Tests For Density Dependence Research Articles

Early instar mortality of a forest pest caterpillar: which mortality sources increase during an outbreak crash?

AbstractCollapses of insect pest outbreaks are often attributed to delayed density dependence of predation. The forest tent caterpillar, Malacosoma disstria Hübner (Lepidoptera: Lasiocampidae), is an outbreaking pest species defoliating mixed wood boreal forests in eastern Canada. This species presents periodic population dynamics with peaks every 10 years and outbreaks lasting 1–3 years impacting the health of its host tree. We asked about the relative importance of various sources of early‐instar mortality during and after the crash of an outbreak, testing for density dependence. We used a triad set‐up of complete predator exclusion, partial exclusion, and free colonies to distinguish between intrinsic mortality (caused by, e.g., pathogens) and mortality caused by flighted and walking natural enemies, and compared defoliated outbreak sites with control sites. Overall, survival was lowest in the free colonies and increased with partial and complete predator exclusion. Survival was also higher in control than in outbreak sites and higher in the final year of the outbreak than in the following year. We observed no changes in mortality from walking enemies, but an increase in intrinsic mortality and mortality from flighted enemies. in the year following the outbreak. This increase is consistent with density dependence of these mortality sources, but its occurrence in the control sites as well was unexpected. These findings show that mortality from flighted natural enemies and intrinsic source increases after the outbreak, but do not contribute to the population crash. However, they help maintain low endemic levels between outbreaks.

Density-dependence mediates coral assemblage structure.

Density dependence (DD) controls community recovery following widespread mortality, yet this principle rarely has been applied to coral assemblages. The reefs of Mo'orea, French Polynesia, provide the opportunity to study DD of coral population growth, because coral assemblages in this location responded to declines in abundance with high recruitment and an increase in cover during which recruitment of pocilloporid corals was inversely associated with density. This study tests for DD in this system, first, by describing the context within which it operates: coral cover changed from 46% in 2005, to <1% in 2010 following an outbreak of a corallivorous sea star and a cyclone, and then increased to 74% by 2017, in large part through inverse density-associated pocilloporid recruitment. Second, a test for DD of recruitment was conducted by decreasing Pocillopora spp. cover from 33% to 19%: one year later, the density of Pocillopora spp. recruits was 1.65-fold higher in the low vs. high cover treatment. Finally, the effects of DD were investigated by comparing simulated and empirical distributions of pocilloporid colonies: as predicted by DD, small colonies were randomly distributed, while large colonies were uniformly distributed. Together these results demonstrate DD of population regulation for Pocillopora spp. corals, thus revealing the potential importance of this ecological principle in determining the resilience of coral assemblages.

High population density enhances recruitment and survival of a harvested coral reef fish

A negative relationship between population growth and population density (direct density dependence) is necessary for population regulation and is assumed in most models of harvested populations. Experimental tests for density dependence are lacking for large-bodied, harvested fish because of the difficulty of manipulating population density over large areas. We studied a harvested coral reef fish, Lutjanus apodus (schoolmaster snapper), using eight large, isolated natural reefs (0.4-1.6 ha) in the Bahamas as replicates. An initial observational test for density dependence was followed by a manipulation of population density. The manipulation weakened an association between density and shelter-providing habitat features and revealed a positive effect of population density on recruitment and survival (inverse density dependence), but no effect of density on somatic growth. The snappers on an individual reef were organized into a few shoals, and we hypothesize that large shoals on high-density reefs were less vulnerable to large piscivores (groupers and barracudas) than the small shoals on low-density reefs. Reductions in predation risk for individuals in large social groups are well documented, but because snapper shoals occupied reefs the size of small marine reserves, these ecological interactions may influence the outcome of management actions.

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.

Predictions of Taylor's power law, density dependence and pink noise from a neutrally modeled time series

There has recently been increasing interest in neutral models of biodiversity and their ability to reproduce the patterns observed in nature, such as species abundance distributions. Here we investigate the ability of a neutral model to predict phenomena observed in single-population time series, a study complementary to most existing work that concentrates on snapshots in time of the whole community. We consider tests for density dependence, the dominant frequencies of population fluctuation (spectral density) and a relationship between the mean and variance of a fluctuating population (Taylor's power law). We simulated an archipelago model of a set of interconnected local communities with variable mortality rate, migration rate, speciation rate, size of local community and number of local communities. Our spectral analysis showed ‘pink noise’: a departure from a standard random walk dynamics in favor of the higher frequency fluctuations which is partly consistent with empirical data. We detected density dependence in local community time series but not in metacommunity time series. The slope of the Taylor's power law in the model was similar to the slopes observed in natural populations, but the fit to the power law was worse. Our observations of pink noise and density dependence can be attributed to the presence of an upper limit to community sizes and to the effect of migration which distorts temporal autocorrelation in local time series. We conclude that some of the phenomena observed in natural time series can emerge from neutral processes, as a result of random zero-sum birth, death and migration. This suggests the neutral model would be a parsimonious null model for future studies of time series data.

