Detection Of Density Dependence Research Articles

Cross-lags and the unbiased estimation of life-history and demographic parameters.

Biological processes exhibit complex temporal dependencies due to the sequential nature of allocation decisions in organisms' life cycles, feedback loops and two‐way causality. Consequently, longitudinal data often contain cross‐lags: the predictor variable depends on the response variable of the previous time step. Although statisticians have warned that regression models that ignore such covariate endogeneity in time series are likely to be inappropriate, this has received relatively little attention in biology. Furthermore, the resulting degree of estimation bias remains largely unexplored.We use a graphical model and numerical simulations to understand why and how regression models that ignore cross‐lags can be biased, and how this bias depends on the length and number of time series. Ecological and evolutionary examples are provided to illustrate that cross‐lags may be more common than is typically appreciated and that they occur in functionally different ways.We show that routinely used regression models that ignore cross‐lags are asymptotically unbiased. However, this offers little relief, as for most realistically feasible lengths of time‐series conventional methods are biased. Furthermore, collecting time series on multiple subjects—such as populations, groups or individuals—does not help to overcome this bias when the analysis focusses on within‐subject patterns (often the pattern of interest). Simulations, a literature search and a real‐world empirical example together suggest that approaches that ignore cross‐lags are likely biased in the direction opposite to the sign of the cross‐lag (e.g. towards detecting density dependence of vital rates and against detecting life‐history trade‐offs and benefits of group living). Next, we show that multivariate (e.g. structural equation) models can dynamically account for cross‐lags, and simultaneously address additional bias induced by measurement error, but only if the analysis considers multiple time series.We provide guidance on how to identify a cross‐lag and subsequently specify it in a multivariate model, which can be far from trivial. Our tutorials with data and R code of the worked examples provide step‐by‐step instructions on how to perform such analyses.Our study offers insights into situations in which cross‐lags can bias analysis of ecological and evolutionary time series and suggests that adopting dynamical models can be important, as this directly affects our understanding of population regulation, the evolution of life histories and cooperation, and possibly many other topics. Determining how strong estimation bias due to ignoring covariate endogeneity has been in the ecological literature requires further study, also because it may interact with other sources of bias.

Assessing the effect of density on population growth when modeling individual encounter data.

The relative role of density-dependent and density-independent variation in vital rates and population size remains largely unsolved. Despite its importance to the theory and application of population ecology, and to conservation biology, quantifying the role and strength of density dependence is particularly challenging. We present a hierarchical formulation of the temporal symmetry approach, also known as the Pradel model, that permits estimation of the strength of density dependence from capture-mark-reencounter data. A measure of relative population size is built in the model and serves to detect density dependence directly on population growth rate. The model is also extended to account for temporal random variability in demographic rates, allowing estimation of the temporal variance of population growth rate unexplained by density dependence. We thus present a model-based approach that enable to test and quantify the effect of density-dependent and density-independent factors affecting population fluctuations in a single modeling framework. More generally, we use this modeling framework along with simulated and empirical data to show the value of including density dependence when modeling individual encounter data without the need for auxiliary data.

Spatiotemporal dynamics of mesocarnivore populations

Mammalian mesocarnivores play critical roles in ecosystems via trophic interactions. The fluctuation of mesocarnivore abundance may cause trophic cascading throughout the ecosystems. However, little was known about density dependence and spatiotemporal dynamics of mesocarnivore populations. Northern raccoon Procyon lotor is a common mammalian mesocarnivore in North America, and is the host of many human infectious diseases. Few studies have investigated density dependence and hierarchical spatiotemporal dynamics of raccoon populations. We used 23‐year time series of raccoon relative abundance from 14 wildlife management areas in Mississippi, USA, to test for spatial synchrony of raccoon populations with nonparametric correlation functions. We developed non‐Gaussian state space models to detect density dependence of raccoon populations, and also used dynamic factor analysis (DFA) to determine the structure of the spatiotemporal dynamics of raccoon populations. The 14 raccoon populations lacked common trends, and were not synchronized. Strength of density dependence varied among raccoon populations, but was not related to the amount of hardwood forests. Differences in the structure of density dependence probably prevented populations from being synchronize by climatic variability. The raccoon populations exhibited greater local or idiosyncratic variability than regional variability in Mississippi. Northern raccoons have plastic life history traits permitting their population dynamics to closely track local variations in resource availability.

