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 These alternative methods are tested using census data, some of which are previously unpublished, from natural populations known from independent evidence to be subject to density dependent processes.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.     

Factors influencing detection of density dependence in British birds

If censuses are taken at less than generation intervals, the number of successive censuses in which a given individual is recorded will depend on longevity. Repeatedly recording the same individuals could produce under-estimates of population variability and influence detection of density dependence. We investigated this possibility in 60 time series of abundances of British birds compiled from the Common Birds Census data and then used simple population models to illustrate the proposed mechanism. Species had average lifespans of 2–10 years and were censused annually. Density dependence was detected (at P<0.05) much more frequently in bird species with long lifespans than in those with short lifespans; 75% of the 12 longest-lived species showed density dependence compared to 46% of all species. Population variability measured in annual censuses (termed annual variability) was lower in bird species with longer lifespans. We used discrete time models based on difference equations to demonstrate how longevity influences population variability and detection of density dependence in series of annual censuses. A model in which only first-year birds experienced density dependence was rejected because annual variability was greater and detection of density dependence was less likely when longevity was greater, the opposite of the observed effects of longevity in birds. A model in which all age classes experienced density dependence gave time series with lower annual variability and in which density dependence was detected more frequently when longevity was greater, which is the pattern observed in British birds. Analysis of data from this model showed that the amount of density dependence actually present caused only small changes in annual variability, whereas detection of density dependence from simulated series was strongly influenced by annual variability. The high annual variability of series from short-lived bird species could mask any density dependence that was present. Correcting for trends lead us to detect density dependence in 75% of the 12 longest lived bird species. There is no reason to believe that this rate is not also representative of short-lived species.     

Estimating density dependence in time-series of age-structured populations

For a life history with age at maturity alpha, and stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time-lags of from 1 to alpha years. Contrary to current interpretations, the coefficients for different time-lags in the autoregressive dynamics do not simply measure delayed density dependence, but also depend on life-history parameters. We define a new measure of total density dependence in a life history, D, as the negative elasticity of population growth rate per generation with respect to change in population size, D = - partial differential lnlambda(T)/partial differential lnN, where lambda is the asymptotic multiplicative growth rate per year, T is the generation time and N is adult population size. We show that D can be estimated from the sum of the autoregression coefficients. We estimated D in populations of six avian species for which life-history data and unusually long time-series of complete population censuses were available. Estimates of D were in the order of 1 or higher, indicating strong, statistically significant density dependence in four of the six species.     

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.     

Estimating density dependence from population time series using demographic theory and life-history data

For populations with a density-dependent life history reproducing at discrete annual intervals, we analyze small or moderate fluctuations in population size around a stable equilibrium, which is applicable to many vertebrate populations. Using a life history having age at maturity alpha, with stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time lags from 1 to alpha yr. Contrary to current interpretations, the coefficients corresponding to different time lags in the autoregressive dynamics are not simply measures of delayed density dependence but also depend on life-history parameters. The theory indicates that the total density dependence in a life history, D, should be defined as the negative elasticity of population growth rate per generation with respect to change in population size, [Formula: see text], where lambda is the asymptotic multiplicative growth rate per year, T is the generation time, and N is adult population size. The total density dependence in the life history, D, can be estimated from the sum of the autoregression coefficients. We estimate D in populations of seven vertebrate species for which life-history studies and unusually long time series of complete population censuses are available. Estimates of D were statistically significant and large, on the order of 1 or higher, indicating strong density dependence in five of the seven species. We also show that life history can explain the qualitative features of population autocorrelation functions and power spectra and observations of increasing empirical variance in population size with increasing length of time series.     