On the analysis of monitoring data: Testing for no trend in population size

The goal of a monitoring program is to find out whether the size of a population is stable, declining, or increasing over time. Whereas statistical tests for temporal trends are straightforward, there is no test for no change or stability. We propose that the combination of traditional trend analyses such as linear regression and tests for density dependence may be used for population stability analyses. We illustrate the approach by analyzing a data set from an orchid monitoring program. Combining statistical tests for temporal trends with tests for statistically significant density dependence is a useful and simple tool in the analysis of monitoring data.

Asymptotic Distribution of Density-Dependent Stage-Grouped Population Dynamics Models

Matrix models are widely used in biology to predict the temporal evolution of stage-structured populations. One issue related to matrix models that is often disregarded is the sampling variability. As the sample used to estimate the vital rates of the models are of finite size, a sampling error is attached to parameter estimation, which has in turn repercussions on all the predictions of the model. In this study, we address the question of building confidence bounds around the predictions of matrix models due to sampling variability. We focus on a density-dependent Usher model, the maximum likelihood estimator of parameters, and the predicted stationary stage vector. The asymptotic distribution of the stationary stage vector is specified, assuming that the parameters of the model remain in a set of the parameter space where the model admits one unique equilibrium point. Tests for density-dependence are also incidentally provided. The model is applied to a tropical rain forest in French Guiana.

Population fluctuations and regulation in great snipe: a time‐series analysis

1. During the last centuries, the breeding range of the great snipe Gallinago media has declined dramatically in the western part of its distribution. To examine present population dynamics in the Scandinavian mountains, we collected and analysed a 19-year time series of counts of great snipe males at leks in central Norway, 1987-2005. 2. The population showed large annual fluctuations in the number of males displaying at lek sites (range 45-90 males at the peak of the mating season), but no overall trend. 3. We detected presence of direct density-dependent mechanisms regulating this population. Inclusion of the density-dependent term in a Ricker-type model significantly improved the fit with observed data (evaluated with Parametric Bootstrap Likelihood Ratio tests and Akaike's Information Criterion for small sample size). 4. An analysis of (a number of a priori likely) environmental covariates suggests that the population dynamics were affected by conditions influencing reproduction and survival of offspring during the summer, but not by conditions influencing survival at the wintering grounds in Africa. This is in contrast to many altricial birds breeding in the northern hemisphere, and supports the idea that population dynamics of migratory nidifugous birds are more influenced by conditions during reproduction. 5. Inclusion of these external factors into our model improved the detectability of density dependence. This illustrates that allowing for external effects may increase statistical power of density dependence tests and thus be of particular importance in relatively short time series. 6. In our best model of the population dynamics, two likely density-independent offspring survival covariates explained 47.3% of the variance in great snipe numbers (predation pressure estimated by willow grouse reproductive success and food availability estimated by the amount of precipitation in June), whereas density dependence explained 35.5%. Demographic stochasticity and unidentified environmental stochasticity may account for the remaining 17.2%.

Effect of Measurement Error on Tests of Density Dependence of Catchability for Walleyes in Northern Wisconsin Angling and Spearing Fisheries

AbstractWe sought to determine how much measurement errors affected tests of density dependence of spearing and angling catchability for walleye Sander vitreus by quantifying relationships between spearing and angling catch rates (catch/h) and walleye population density (number/acre) in northern Wisconsin lakes. The mean measurement error of spearing catch rates was 43.5 times greater than the mean measurement error of adult walleye population densities, whereas the mean measurement error of angling catch rates was only 5.6 times greater than the mean measurement error of adult walleye population densities. The bias‐corrected estimate of the relationship between spearing catch rate and adult walleye population density was similar to the ordinary‐least‐squares regression estimate but differed significantly from the geometric mean (GM) functional regression estimate. In contrast, the bias‐corrected estimate of the relationship between angling catch rate and total walleye population density was intermediate between ordinary‐least‐squares and GM functional regression estimates. Catch rates of walleyes in both spearing and angling fisheries were not linearly related to walleye population density, which indicated that catch rates in both fisheries were hyperstable in relation to walleye population density. For both fisheries, GM functional regression overestimated the degree of hyperdepletion in catch rates and ordinary‐least‐squares regression overestimated the degree of hyperstability in catch rates. However, ordinary‐least‐squares regression induced significantly less bias in tests of density dependence than GM functional regression, so it may be suitable for testing the degree of density dependence in fisheries for which fish population density is estimated with mark– recapture methods similar to those used in our study.

