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.     

A test of statistical techniques for detecting density dependence in sequential censuses of animal populations

Summary Principal and reduced major axes, and Bulmer's (1975) tests have been suggested as methods for detecting the presence of density dependence in a series of population censuses that are unsuitable for analysis by alternative means e.g. by k-factor analysis. These alternative methods are tested using census data, some of which are previously unpublished, from natural populations known from independent evidence to be subject to density dependent processes. All the methods fail to detect density dependence reliably, irrespective of sample size and the dynamics of the population. We conclude that none of the methods tested is sufficiently reliable to be useful as a test of density dependence in sequential censues of animal populations.     

Individual‐based modelling of resource competition to predict density‐dependent population dynamics: a case study with white storks

Density regulation influences population dynamics through its effects on demographic rates and consequently constitutes a key mechanism explaining the response of organisms to environmental changes. Yet, it is difficult to establish the exact form of density dependence from empirical data. Here, we developed an individual‐based model to explore how resource limitation and behavioural processes determine the spatial structure of white stork Ciconia ciconia populations and regulate reproductive rates. We found that the form of density dependence differed considerably between landscapes with the same overall resource availability and between home range selection strategies, highlighting the importance of fine‐scale resource distribution in interaction with behaviour. In accordance with theories of density dependence, breeding output generally decreased with density but this effect was highly variable and strongly affected by optimal foraging strategy, resource detection probability and colonial behaviour. Moreover, our results uncovered an overlooked consequence of density dependence by showing that high early nestling mortality in storks, assumed to be the outcome of harsh weather, may actually result from density dependent effects on food provision. Our findings emphasize that accounting for interactive effects of individual behaviour and local environmental factors is crucial for understanding density‐dependent processes within spatially structured populations. Enhanced understanding of the ways animal populations are regulated in general, and how habitat conditions and behaviour may dictate spatial population structure and demographic rates is critically needed for predicting the dynamics of populations, communities and ecosystems under changing environmental conditions.     

Host-parasite population dynamics under combined frequency- and density-dependent transmission

Many host‐parasite models assume that transmission increases linearly with host population density (‘density‐dependent transmission’), but various alternative transmission functions have been proposed in an effort to capture the complexity of real biological systems. The most common alternative (usually applied to sexually transmitted parasites) assumes instead that the rate at which hosts contact one another is independent of population density, leading to ‘frequency‐dependent’ transmission. This straight‐forward distinction generates fundamentally different dynamics (e.g. deterministic, parasite‐driven extinction with frequency‐ but not density‐dependence). Here, we consider the situation where transmission occurs through two different types of contact, one of which is density‐dependent (e.g. social contacts), the other density‐independent (e.g. sexual contacts). Drawing on a range of biological examples, we propose that this type of contact structure may be widespread in natural populations. When our model is characterized mainly by density‐dependent transmission, we find that allowing even small amounts of transmission to occur through density‐independent contacts leads to the possibility of deterministic, parasite‐driven extinction (and lowers the threshold for parasite persistence). Contrastingly, allowing some density‐dependent transmission to occur in a model characterized mainly by density‐independent contacts (i.e. by frequency‐dependent transmission) does not affect the extinction threshold, but does increase the likelihood of parasite persistence. The idea that directly transmitted parasites exploit different types of host contact is not new, but here we show that the impact on dynamics can be fundamental even in the simplest cases. For example, in systems where density‐dependent transmission is normally assumed de facto, we show that parasite‐driven extinction can occur if a small amount of transmission occurs through density‐independent contacts. Many empirical studies are still guided by the traditional density/frequency dichotomy, but our combined transmission function may provide a better model for systems in which both types of transmission occur.     

Density‐dependent mortality in Pacific salmon: the ghost of impacts past?