Delayed and inverse density dependence in a chamois population of the Italian Alps

Both density dependent and density independent factors have been considered important determinants of the dynamics of ungulate populations Intraspecific competition for food and the amount of snow cover were suggested in the past as factors that influence the demographic parameters of the chamois Rupicapra rupicapra We present a 10 yr study on a closed population of the Italian Alps Animals, divided by sex and age class (kid, yearling, subadult, adult, old), were counted over the period 1981–1990 The number of chamois hunted and the number of carcasses found each year and the daily snow height were also available We investigated possible correlations between several demographic parameters and both snow cover and chamois density, accounting for sex- and age-differential mortality and a possible delay in density dependence Results are as follows a) there is no statistically significant correlation between snow cover and demographic rates, b) there is no detectable compensation between natural and hunting-related mortality, c) birth rate is density independent for any time delay, d) when calculated from carcasses, total mortality, mortality of 1-yr-old and older males and females significantly depend on total density with 2 years' lag, while kid mortality is not related to density for any time delay, e) when calculated from censuses, all mortality rates significantly depend on total density with 2 years' lag, although the variance explained by delayed density is definitely smaller for kids, f) nonlinear regression of kid mortality from censuses against density of kids in the same year yields a much higher coefficient of determination and inverse density dependence is evidenced However, determination between delayed and inverse density dependence in kid mortality is impossible, given our dataset In general, results support the hypothesis that intraspecific competition, epidemics and predation, rather than weather, play a role in the dynamics of this ungulate population     

Differing contributions of density dependence and climate to the population dynamics of three eruptive herbivores

1. Although both endogenous and exogenous processes regulate populations, the current understanding of the contributions from density dependence and climate to the population dynamics of eruptive herbivores remains limited. 2. Using a 17‐year time series of three cereal aphid species [Rhopalosiphum padi L., Metopolophium dirhodum (Walker), and Diuraphis noxia (Kurdumov)] compiled from a trapping network spanning the northwestern U.S.A., temporal and spatial patterns associated with population fluctuations, and modelled density dependence in aphid abundances were tested. These models were used to analyse correlations between climate and aphid abundances in the presence and absence of residual variance as a result of density‐dependent effects. 3. The temporal dynamics of aphid population fluctuations indicated periodicity, with no clear evidence for a spatial pattern underlying population fluctuations. 4. Aphid abundances oscillated in a manner consistent with delayed density dependence for all three aphid species, although the strength of these feedbacks differed among species. 5. Diuraphis noxia abundances were negatively correlated with increasing temperatures in the absence of density‐dependent effects, whereas M. dirhodum abundances were positively correlated with increasing cumulative precipitation in the presence of density‐dependent effects; yet, R. padi abundances were unrelated to climate variables irrespective of population feedbacks. 6. Our analysis suggests that endogenous feedbacks differentially regulate aphid populations in the northwestern U.S.A., and these feedbacks may operate at an expansive spatial scale. It is concluded that the contributions of density dependence and climate to aphid population dynamics are species‐specific in spite of similar ecological niches, with implications for assessing species responses to climate variability.     

Study of dipeptidyl peptidase IV as a surface marker of human natural killer cells

The enriched populations of natural killer (NK) cells have been obtained using two different approaches. The first one was based on the separation in a density gradient of Percoll and further formation of rosettes with sheep erythrocytes. This method allowed to isolate the population containing approximately 70% of CD16(+)-cells. The second approach consisted in separating lymphocytes on a flow cytofluorometer FACS II. Using this method the population with 80% CD16(+)-cells was isolated from PBMC. Studies on morphological, phenotypical and functional characteristics of the first population revealed that NK cells constituted 70% of total number of cells; T-lymphocytes, 8-lymphocytes and monocytes constituted the minor population (10%, 8% and 1% respectively). Activity of DPIV was determined on both cell populations obtained. As it was shown, approximately 27% of the cells isolated using percoll density gradient and 22% of the cells after the separation on a flow cytofluorometer carried the enzyme molecules on the cell surface. The results of the present study apparently indicate that part of NK cells (about 10%) is characterised by the presence of DPIV on the cell surface.     