Foraging Behavior of Field Populations of Diadegma Spp. (Hymenoptera: lchneumonidae):Testing for Density-Dependence at Two Spatial Scales

The foraging behavior of populations of Diadegma spp. (Hymenoptera: Ichneumonidae) attacking the diamondback moth, Plutella xylostella L. (Lepidoptera: Plutellidae), was studied in the field. The effect of host density on percentage parasitism was investigated at two spatial scales: that of the individual plant, as well as a “cluster of plants” at low, medium and high densities. Using binoculars, parasitoid searching was observed on host plants at different host densities over an 8-h period. Behavior was compared to that predicted under the Patch Selection Theory. Percentage parasitism was independent of host density at both spatial scales. However, the behavioral studies showed parasitoid aggregation behavior at higher host densities. The population displayed an imperfect preference for higher host densities in the first 4 h of foraging. In the second 4-h period, no preference was observed.

DENSITY DEPENDENCE IN NORTH AMERICAN DUCKS

Knowing whether, and to what extent, populations are regulated by density-dependent factors is important both in its own right and when developing management strategies for wildlife species. However, available tests for density dependence are typically sensitive to sampling errors in the data. By using a state-space modeling approach, incorporating both an ecological process model and an observation model, it is possible to account for both measurement and process error. Here we focus on the detection and estimation of direct density dependence in two species of North American ducks: the Mallard (Anas platyrhynchos) and the Canvasback (Aythya valisineria). Yearly aerial counts on the major breeding grounds of ducks in North America provide estimates of abundances as well as standard errors of these estimates for both species. Including the number of ponds as a covariate, we demonstrate evidence for density dependence in prairie areas for both species. The appropriateness of the applied state-space method is validated through a simulation study.

Spatially explicit analyses unveil density dependence

Density-dependent processes are fundamental in the understanding of species population dynamics. Whereas the benefits of considering the spatial dimension in population biology are widely acknowledged, the implications of doing so for the statistical detection of spatial density dependence have not been examined. The outcome of traditional tests may therefore differ from those that include ecologically relevant locational information on both the prey species and natural enemy. Here, we explicitly incorporate spatial information on individual counts when testing for density dependence between an insect herbivore and its parasitoids. The spatially explicit approach used identified significant density dependence more frequently and in different instances than traditional methods. The form of density dependence detected also differed between methods. These results demonstrate that the explicit consideration of patch location in density-dependence analyses is likely to significantly alter current understanding of the prevalence and form of spatial density dependence in natural populations.

RELATIVE IMPORTANCE OF ABIOTICALLY INDUCED DIRECT AND INDIRECT EFFECTS ON A SALT-MARSH HERBIVORE

Few studies have attempted to determine experimentally the relative importance of direct and indirect effects of host plants on herbivorous insects in the field. This study identifies important direct and indirect effects of a coastal plant on its most common insect herbivore and assesses the relative importance of those effects. The direct effects of increased interstitial soil salinity and nitrogen on the abundance of Pissonotus quadripustulatus (Homoptera: Delphacidae), which feeds on Borrichia frutescens (Asteraceae), are reported. Also reported are the indirect effects of these treatments on parasitism of P. quadripustulatus eggs laid in plant stems by the fairyfly parasitoid Anagrus sp. nr. armatus (Hymenoptera: Mymaridae). Soil salinity was experimentally elevated by the addition of salt pellets, and plant foliar nitrogen was increased by the addition of fertilizer. Both salt and fertilizer increased the abundance of P. quadripustulatus. There was a significant salt × fertilizer interaction, suggesting that salt stress may be more important when plants are more nitrogen limited. Salt, by increasing the frequency of tough B. frutescens stems, decreased the rate at which Anagrus parasitized P. quadripustulatus eggs. Fertilizer, by increasing the frequency of B. frutescens stems that were softer and easier to penetrate, increased the rate of parasitism. Changes in parasitism, however, did not affect P. quadripustulatus density. Tests for density dependence showed that the results reported here were attributable to application of the treatments and not to spatial density dependence. This study suggests that, in a stressful salt-marsh system, the direct effects of plant quality on herbivores are more important than indirect effects of plant morphology mediated by natural enemies.