Conservation biologists often ignore density dependence because at‐risk populations are typically small relative to historical levels. However, if populations are reduced as a result of impacts that lower carrying capacity, then density‐dependent mortality may exist at low population abundances. Here, we explore this issue in threatened populations of juvenile chinook salmon (Oncorhynchus tshawytscha). We followed the fate of more than 50 000 juvenile chinook in the Snake River Basin, USA to test the hypothesis that their survival was inversely associated with juvenile density. We also tested the hypotheses that non‐indigenous brook trout and habitat quality affect the presence or strength of density dependence. Our results indicate that juvenile chinook suffer density‐dependent mortality and the strength of density dependence was greater in streams in which brook trout were absent. We were unable to detect an effect of habitat quality on the strength of density dependence. Historical impacts of humans have greatly reduced population sizes of salmon, and the density dependence we report may stem from a shortage of nutrients normally derived from decomposing salmon carcasses. Cohorts of juvenile salmon may experience density‐dependent mortality at population sizes far below historical levels and recovery of imperiled populations may be much slower than currently expected.     

Testing for density-dependent effects in sequential censuses

Summary In response to Gaston and Lawton (1987), we evaluated the ability of four statistical procedures to detect density dependence. We used data from the same 16 populations as Gaston and Lawton (1987). In each population, density dependence had been previously established with techniques that use more extensive data. The major axis test (Slade 1977) was rarely (3 populations of 16) capable of detecting density dependence. The autocorrelation test (Bulmer 1975) detected density dependence in 5 of 16 species (14 of 59 tests overall). The randomization procedure (Pollard et al. 1987) detected density dependence in 7 of the 16 data sets (10 of 59 tests overall). The simulation procedure (Vickery and Nudds 1984) detected density dependence in 5 of the 16 data sets (11 of 59 tests overall). We suggest that not all annual census data taken from populations subject to density-dependent effects will actually show evidence of such effects. We conclude that Pollard et al. 's (1987) randomization procedure is the best test for detecting density dependence in sequential census data but it is not as powerful as more elaborate techniques (k-factor analysis, experimentation, etc.), nor is it meant to replace more extensive analyses.     

Predicting conditions for migration: effects of density dependence and habitat quality

Migration is widespread among animals, but the factors that influence the decision to migrate are poorly understood. Within a single species, populations may be completely migratory, completely sedentary or partially migratory. We use a population model to derive conditions for migration and demonstrate how migratory survival, habitat quality and density dependence on both the breeding and non-breeding grounds influence conditions for migration and the proportion of migrants within a population. Density dependence during the season in which migratory and sedentary individuals use separate sites is necessary for partial migration. High levels of density dependence at the non-shared sites widen the range of survival values within which we predict partial migration, whereas increasing the strength of density dependence at the shared sites narrows the range of survival values within which we predict partial migration. Our results have important implications for predicting how contemporary populations with variable migration strategies may respond to changes in the quality or quantity of habitat.     

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.     

Density dependent population growth of the two-spotted spider mite, Tetranychus urticae, on the host plant Leonurus cardiaca

We observed Tetranychus urticae (Koch), a polyphagous spider mite herbivore, on Leonurus cardiaca (L.) at several sites in eastern North America at variable density, ranging from extremely dense to sparse. To understand the nature of T. urticae 's population dynamics we experimentally manipulated population densities on L. cardiaca and assessed per capita growth after 1 to 2 generations in laboratory and field experiments. In particular, we took a 'bottom-up' approach, manipulating both plant size and quality to examine effects on mite dynamics. Per capita growth was strongly dependent on the initial density of the mite population. Spider mite populations grew (1) in a negatively density dependent manner on small plants and (2) unhindered by density dependence on large plants. Mean per capita growth was 59% higher on small plants compared to large plants, irrespective of mite density. We also found evidence for density dependent induced susceptibility to spider mites in small plants and density dependent induced resistance in large plants. Hence, spider mite populations grew at a relatively fast rate on small plants, and this was associated with negative density dependence due to factors that depress population growth, such as food deterioration or limitation. On large plants, spider mite populations grew at a relatively slow rate, apparently resulting in herbivore densities that may not have been high enough to cause intraspecific competition or other forms of negative density dependence.     