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.     

Predator-driven component Allee effects in a wild ungulate

Negative density dependence is an important driver of population dynamics of large vertebrates. Allee effects (positive density dependence), however, can affect small populations. Allee effects can be generated by predation and recent research has revealed potentially important indirect effects of predation on population dynamics. For wild populations, however, quantification of both Allee effects and indirect effects of predation remains scarce. We monitored for 27 years a bighorn sheep (Ovis canadensis) population that declined dramatically as episodes of cougar (Puma concolor) predation depressed survival. Predation led to a positive relationship between lamb survival and population size below a threshold, and to an overall positive relationship between yearling and adult ewe survival and population size. During years of high predation, lambs also suffer mortality through reduced growth, contributing a third of the total impact of predation on lamb survival. There was no positive association between population growth and population size, probably because growth was affected by several factors other than predation, including disease. Our results support the contention that predator-driven component Allee effects may exacerbate the effects of other environmental drivers and increase the risk of extinction of small populations.     

Predicting fluctuations of reintroduced ibex populations: the importance of density dependence, environmental stochasticity and uncertain population estimates

1. Development of population projections requires estimates of observation error, parameters characterizing expected dynamics such as the specific population growth rate and the form of density regulation, the influence of stochastic factors on population dynamics, and quantification of the uncertainty in the parameter estimates. 2. Here we construct a Population Prediction Interval (PPI) based on Bayesian state space modelling of future population growth of 28 reintroduced ibex populations in Switzerland that have been censused for up to 68 years. Our aim is to examine whether the interpopulation variation in the precision of the population projections is related to differences in the parameters characterizing the expected dynamics, in the effects of environmental stochasticity, in the magnitude of uncertainty in the population parameters, or in the observation error. 3. The error in the population censuses was small. The median coefficient of variation in the estimates across populations was 5.1%. 4. Significant density regulation was present in 53.6% of the populations, but was in general weak. 5. The width of the PPI calculated for a period of 5 years showed large variation among populations, and was explained by differences in the impact of environmental stochasticity on population dynamics. 6. In spite of the high accuracy in population estimates, the uncertainty in the parameter estimates was still large. This uncertainty affected the precision in the population predictions, but it decreased with increasing length of study period, mainly due to higher precision in the estimates of the environmental variance in the longer time-series. 7. These analyses reveal that predictions of future population fluctuations of weakly density-regulated populations such as the ibex often become uncertain. Credible population predictions require that this uncertainty is properly quantified.     

Population cycles produced by delayed density dependence in an annual plant

In contrast to insect and animal populations, little attention has been directed to the study of cycles in plant populations. It has been argued on theoretical grounds that plants present stable dynamics. Nevertheless, there are examples where plant populations appear to exhibit oscillatory dynamics, but the oscillatory signal is variable and comes from very short time series data. Using a combination of time series, models, and empirical results, we present evidence of population cycles for Descurania sophia in a 16-year field experiment. Endogenous and exogenous causal mechanisms were studied to identify processes underlying this temporal dynamic. Our results show a 4-year cycle produced by delayed density dependence. We suggest that high nutrient levels might be responsible for the observed dynamics of D. sophia. Our results suggest that although plant population dynamics may be stabilized by direct density dependence, delayed density dependence could destabilize dynamics.     

Inter- and intra-specific patterns of density dependence and population size variability in Salmoniformes