POPULATION DYNAMICS OF TREE-DWELLING APHIDS:THE IMPORTANCE OF SEASONALITY AND TIME SCALE

Changes in the weekly abundance in two natural populations of the Turkey- oak aphid, Myzocallis boerneri, from 1975 to 1992, were analyzed using autoregression methodology to determine the nature of dynamic processes. Seasonality forms the basis of aphid population dynamics. Analysis of time series of weekly and monthly data indicate statistically detectable seasonality in density changes. The monthly data statistically ad- justed for seasonal effects (deseasoned) show that density fluctuates around a seasonally changing equilibrium value. Bulmer's test of density dependence applied to the seasonally adjusted monthly data reveals density dependence. The partial autocorrelation function (PACF) plots of smoothed deseasoned monthly density indicate time-lagged density-de- pendent processes operating between seasons and possibly on a shorter time scale of between 2 wk and 2 mo. The PACFs of smoothed deseasoned data provide statistical evidence for the existence of a relationship between density in spring, autumn, and the following spring. Analysis of annual abundances calculated from the weekly data suggests that overall abundance in any year is influenced by abundance the previous year. The pattern of changes in abundance between years is most likely the consequence of the see-saw effect operating between seasons. It is argued that aphid population density is regulated by means of density-dependent processes acting within years, which is reflected in the year-to-year changes in overall abundance.

Testing for density dependence allowing for weather effects.

A test for density dependence in time-series data allowing for weather effects is presented. The test is based on a discrete time autoregressive model for changes in population density with a covariate for the effects of weather. The distribution of the test statistic on the null hypothesis of density independence is obtained by parametric bootstrapping. A computer simulation exercise is used to demonstrate the gain in statistical power by allowing for weather effects. Application of the method to time-series data on three species of butterflies and two species of songbirds showed stronger evidence of density dependence than two standard tests.

Population Persistence Time: Estimates, Models, and Mechanisms

The conservation and management of populations require some insight into mechanisms of population regulation, yet unambiguous identification of density dependence in vital rates is notoriously difficult. Through the reanalysis of data published by Stacey and Taper for a semi-isolated sub-population of the Acorn Woodpecker we demonstrate the utility of an approach in which a single data set is “attacked” using a suite of models with different assumptions. Tests for density dependence of the reproductive rate and of juvenile survival are inconclusive, but there is evidence for density-dependent adult survival. Since “survival” rates estimated from banded birds confound the effects of mortality and immigration/emigration, we construct and analyze three models: (1) a closed population with density-independent vital rates and an upper limit to population size, (2) a regulated closed population, (3) a regulated sub-population with immigration and emigration. Very small interchanges with other sub-populations can have a very large effect on population persistence; thus our results highlight the importance of distinguishing the effects of interchange from density dependencies in vital rates.

POPULATION PERSISTENCE TIME: ESTIMATES, MODELS, AND MECHANISMS

The conservation and management of populations require some insight into mechanisms of population regulation, yet unambiguous identification of density dependence in vital rates is notoriously difficult. Through the reanalysis of data published by Stacey and Taper for a semi-isolated sub-population of the Acorn Woodpecker we demonstrate the utility of an approach in which a single data set is “attacked” using a suite of models with different assumptions. Tests for density dependence of the reproductive rate and of juvenile survival are inconclusive, but there is evidence for density-dependent adult survival. Since “survival” rates estimated from banded birds confound the effects of mortality and immigration/emigration, we construct and analyze three models: (1) a closed population with density-independent vital rates and an upper limit to population size, (2) a regulated closed population, (3) a regulated sub-population with immigration and emigration. Very small interchanges with other sub-populations can have a very large effect on population persistence; thus our results highlight the importance of distinguishing the effects of interchange from density dependencies in vital rates.

Tests for density dependence.