Density‐dependent population regulation detected in short time series of saproxylic beetles

AbstractUnderstanding the regulation of natural populations has been a long‐standing problem in ecology. Here we analyze the population dynamics of 17 species of saproxylic beetles in Shizuoka Prefecture, Japan collected over 11–12 years using autoregressive integrated moving average (ARIMA) models. We first examined the dynamics for indications of the order of the ARIMA models and evaluated the time series to determine that it was not simply a random, white noise sequence. All species dynamics were not mere random noise, and ARIMA models up to lag 3 were considered. The best model was selected from the possible ones using several criteria: model convergence, weak residual autocorrelation, the small sample AIC must be among the smallest that were not significantly different, and the lag indicated by the cutoff values in the detrended partial autocorrelation function. We found significant and nearly significant direct density‐dependence for 14 of the 17 species, varying from −0.709 and stronger. The characteristic return rates were strong and only one species had a weak return rate (>0.9), implying that these species were strongly regulated by density‐dependent factors. We found that populations with higher order ARIMA models (lag 2 and 3) had weaker return rates than populations with ARIMA models with only one lag, suggesting that species with more complex dynamics were more weakly regulated. These results contrast with previous suggestions that 20+ years are needed to detect density dependence from population time series and that most populations are weakly regulated.

Detecting density dependence on tree survival in a deciduous broadleaved forest in Baotianman National Nature Reserve

It has been found that density dependence plays a crucial role in determination of species distribu- tion and coexistence, and the effect of negative density dependence also plays an important part among phy- logenetically related species. Based on two census datasets in 2009 and 2014 of the 1-ha deciduous broad- leaved forest plot in Baotianman National Nature Reserve, generalized linear mixed models (GLMMs) were used to examine the density dependence on individual survival of the top 11 species (with high important value) at different neighborhood scales and different DBH sizes (1 cm ≤ DBH< 5 cm, 5 cm ≤ DBH < 10 cm, DBH ≥ 10 cm). The results showed that (1) mean annual mortality and recruitment rate of indi- viduals (DBH ≥ 1 cm) were 5.85% and 0.27%, respectively; (2) survival rate of 5 tree species was nega- tively correlated with abundance or neighbor conspecific basal area; (3) density dependence and phylogenetic diversity exerted significant effects on survival of small individuals (at 5 m neighborhood scale), whereas no significant influence on medium trees. With increasing tree size, phylogenetic diversity exerted important ef- fect on large individuals at 7.5 m and 10 m neighborhood scales. In conclusion, density dependence and phy- logenetic diversity play different roles on tree survival at different life stages and neighborhood scales in the deciduous broad-leaved forest in Baotianman National Nature Reserve. ·研究报告·

Detecting density dependence from spatial patterns in a heterogeneous subtropical forest of central China

Accumulating evidence suggests that density dependence, whether at early or late life stages, is an important mechanism regulating plant population structure. However, the opposing effects of habitat heterogeneity and species-level variation might have confounded the prevalence of density dependence in natural forests. These compatible ideas were rarely considered simultaneously. In this study, we applied a spatial statistical technique to examine (i) the prevalence of density dependence at late life stages after controlling for habitat heterogeneity and (ii) the relationships between species traits and the strength of density dependence in a newly established, 25 ha subtropical mountain forest plot in central China. Of the 88 (75%) tree species analyzed, 66 were found to exhibit density dependence predominantly at very close distances among neighbors in the species-rich subtropical forest. In addition, the strength of density dependence was associated with species traits. Our findings identified strong density dependence among trees that had greater stature and were rarer. We concluded that density dependence was a prevalent mechanism for regulating the population structure of most tree species and both habitat heterogeneity and species-level variation played crucial roles in shaping the strength of density dependence in natural forests.

Density dependence across multiple life stages in a temperate old-growth forest of northeast China.

Recent studies on species coexistence suggest that density dependence is an important mechanism regulating plant populations. However, there have been few studies of density dependence conducted for more than one life-history stage or that control for habitat heterogeneity, which may influence spatial patterns of survival and mask density dependence. We explored the prevalence of density dependence across multiple life stages, and the effects of controlling for habitat heterogeneity, in a temperate forest in northeast China. We used generalized linear mixed-effects models to test for density-dependent mortality of seedlings and spatial point pattern analysis to detect density dependence for sapling-to-juvenile transitions. Conspecific neighbors had a negative effect on survival of plants in both life stages. At the seedling stage, we found a negative effect of conspecific seedling neighbors on survival when analyzing all species combined. However, in species-level analyses, only 2 of 11 focal species were negatively impacted by conspecific neighbors, indicating wide variation among species in the strength of density dependence. Controlling for habitat heterogeneity did not alter our findings of density dependence at the seedling stage. For the sapling-to-juvenile transition stage, 11 of 15 focal species showed patterns of local scale (<10 m) conspecific thinning, consistent with negative density dependence. The results varied depending on whether we controlled for habitat heterogeneity, indicating that a failure to account for habitat heterogeneity can obscure patterns of density dependence. We conclude that density dependence may promote tree species coexistence by acting across multiple life-history stages in this temperate forest.Electronic supplementary materialThe online version of this article (doi:10.1007/s00442-012-2481-y) contains supplementary material, which is available to authorized users.