Population dynamics are typically affected by a combination of density-independent and density-dependent factors, the latter of which have been conceptually and theoretically linked with how variable population sizes are over time—which in turn has been tied to how prone populations are to extinction. To address evidence for the occurrence of density dependence and its relationship with population size variability (pv), we quantified each of these for 126 populations of 8 species of Salmoniformes. Using random-effects models, we partitioned variation in the strength of density dependence and the magnitude of pv between and within species and estimated the correlation of density dependence and population size variability at both the between- and within-species levels. We found that variation in the strength of density dependence was predominately within species (I ² = 0.47). In contrast, variation in population size variability was distributed both between and within species (I ² = 0.40). Contrary to theoretical and conceptual expectations, the strength of density dependence and the magnitude of population size variability were positively correlated at the between species level (r = 0.90), although this estimate had 95 % credibility intervals (Bayesian analogues to confidence intervals) that overlapped zero. The within-species correlation between density dependence and population size variability was not distinguishable from zero. Given that density dependence for Salmoniformes was highly variable within species, we next determined the joint effects of intrinsic (density-dependent) and extrinsic (density-independent) factors on the population dynamics of a threatened salmonid, the Lahontan cutthroat trout (Oncorhynchus clarkii henshawi). We found that density-dependent and -independent factors additively contributed to population dynamics. This finding suggests that the observed within-species variability in density dependence might be attributable to local differences in the strength of density-independent factors.     

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.     

Variation in predation pressure as a mechanism underlying differences in numerical abundance between populations of the poeciliid fish Heterandria formosa

We explored whether a variation in predation and habitat complexity between conspecific populations can drive qualitatively different numerical dynamics in those populations. We considered two disjunct populations of the least killifish, Heterandria formosa, that exhibit long-term differences in density, top fish predator species, and dominant aquatic vegetation. Monthly censuses over a 3-year period found that in the higher density population, changes in H. formosa density exhibited a strong negative autocorrelation structure: increases (decreases) at one census tended to be followed by decreases (increases) at the next one. However, no such correlation was present in the lower density population. Monthly census data also revealed that predators, especially Lepomis sp., were considerably more abundant at the site with lower H. formosa densities. Experimental studies showed that the predation by Lepomis gulosus occurred at a much higher rate than predation by two other fish and two dragonfly species, although L. gulosus and L. punctatus had similar predation rates when the amount of vegetative cover was high. The most effective predator, L. gulosus, did not discriminate among life stages (males, females, and juveniles) of H. formosa. Increased predation rates by L. gulosus could keep H. formosa low in one population, thereby eliminating strong negative density-dependent regulation. In support of this, changes in H. formosa density were positively correlated with changes in vegetative cover for the population with a history of lower density, but not for the population with a history of higher density. Our results are consistent with the hypothesis that the observed differences among natural populations in numerical abundance and dynamics are caused in part by the differences in habitat complexity and the predator community.     

Density dependence in northern ungulates: interactions with predation and resources

Variation in the abundance of animals has traditionally been explained as the outcome of endogenous forcing from density dependence and exogenous forcing arising from variation in weather and predation. Emerging evidence suggests that the effects of density dependence interact with external influences on population dynamics. In particular, spatial heterogeneity in resources and the presence of capable predators may weaken feedbacks from density dependence to growth of populations. We used the Kalman filter to analyze 23 time series of estimates of abundance of northern ungulate populations arrayed along a latitudinal gradient (latitude range of 40°–70°N) to evaluate the influence of spatial heterogeneity in resources and predation on density dependence. We also used contingency tables to test whether density dependence was independent of the presence of carnivores (our estimate of predation) and multiple regressions to determine the effects of spatial heterogeneity in resources, predation, and latitude on the strength of density dependence. Our results showed that the strength of density dependence of ungulate populations was low in the presence of large carnivores, particularly at northern latitudes with low primary productivity. We found that heterogeneity in elevation, which we assume acted as a surrogate for spatial heterogeneity in plant phenology, also reduced effects of density dependence. Thus, we show that external forces created by heterogeneity in resources and predation interact with internal feedbacks from population density to shape dynamics of populations of northern ungulates.     

Can population growth rates vary with the spatial scale at which they are measured?