Several statistical tests for 'density dependence' have been proposed in the literature, and so in any practical case the question poses itself which one of these tests to choose. This paper offers a few remarks additional to those made by Fox and Ridsill-Smith (1995) and others. Parametric statistical tested are based on a fully specified mathematical model. Examples of such tests are Bulmer's (1975) first test, and the test of Dennis and Taper (1994). Distribution-free tests are based on far less stringent assumptions. An example of such a test is the one proposed by Pollard et al. (1987). The choice between parametric tests can best be made by considering which one of the underlying mathematical models ist most plausible. If all models are almost equally plausible, considerations of computational requirement and ease of application may be important. Strong doubts concerning the plausibility of mathematical models may lead one to prefer a distribution-free test. An important feature of any test is its power, i.e. the probability of its rejecting the null hypothesis when this hypothesis is not true. Other things being equal, tests are preferable when they have superior powers. But power of a test depends on 'the true state of nature', and the only way to study power quantitatively is by assuming some mathematical model as approximately representing this 'true state'. As any mathematical model can at best only be an approximation to the situation in nature, a mathematical model and the statistical tests based on it should be robust against small deviations from model assumptions. Solow (1990) showed that Bulmer's test is not robust with respect to the assumption that the residuals in the underlying autoregression model be stochastically independent. Contrary to what was suggested by Fox and Ridsill-Smith (1995), who misinterpreted some statements in Reddingius (1990), the present author thinks this is a serious shortcoming of this test since an ecologist cannot assume a priori that important density-independent ecological factors are not somehow serially correlated. Moreover, he is rather sceptical about the usefulness of statistical tests for density dependence. They have contributed more to misunderstandings than to a significant increase in ecological insight. In any case, statistical tests are designed to test hypotheses that are stated before data are collected, and the question which test to use also has to be answered before the data have been collected. Designing and using statistical tests a posteriori to 'detect' things in data mainly leads to confusion and controversy.

Factors influencing detection of density dependence in British birds : I. Population trends.

We question why density dependence has remained elusive in series of annual abundances of British birds. In particular, an earlier study reported that significant temporal trends in abundances occur in up to 74% of time series from the Common Birds Census. Several studies showed that such trends can hinder detection of density dependence. Temporal trends do not preclude the presence of density dependence and two published tests for density dependence include temporal trends in the null hypothesis model. We explore the extent to which detection of density dependence was hindered by temporal trends in bird abundance data. We used a conservative method to test for trends, which found significant (P<0.05) linear population trends in only 7 of 60 time series of abundances (of 17-31 years) compiled from the Common Birds Census data. However, both of the tests for density dependence that allow for trends and a third method gave P-values that were strongly influenced by the strength of trends, including trends that were not significant (P>0.05). This shows that density dependence may be falsely rejected or detected when trends are present, even when these trends are weak and not statistically significant. To circumvent this problem we detrended the time-series prior to testing for the presence of density dependence. To minimize subjectivity we used simulated time series to check that this procedure did not increase the level of type I error (false rejection of density independence). Additionally, we confirmed that the method gave acceptable levels of type II error, where the test fails to reject density independence in series generated using a density dependent model. This showed that the detrending method was acceptable and represents a major improvement in our ability to detect density dependence in time series that contain temporal trends. Detrending the bird time series increased the number of series in which significant (P<0.05) density dependence was found from 10 (17%), when trends are ignored, to 27 (45%) when series are detrended. However, this rate of 45% is still surprisingly low by comparison to other taxa, and we believe that other factors may contribute to this, which we explore in the second of this pair of papers.

The Changing Basis of Competition in Organizational Populations: The Manhattan Hotel Industry, 1898-1990

Density-dependence theory cannot account for the widely observed pattern of proliferation and concentration in organizational populations. Although density dependence provides an explanation for initial proliferation, it cannot explain subsequent concentration because it does not allow some organizations to become dominant competitors. To address this basic limitation, I combine density dependence with three ecological models that permit size-based competitive asymmetries among a population's members and let the intensity of competitive processes vary over time. My analysis shows that Manhattan hotels of different sizes generate and experience different strengths of competition and that size-based competitive processes increase in strength over time, contrbuting to industry concentration. Separating empirically the effects of low-density conditions that occur early and late in a population's history also clarifies tests of density dependence in populations that have evolved beyond their peak density. The evolutionary trajectories of diverse organizational populations appear to follow a common path. The number of organizations grows slowly initially, then increases rapidly to a peak. Once the maximum is reached, the number of organizations declines as one or a few large organizations come to dominate a much larger number of small organizations. Populations of newspaper publishers, labor unions, breweries, and banks, to list only a few, follow this basic pattern (Hannan & Carroll 1992). The application of ecological models of competition to explain this pattern has been a frequent topic in recent research in organizational sociology. An impressive array of evidence has been assem