Detecting and estimating density dependence in wildlife populations

AbstractWe 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.

Estimating the strength of density dependence in the presence of observation errors using integrated population models

Assessing the strength of density dependence is crucial for understanding population dynamics, but its estimation is difficult. Because estimates of population size and demographic parameters usually include errors due to imperfect detection, estimations of the strength of density dependence will be biased if obtained with conventional methods and lack statistical power to detect density dependence. We propose a Bayesian integrated population model to study density dependence. The model allows assessing the effect of density both on the population growth rate as well as the demographic parameters while accounting for imperfect detection. We studied the performance of this model using simulation and illustrate its use with data on red-backed shrikes Lanius collurio. Our simulation results showed that the strength of density dependence is identifiable and it was estimated with higher precision using the integrated population model than the conventional regression model. As expected, the conventional regression model tended to overestimate density dependence at the population level whereas underestimates at the demographic level, but the bias was small. The analysis of the red-backed shrike data revealed negative density dependence at the population level most likely mediated by a density-dependent decline in adult survival. This work highlights the potential of integrated population models in assessing density dependence and its practical application in population studies.

Tests of density dependence using indices of relative abundance in a deer population

A major question in animal ecology is explaining the causes of population fluctuations. Consensus about the most reliable method to detect density dependence (DD) or environmental effects from time‐series data, however, has not yet been achieved. Times series analyses have been used with indices of relative abundance in numerous studies, although these indices are rarely validated. Here, we used three different time series of relative abundance (number of deer seen per hunter per day, hunting success and proportion of males in the harvest) to explore direct and delayed DD in a white‐tailed deer Odocoileus virginianus population on Anticosti Island, Québec, Canada. Three mathematical approaches were tested: linear models, autoregressive (AR) models, and total DD in life history. Tests of DD using different indices of abundance on the same population should lead to similar results if all indices exhibit similar behaviour. Indices of relative abundance correlated with each other, although sometimes weakly, such that we obtained similar DD estimates with each index using detrended non‐stationary series. In most time series, linear regression of Nt−1 and Nt and AR models did not detect DD, while we obtained strong evidence for DD from the life‐history approach. This meant that contrasting conclusions about the role of density dependence within this population were reached depending on which method was used. We conclude that the method that incorporates most biological realism, the life‐history approach, provided a different result than classical interpretation of autoregressive coefficients. Only the life‐history interpretation supported our a priori belief that density dependence operating through competition for food regulates the Anticosti deer population. Phenomenological analysis aiming to investigate changes in abundance should be carefully conducted as the use of inappropriate indices or methods could lead to inappropriate conclusions or management strategies. Preferably, the method used should match the time scale of the population sampling regime and species life history.

Detecting Density Dependence in Recovering Seal Population is Difficult: A Response to Svensson et al. (2011)

Comment to: Svensson, C. J., A. Eriksson, T. Harkonen and K. C. Harding. 2011. Detecting density dependence in recovering seal populations. AMBIO 40:52–59. A recent simulation study (Svensson et al. 2011) proposed the use of changes in age-structure as an indicator of density dependent effects on the growth of the Baltic grey seal (Halichoerus grypus) population. That approach provides a clever alternative to the direct examination of abundance estimates, and sidesteps the well-known difficulty of detecting trends in marine mammal populations from survey data (Taylor et al.2007). However, there are three features of Svensson et al.’s analysis that limit its utility as a demonstration of the practicality of their methodology as a tool for investigating real-world problems.