1.  The ratio of successive population censuses is often assumed to reflect population growth rates. We identify three simple potential sources of bias in the estimation of population growth rates that relate to either the total number of censused individuals or the spatial areas over which censuses are conducted.
2.  The commonly used method of adding a constant to time series data to avoid problems caused by division by zero can lead to underestimation of growth rates at low densities in increasing populations.
3.  Variances associated with density estimates can lead to positive bias in estimation of growth rates when populations are distributed in ephemeral patches. The spatial variance and spatio-temporal covariance in bank vole census data suggest that this bias could be severe when small trapping grids are used. Use of logged estimators of growth rate avoids this problem.
4.  Using census data from non-randomly placed trapping grids that are smaller than twice the maximum range of natal dispersal to estimate population growth rates can lead to negatively biased estimates, particularly at low population densities.
5.  These three sources of bias are evaluated as explanations for scale-dependent changes in the estimates of growth rates identified in populations of snowshoe hare ( Lepus americanus ), bank voles ( Clethrionomys glareolus ) and lemmings ( Lemmus lemmus ).     

Natural enemy ravine revisited: the importance of sample size for determining population growth

Abstract. 1. The population growth of three aphid species, Metopolophium dirhodum (Walker), Rhopalosiphum padi (L.), and Sitobion avenae (F.), on winter wheat, was analysed by regression. The calculations were based on censuses of aphids made in 268 plots at 3- or 7-day intervals for 10 years on leaves and 6 years on ears. The calculations were made separately for each plot each year, then repeated on the pooled data from all plots monitored in a year.
2. At the level of individual plots, no population growth was detected at very low densities. At high densities, the populations grew exponentially and the growth rates did not decrease with increasing aphid density.
3. Significant growth was always detected in the pooled data. These growth rates decreased significantly at the highest densities. Field estimates of the intrinsic rate of increase derived from these data ranged from 0.010 to 0.026 for M. dirhodum , 0.0071–0.011 for R. padi , and 0.00078–0.0061 and 0.0015–0.13 for S. avenae , on leaves and ears respectively .
4. The apparent lack of growth in the individual plots at low densities is attributable to small sample size. It is concluded that the natural enemy ravine in the population dynamics of cereal aphids, identified by Southwood and Comins (1976), is a consequence of low population densities at which population increase is undetectable unless very large samples are taken.     

Density‐dependent and density‐independent drivers of population change in Barton Springs salamanders

Understanding population change is essential for conservation of imperiled species, such as amphibians. Worldwide amphibian declines have provided an impetus for investigating their population dynamics, which can involve both extrinsic (density‐independent) and intrinsic (density‐dependent) drivers acting differentially across multiple life stages or age classes. In this study, we examined the population dynamics of the endangered Barton Springs Salamander (Eurycea sosorum) using data from a long‐term monitoring program. We were interested in understanding both the potential environmental drivers (density‐independent factors) and demographic factors (interactions among size classes, negative density dependence) to better inform conservation and management activities. We used data from three different monitoring regimes and multivariate autoregressive state‐space models to quantify environmental effects (seasonality, discharge, algae, and sediment cover), intraspecific interactions among three size classes, and intra‐class density dependence. Results from our primary data set revealed similar patterns among sites and size classes and were corroborated by our out‐of‐sample data. Cross‐correlation analysis showed juvenile abundance was most strongly correlated with a 9‐month lag in aquifer discharge, which we suspect is related to inputs of organic carbon into the aquifer. However, sedimentation limited juvenile abundance at the surface, emphasizing the importance of continued sediment management. Recruitment from juveniles to the sub‐adult size class was evident, but negative density‐dependent feedback ultimately regulated each size class. Negative density dependence may be an encouraging sign for the conservation of E. sosorum because populations that can reach carrying capacity are less likely to go extinct compared to unregulated populations far below their carrying capacity. However, periodic population declines coupled with apparent migration into the aquifer complicate assessments of species status. Although both density‐dependent and density‐independent drivers of population change are not always apparent in time series of animal populations, both have important implications for conservation and management of E. sosorum.     

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.