Density dependence in resource exploitation: empirical test of Levins' metapopulation model

Levins' model of metapopulation dynamics is modified to incorporate variable degrees of density dependence in the per capita exploitation of resource patches. We demonstrate a simple means of testing for this density dependence in a sample of metapopulations, each at its equilibrium balance of local colonization to extinction. The fraction of habitable unoccupied patches equilibrates to a constant number under the null model of density independent colonization, and to a constant proportion under strong density dependence. We compare the null model to two density dependent alternatives, using data on exploitation of nest boxes by collared flycatchers Ficedula albicollis . The analysis shows how predicted trends in the equilibrium unoccupied fraction are similar for both spatial interference and net immigration. This needs to be recognized, since the null hypothesis of a constant unused resource applies also to the dynamics of consumable resources, where it is expressed in a constant stock of uneaten prey at the dynamic equilibrium of predators to prey.     

A general approach to sample size determination for prevalence surveys that use dual test protocols

We develop a Bayesian simulation based approach for determining the sample size required for estimating a binomial probability and the difference between two binomial probabilities where we allow for dependence between two fallible diagnostic procedures. Examples include estimating the prevalence of disease in a single population based on results from two imperfect diagnostic tests applied to sampled individuals, or surveys designed to compare the prevalences of two populations using diagnostic outcomes that are subject to misclassification. We propose a two stage procedure in which the tests are initially assumed to be independent conditional on true disease status (i.e. conditionally independent). An interval based sample size determination scheme is performed under this assumption and data are collected and used to test the conditional independence assumption. If the data reveal the diagnostic tests to be conditionally dependent, structure is added to the model to account for dependence and the sample size routine is repeated in order to properly satisfy the criterion under the correct model. We also examine the impact on required sample size when adding an extra heterogeneous population to a study.     

A reassessment of equivalence in yield from marine reserves and traditional fisheries managament

Lively debate continues over whether marine reserves can lead to increased fishery yields when compared to conventional, quota‐based management, apparently driven by differences in the complexity and biological richness of the models being used. In an influential article, Hastings and Botsford used an analytically tractable, spatially implicit, non‐age‐structured model to assert that reserves are typically incapable of increasing yields relative to conventional management, regardless of the type (pre‐ or post‐dispersal, involving adults and/or larvae) or functional form (Ricker or Beverton‐Holt) of density dependence present. A recent numerical (simulation) model by Gaylord et al. concludes that reserves can enhance yield compared to conventional management, a result the authors attribute to their spatially‐explicit evaluation of stage‐structured adult growth, survivability and fecundity; and intercohort (adult‐on‐larvae) post‐dispersal density dependent population dynamics. Here we demonstrate that the increased model complexity is not responsible for the different conclusions. We analyze a spatially‐implicit model without stage structure that incorporates intercohort post‐dispersal density dependence. In this simple model we still find annual extirpation of adult populations outside reserves due to fishing to enhance larval recruitment there, allowing for increased yields compared to those achieved when harvest is evenly spread across the entire domain under conventional management. Consideration of neither spatially‐explicit dispersal dynamics nor stage‐structure in adult demographics is required for reserves to substantially improve yield beyond that attainable under conventional management. In contrast, consideration of within cohort post‐dispersal density dependence among larva during settlement in an otherwise identical model generates equivalence in yield between the two management strategies. These results recast a common message characterizing the relative benefit of reserve versus non‐reserve management from “equivalence at best” to “potentially improved”.     

