar pattern was found for the probability of successful breeding. Annual survival declined with age even when individual heterogeneity was not accounted for. The rate of senescence in survival, however, depends on the variance of individual heterogeneity and vice versa; hence, both cannot be simultaneously estimated with precision. Model selection supported individual heterogeneity in breeding performance, but we found no correlation between individual heterogeneity in survival and breeding performance. We argue that individual random effects, unless unambiguously identified, should be treated as statistical nuisance or taken as a starting point in a search for mechanisms rather than given direct biological interpretation.