Delayed Density Dependence Research Articles

Seasonally limited host supply generates microparasite population cycles

Cycles in biological populations have been shown to arise from enemy–victim systems, delayed density dependence, and maternal effects. In an initial effort to model the year-to-year dynamics of natural populations of entomopathogenic nematodes and their insect hosts, we find that a simple, nonlinear, mechanistic model produces large amplitude, period two population cycles. The cycles are generated by seasonal dynamics within semi-isolated populations independently of inter-annual feedback in host population numbers, which differs from previously studied mechanisms. The microparasites compete for a fixed number of host insect larvae. Many nematodes at the beginning of the year quickly eliminate the pool of small hosts, and few nematodes are produced for the subsequent year. Conversely, initially small nematode populations do not over-exploit the host population, so the surviving hosts grow to be large and produce many nematodes that survive to the following year.

AUTOCORRELATED EXOGENOUS FACTORS AND THE DETECTION OF DELAYED DENSITY DEPENDENCE

Coupled trophic interactions with specialist predators or resources are thought to be primarily responsible for generating delayed density dependence. Previous theoretical studies suggest that autocorrelation in exogenous factors could generate apparent negative delayed density dependence in populations regulated only by direct density dependence. Using both linear and nonlinear models, we show that autocorrelated exogenous factors can generate the spurious appearance of not only negative, but also positive, delayed density dependence in populations regulated only by direct density dependence. Evidence for negative delayed density dependence is found mainly in populations exhibiting monotonic deterministic stability, whereas evidence for positive delayed density dependence is found mainly in populations exhibiting damped or persistent two-point cycles, or more complex deterministic dynamics. We argue that fluctuating resources (e.g., mast seeding) in bottom-up controlled communities could qualify as autocorrelated exogenous factors and cause apparent delayed density dependence in the population of their consumers.

Are indirect measures of abundance a useful index of population density? The case of red grouse harvesting

Indirect measures of population abundance, such as harvest data, are often used to make inference on long term population dynamics when direct data are either not available or are logistically difficult to obtain. However, when harvesting records are used, a common concern is that they may not reflect actual population abundance. We investigated the extent to which harvest data reflected changes in population density of the red grouse Lagopus lagopus scoticus in Great Britain. We used 92 independently managed populations over the period 1977–2000 and examined the temporal and spatial variability of the hunting records and independently obtained count data from each of these managed estates. Three different analyses support the conclusion that grouse hunting records are a reliable indicator of grouse abundance: 1) the number of red grouse shot in autumn showed a tendency to be linearly related to the density of individuals counted in the summer prior to the harvesting, 2) the relationships between the variance and the mean in the harvesting and corresponding count data, calculated over different populations at the same time, or the same locations at different times, were not statistically distinguishable, 3) similar direct and delayed density dependence patterns were observed in hunting records and count data. Our results suggest that red grouse hunting time series are a good proxy for population abundance.

PHASE DEPENDENCE AND POPULATION CYCLES IN A LARGE-MAMMAL PREDATOR–PREY SYSTEM

Specialized enemies, such as predators and parasitoids, play an important role in the population cycles of small animals by generating delayed density dependence. We investigated the role of predation in population cycles in an undisturbed large-mammal system using long-term data on the sustained density fluctuations of wolves and moose on Isle Royale (Michigan, USA). Nonlinear time-series analysis revealed that wolves display phase-dependent dynamics with stronger density dependence during the decline phase than during the increase phase. This phase dependence was also reflected in predation rates: the number of moose killed daily by wolves was greater during the wolf increase phase than during the wolf decline phase. Accordingly, moose displayed multi-annual cycles generated by an interaction between weak self-regulation and strong delayed density dependence during periods of wolf increase, and strong self-regulation with negligible delayed density dependence during periods of wolf decline. This constitutes, to our knowledge, the first formal documentation of population cycles in large mammals. By making use of long-term data at both trophic levels, as well as data on predator behavior, this analysis may shed light on the mechanisms through which predators contribute to population cycles of prey in other taxa.

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.

Interaction between seasonal density-dependence structures and length of the seasons explain the geographical structure of the dynamics of voles in Hokkaido: an example of seasonal forcing.

The grey-sided vole (Clethrionomys rufocanus) is distributed over the entire island of Hokkaido, Japan, across which it exhibits multi-annual density cycles in only parts of the island (the north-eastern part); in the remaining part of the island, only seasonal density changes occur. Using annual sampling of 189 grey-sided vole populations, we deduced the geographical structure in their second-order density dependence. Building upon our earlier suggestion, we deduce the seasonal density-dependent structure for these populations. Strong direct and delayed density dependence is found to occur during winter, whereas no density dependence is seen during the summer period. The direct density dependence during winter may be seen as a result of food being limited during that season: the delayed density dependence during the winter is consistent with vole-specialized predators (e.g. the least weasel) responding to vole densities so as to have a negative effect on the net growth rate of voles in the following year. We conclude that the observed geographical structure of the population dynamics may be properly seen as a result of the length of the summer in interaction with the differential seasonal density-dependent structure. Altogether, this indicates that the geographical pattern in multi-annual density dynamics in the grey-sided vole may be a result of seasonal forcing.

Long‐term responses in arctic ungulate dynamics to changes in climatic and trophic processes

AbstractFollowing predictions from climatic general circulation models, the effects of perturbations in global climate are expected to be most pronounced in the Northern Hemisphere. Elaborating on a recently developed plant–herbivore–climate model, we explore statistically how different winter climate regimes and density‐dependent processes during the past century have affected population dynamics of two arctic ungulate species. Our analyses were performed on the dynamics of six muskox and six caribou populations. In muskoxen, variation in winter climate, mediated through the North Atlantic Oscillation (NAO), explained up to 24% of the variation in interannual abundance, whereas in caribou up to 16% was explained by the NAO. Muskoxen responded negatively following warm and snowy winters, whereas caribou responded negatively to dry winters. Direct and delayed density dependence was recorded in most populations and explained up to 32% and 90% of variations in abundance of muskoxen and caribou, respectively.