Detecting Density Dependence in Recovering Seal Populations

Time series of abundance estimates are commonly used for analyses of population trends and possible shifts in growth rate. We investigate if trends in age composition can be used as an alternative to abundance estimates for detection of decelerated population growth. Both methods were tested under two forms of density dependence and different levels of environmental variation in simulated time series of growth in Baltic gray seals. Under logistic growth, decelerating growth could be statistically confirmed after 16 years based on population counts and 14 years based on age composition. When density dependence sets in first at larger population sizes, the age composition method performed dramatically better than population counts, and a decline could be detected after 4 years (versus 10 years). Consequently, age composition analysis provides a complementary method to detect density dependence, particularly in populations where density dependence sets in late.

Density dependence is prevalent in a heterogeneous subtropical forest

Although negative conspecific density dependence among neighbours is widely studied, the general prevalence of the effects is still poorly understood due to a lack of studies from zonal forests other than the tropics. In addition, the detection of density dependence may be confounded by the influence of habitat heterogeneity. Here we examined the spatial distributions of 47 common tree species (diameter at breast height≥1 cm) using the pair-correlation function g(r) in a fully mapped 24-ha subtropical forest in China. We first investigated whether habitat heterogeneity influenced tree distributions, and then examined the conspecific tree patterns and density dependence after removing the effects of habitat heterogeneity. We found that the forest plot exhibited strong large-scale heterogeneity in the distribution of both large adult trees of different growth forms and individual species. After the habitat heterogeneity was accounted for, 39 of the 47 species (83.0%) were found to exhibit density dependence predominantly at close distances among neighbors. Our findings highlight density dependence as a prevalent mechanism for regulating the population spatial structure of most tree species in the species-rich subtropical forest studied here. Furthermore, the occurrence of density dependence is closely associated with species abundance and the strength of conspecific aggregation at local scales. Abundant species with high strength of conspecific aggregation tend to show density dependence.

Escapement goal analysis and stock reconstruction of sockeye salmon populations (Oncorhynchus nerka) using life-history models

We compare life-history models with the Beverton–Holt approach of escapement goal analysis. We model the life history of a sockeye salmon ( Onchorhynchus nerka ) population from a spawning stage, through juvenile and adult stages, and ending with adults that return to spawn. We fit models to data by statistically comparing predicted and observed numbers of four dominant adult ages. Posterior estimates of parameters from Markov chain Monte Carlo simulations are then used to assess optimal harvest policies. We search for policies that produce the highest average yield. We find that it is possible to detect density dependence with a life-history model where analysis of Beverton–Holt stock–recruitment relationship fails to do so. We find that Beverton–Holt relationships produce policies and long-term yield estimates that are inconsistent with empirical trends. Conversely, we find that optimal spawning stock sizes and maximum sustained yield estimates using the life-history model estimate are consistent with the historical behavior of fisheries examined. Adding smolt data to the analysis does not substantially change predicted optimal spawning stock size, but decreases the variance in estimated posterior parameter distributions and policy variable distributions.

Pathogens, density dependence and the coexistence of tropical trees

There is increasing interest in the role played by density-dependent mortality from natural enemies, particularly plant pathogens, in promoting the coexistence and diversity of tropical trees. Here, we review four issues in the analysis of pathogen-induced density dependence that have been overlooked or inadequately addressed. First, the methodology for detecting density dependence must be robust to potential biases. Observational studies, in particular, require a careful analysis to avoid biases generated by measurement error, and existing studies could be criticized on these grounds. Experimental studies manipulating plant density and pathogen incidence will often be preferable, or should be run in parallel. Second, the form of density dependence is not well understood and, in particular, there are no data indicating whether pathogens cause compensating or overcompensating density responses. Owing to this, we argue that the potential for pathogen-induced density dependence to generate diversity-enhancing outcomes, such as the Janzen-Connell effect, remains uncertain, as coexistence is far more probable if density dependence is overcompensating. Third, there have been few studies examining the relative importance of intra- or interspecific density dependence resulting from pathogens (or, more widely, natural enemies). This is essentially equivalent to asking to what extent pathogens are host-specific. If pathogens are generalists, then mortality rates will respond to overall plant density, irrespective of plant species identity. This will weaken the intraspecific density dependence and reduce the diversity-promoting effects of pathogens. Finally, we highlight the need for studies that integrate observations and experiments on pathogens and density dependence into the whole life cycle of trees, because as yet it is not possible to be certain of the degree to which pathogens contribute to observed dynamics.