Density dependence in blowfly populations: experimental evaluation of non‐parametric time‐series modelling

Two approaches for describing density dependence in demographic rates of stage‐structured populations are compared in this study. Time‐series data from laboratory blowfly populations (Lucilia sericata) have been analysed in a separate study, with a statistical modelling approach that incorporated density dependences as unspecified (non‐parametric) functions. In this study, we assessed density‐dependent structures by manipulating densities of larvae and adults in cohorts of blowflies and measuring the demographic rates. We here compare the density‐dependent structures revealed by the cohort experiments with those estimated by the non‐parametric model. This model estimates the demographic rates to have the following density‐dependent structures: (i) larval survival was non‐linearly density‐dependent (a ‘humped’ function), (ii) adult survival was density‐independent, and (iii) reproductive rate decreased with adult density. In the cohort experiments reported here, (i) juvenile survival exhibited a positive density dependence in low densities (facilitation), which became negative at higher densities (competition). Pupal and adult size decreased with initial larval density. (ii) Adult survival was reduced by high initial larval density, but it was independent of adult density. (iii) Reproductive rate was reduced by high initial larval density, and by high adult density in populations of large individuals (from low larval density). Hence, the results from these experiments support the non‐parametric model estimates regarding density‐dependent structures of demographic rates in the blowfly populations. The mean demographic rates, however, were apparently underestimated by the model. We conclude that non‐parametric modelling is a useful first approach for exploratory analysis of ecological time‐series data.     

Structural risk minimization: a robust method for density-dependence detection and model selection

Statistically distinguishing density‐dependent from density‐independent populations and selecting the best demographic model for a given population are problems of primary importance. Traditional approaches are PBLR (parametric bootstrapping of likelihood ratios) and Information criteria (IC), such as the Schwarz information criterion (SIC), the Akaike information criterion (AIC) or the Final prediction error (FPE). While PBLR is suitable for choosing from a couple of models, ICs select the best model from among a set of candidates. In this paper, we use the Structural risk minimization (SRM) approach. SRM is the model selection criterion developed within the Statistical learning theory (SLT), a theory of great generality for modelling and learning with finite samples. SRM is almost unknown in the ecological literature and has never been used to analyze time series. First, we compare SRM with PBLR in terms of their ability to discriminate between the Malthusian and the density‐dependent Ricker model. We rigorously repeat the experiments described in a previous study and find out that SRM is equally powerful in detecting density‐independence and much more powerful in detecting density‐dependence. Then, we compare SRM against ICs in terms of their ability to select one of several candidate models; we generate, via stochastic simulation, a huge amount of artificial time series both density‐independent and dependent, with and without exogenous covariates, using different dataset sizes, noise levels and parameter values. Our findings show that SRM outperforms traditional ICs, because generally a) it recognizes the model underlying the data with higher frequency, and b) it leads to lower errors in out‐of‐samples predictions. SRM superiority is specially apparent with short time series. We finally apply SRM to the population records of Alpine ibex Capra ibex living in the Gran Paradiso National Park (Italy), already investigated by other authors via traditional statistical methods; we both analyze their models and introduce some novel ones. We show that models that are best according to SRM show also the lowest leave‐one‐out cross‐validation error.     

Predators reverse the direction of density dependence for juvenile salmon mortality

The effect of predators on prey populations depends on how predator-caused mortality changes with prey population density. Predators can enforce density-dependent prey mortality and contribute to population stability, but only if they have a positive numerical or behavioral response to increased prey density. Otherwise, predator saturation can result in inversely density-dependent mortality, destabilizing prey populations and increasing extinction risk. Juvenile salmon and trout provide some of the clearest empirical examples of density-dependent mortality in animal populations. However, although juvenile salmon are very vulnerable to predators, the demographic effects of predators on juvenile salmon are unknown. We tested the interactive effects of predators and population density on the mortality of juvenile Atlantic salmon (Salmo salar) using controlled releases of salmon in natural streams. We introduced newly hatched juvenile salmon at three population density treatments in six study streams, half of which contained slimy sculpin (Cottus cognatus), a common generalist predator (18 release sites in total, repeated over two summers). Sculpin reversed the direction of density dependence for juvenile salmon mortality. Salmon mortality was density dependent in streams with no sculpin, but inversely density dependent in streams where sculpin were abundant. Such predator-mediated inverse density dependence is especially problematic for prey populations suppressed by other factors, thereby presenting a fundamental challenge to persistence of rare populations and restoration of extirpated populations.     

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.     