Census error and the detection of density dependence

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

STRENGTH OF EVIDENCE FOR DENSITY DEPENDENCE IN ABUNDANCE TIME SERIES OF 1198 SPECIES

Population limitation is a fundamental tenet of ecology, but the relative roles of exogenous and endogenous mechanisms remain unquantified for most species. Here we used multi-model inference (MMI), a form of model averaging, based on information theory (Akaike's Information Criterion) to evaluate the relative strength of evidence for density-dependent and density-independent population dynamical models in long-term abundance time series of 1198 species. We also compared the MMI results to more classic methods for detecting density dependence: Neyman-Pearson hypothesis-testing and best-model selection using the Bayesian Information Criterion or cross-validation. Using MMI on our large database, we show that density dependence is a pervasive feature of population dynamics (median MMI support for density dependence = 74.7-92.2%), and that this holds across widely different taxa. The weight of evidence for density dependence varied among species but increased consistently, with the number of generations monitored. Best-model selection methods yielded similar results to MMI (a density-dependent model was favored in 66.2-93.9% of species time series), while the hypothesis-testing methods detected density dependence less frequently (32.6-49.8%). There were no obvious differences in the prevalence of density dependence across major taxonomic groups under any of the statistical methods used. These results underscore the value of using multiple modes of analysis to quantify the relative empirical support for a set of working hypotheses that encompass a range of realistic population dynamical behaviors.

An analysis of the analysis of herbivore population dynamics

Time series analysis of herbivore data with weather included as covariate is commonly used as a mean to shed light on the state and ecology of the studied population. Conclusions about the herbivore population are drawn from statistical parameter values and presence/absence in the most parsimonious model. However, this procedure is only reliable if the statistical parameters have general interpretations regardless of system characteristics. Here we investigated the extent to which this is true by deriving six different vegetation–herbivore‐systems and analyzing their respective statistical parameters. The analysis was done in both continuous and discrete time. It turned out that both density parameters (a1 and a2) and rainfall coefficients change with biological interactions and amount of average rainfall, and they do so in different ways in different systems. This means that there is no valid general interpretation of them and, most important, the probability of detecting density dependence and effects of rainfall vary between systems. Hence, you can not make inference about the biological processes from statistical analysis without knowing the system that you study and what model best describes the interactions within it.

DETECTION OF DENSITY DEPENDENCE REQUIRES DENSITY MANIPULATIONS AND CALCULATION OF λ

To investigate density-dependent population regulation in the perennial bunchgrass Bouteloua rigidiseta, we experimentally manipulated density by removing adults or adding seeds to replicate quadrats in a natural population for three annual intervals. We monitored the adjacent control quadrats for 14 annual intervals. We constructed a population projection matrix for each quadrat in each interval, calculated lambda, and did a life table response experiment (LTRE) analysis. We tested the effects of density upon lambda by comparing experimental and control quadrats, and by an analysis of the 15-year observational data set. As measured by effects on lambda and on N(t+1/Nt in the experimental treatments, negative density dependence was strong: the population was being effectively regulated. The relative contributions of different matrix elements to treatment effect on lambda differed among years and treatments; overall the pattern was one of small contributions by many different life cycle stages. In contrast, density dependence could not be detected using only the observational (control quadrats) data, even though this data set covered a much longer time span. Nor did experimental effects on separate matrix elements reach statistical significance. These results suggest that ecologists may fail to detect density dependence when it is present if they have only descriptive, not experimental, data, do not have data for the entire life cycle, or analyze life cycle components separately.

Density‐dependent regulation in populations of potato‐colonizing aphids

AbstractScarcity of long‐term (over 30 years) data series represents a major challenge for an accurate estimation of the role of density‐dependent processes in population regulation. We analyzed population densities of the wingless parthenogenic morphs of buckthorn aphid (BA), Aphis nasturtii Kaltenbach, potato aphid (PA), Macrosiphum euphorbiae (Thomas), and green peach aphid (GPA), Myzus persicae (Sulzer) from 1949 to 2003 for signs of density‐dependent regulation. We found strong evidence of density‐dependent regulation, with detection of density dependence being fairly consistent among the different statistical techniques. Direct density dependence was detected for the populations of all three species. There was also evidence of delayed density dependence for PA. The periodicity of population fluctuations for BA and GPA was 6.1 years and 3.9 years, respectively. The periodicity for PA was not explicit, being highly variable throughout the time series. Effects of density‐independent weather factors were relatively minor compared to density‐dependent regulation. The BA populations experienced a significant reduction in both density and annual oscillations starting in 1995, while GPA populations experienced a similar reduction in 1991. No such change was apparent for PA. The most likely explanation for the observed phenomenon is a change in the composition of the lady beetle community following the establishment of two alien coccinellid species, and/or changes in insecticide use by commercial growers in the area of the study.