Population dynamics of three songbird species in a nestbox population in Central Europe show effects of density,climate and competitive interactions

Unravelling the contributions of density‐dependent and density‐independent factors in determining species population dynamics is a challenge, especially if the two factors interact. One approach is to apply stochastic population models to long‐term data, yet few studies have included interactions between density‐dependent and density‐independent factors, or explored more than one type of stochastic population model. However, both are important because model choice critically affects inference on population dynamics and stability. Here, we used a multiple models approach and applied log‐linear and non‐linear stochastic population models to time series (spanning 29 years) on the population growth rates of Blue Tits Cyanistes caeruleus, Great Tits Parus major and Pied Flycatchers Ficedula hypoleuca breeding in two nestbox populations in southern Germany. We focused on the roles of climate conditions and intra‐ and interspecific competition in determining population growth rates. Density dependence was evident in all populations. For Blue Tits in one population and for Great Tits in both populations, addition of a density‐independent factor improved model fit. At one location, Blue Tit population growth rate increased following warmer winters, whereas Great Tit population growth rates decreased following warmer springs. Importantly, Great Tit population growth rate also decreased following years of high Blue Tit abundance, but not vice versa. This finding is consistent with asymmetric interspecific competition and implies that competition could carry over to influence population dynamics. At the other location, Great Tit population growth rate decreased following years of high Pied Flycatcher abundance but only when Great Tit population numbers were low, illustrating that the roles of density‐dependent and density‐independent factors are not necessarily mutually exclusive. The dynamics of this Great Tit population, in contrast to the other populations, were unstable and chaotic, raising the question of whether interactions between density‐dependent and density‐independent factors play a role in determining the (in) stability of the dynamics of species populations.     

Large dam reservoirs are probably long-period oscillators of fish diversity

Long‐term fish population time series obtained annually in a backwater (upstream) and a tailwater (downstream) site of the large lowland Jeziorsko Reservoir, Poland, were analysed and compared to detect impoundment influence on the fluctuation of fish population density and on the fluctuation of a fish diversity measure. The partial‐rate correlation function (PRCF) of all constantly occurring fish species displayed negative first‐order feedback of past density on present density, both upstream and downstream. Weak and irregular cyclic patterns were observed in the autocorrelation function (ACF) of populations of several species upstream and of two species downstream. Most fish species exhibited no significant concordant variations between the two sites, but there were no data supporting different regulation. Probably, different exogenous (environmental) factors control fishes at the two sites. The ACFs of the time series of the exponential of Shannon entropy (N₁ diversity measure) obtained at the Jeziorsko tailwater site, and in the main body of the smaller ?ímov Reservoir, Czech Republic, revealed strong fluctuation patterns. The fluctuation was well fitted by a sine‐wave model of a 9 year period at the ?ímov, although it co‐occurred with a positive linear trend. A sine‐wave model also fitted well with the trend at the Jeziorsko tailwater site, where, however, only one 16·5 year period occurred; hence, it is indicative of cyclicity. The results indicate that dam reservoirs may be oscillators of fish diversity and that part of the literature controversy over the effect of a reservoir on fish populations may be due to a too short sampling period: it is shown that both increase and decrease in diversity may be observed on the basis of samples selected from one diversity time series obtained at the tailwater.     

Red environmental noise and the appearance of delayed density dependence in age-structured populations

Previous work suggests that red environmental noise can lead to the spurious appearance of delayed density dependence (DDD) in unstructured populations regulated only by direct density dependence. We analysed the effect of noise reddening on the pattern of spurious DDD in several variants of the density-dependent age-structured population model. We found patterns of spurious DDD in structured populations with either density-dependent fertility or density-dependent survival of the first age class, inconsistent with predictions from unstructured population models. Moreover, we found that nonspurious negative DDD always emerges in populations with deterministic chaotic dynamics, regardless of population structure or the type of environmental noise. The effect of noise reddening in generating spurious DDD is often negligible in the chaotic region of population deterministic dynamics. Our findings suggest that differences in species' life histories may exhibit different patterns of spurious DDD (owing to noise reddening) than predicted by unstructured models.