Statistical modelling of the population dynamics of a raptor community in a semi‐desert environment

Summary We performed an extensive statistical modelling study on the population fluctuations and population growth rates of 15 raptor species in the Kalahari desert in South Africa. The correlation pattern between rainfall and population abundance changed systematically with raptor body weight and diet type. The abundance of heavier raptors feeding on larger prey‐items had lower correlations with rainfall than lighter raptors feeding on small prey‐items. Whereas raptor species feeding on small prey‐items were more affected by immediate rainfall, species feeding on large prey‐items were more affected by rainfall in the previous year. Population abundances were explained most parsimoniously by direct and delayed density dependence and rainfall during the current and previous breeding season. Interspecific competition was never a predictor variable. Population abundances of species best described by rainfall fed on larger prey‐items than population abundances of species best described by density dependence. Population growth rates were always best described by direct density dependence. The strength of density dependence was positively correlated with reproduction rate, due mainly to Falconiform species having higher reproduction rates than Accipitrid species. Shifting from the species to the guild level, we found that abundance and biomass shares of feeding guilds did not vary significantly over time, supporting the hypothesis of guild constancy.

Erratum

After the paper was published, a writing error was detected in the mathematical formula used to calculate the population increase rates. Because of this error, the statistical analyses of population increase rates were based on erroneous values. We recalculated the population increase rates using a corrected formula: where Nt is the catch index for a trapping occasion, Nt+T is the catch index for the following trapping occasion, and T is the time (in months) elapsed between the trapping occasions. To avoid division by zero, zero values were replaced with a value corresponding to a catch of 0.5 individuals in the trapping occasion. A reanalysis of the population increase rates revealed that the results published under subheading ‘Population increase rate’ (page 336 in the original article) and in Fig. 7 (page 339) were partly misleading. The main difference between the published results and the corrected results can be seen by comparing the previously published Fig. 7 with the corrected Fig. 7. In the corrected results, direct density dependence is more prevalent than in the previously published results. The difference is obvious particularly in autumn (population growth from August to October). In addition to the changes in Fig. 7, the results of regression analyses (page 336 right column) changed somewhat. In contrast to the previously published results, age structure did not explain a significant proportion of the variation in the population increase rates. The only variable that entered the stepwise regression models was productivity (the mean litter size multiplied by the proportion of females breeding), and even this variable could only explain 9% of the current population increase rate of bank voles (F1,48=5.0, P=0.03). In other species none of the variables studied entered the models. Corrected Fig. 7. Density dependence of the population increase rate. Pearson correlation coefficients for the relationship of the population increase rate with the density of the species studied (dots), pooled density of voles (circles), and regional mean density of voles (squares) with time lags from 0 to 12 months, separately for each species (field voles, sibling voles, bank voles, and common shrews) and season (spring=April to June, summer=June to August, autumn=August to October, and winter=October to April). Data from short line trappings in 1986–1992. Significant correlations are shown with an asterisk above (positive correlations) or below (negative correlations) the line. The corrected results reveal clear interspecific and seasonal differences in the relative importance of direct and delayed density dependence. In common shrews and bank voles, direct density dependence appears to prevail throughout the year (Fig. 7). The only exception is a negative relationship with previous vole densities (a time lag of 8–10 months) in bank voles in spring (population growth from April to June). In field voles, direct density dependence dominates in autumn but delayed density dependence from winter to the following summer (October to June). In sibling voles, the results resemble those of field voles with the exception that direct density dependence appears to be relatively more important in spring (Fig. 7). In contrast to the results of the original article, the corrected results suggest that the cessation of population growth at the population peak in August should be attributed to factors operating in a directly density dependent way at that part of the year. The corrected results also suggest that the delayed density dependent feedback loop necessary to generate the 3-year population cycle in Microtus voles operates during the period from late autumn to the following summer (October to June). These corrected results do not change the main conclusion of the original article: our results indicate that changes in survival rather than in reproduction drive the 3-year population cycles of voles.

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.

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 α, with stochasticity and density dependence in adult recruitment and mortality, we derive a linearized autoregressive equation with time lags from 1 to α 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, $$D=-\partial \mathrm{ln}\,\lambda ^{T}/ \partial \mathrm{ln}\,N$$, where λ 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.

OBSERVATION ERROR AND THE DETECTION OF DELAYED DENSITY DEPENDENCE

In an influential 1990 paper, Turchin concluded that delayed density dependence is common among insect populations. The statistical methods on which this conclusion was based assume that populations are observed without error. This note explores the effect of observation error on these methods. The results suggest that observation error can lead to a high rate of spurious detection of delayed density dependence.

Observation Error and the Detection of Delayed Density Dependence

In an influential 1990 paper, Turchin concluded that delayed density dependence is common among insect populations. The statistical methods on which this conclusion was based assume that populations are observed without error. This note explores the effect of observation error on these methods. The results suggest that observation error can lead to a high rate of spurious detection of delayed density dependence.

Effects of food addition on the seasonal density‐ dependent structure of bank vole Clethrionomys glareolus populations

Summary Population growth rates of bank vole populations in northern Finland were studied using long‐term Capture–Mark–Recapture (CMR) data from two large grids (food‐addition and control), in 1982–94. A marked seasonal structure was found for direct density dependence, with a stronger density dependence in summer than in other seasons. There was no detectable evidence of delayed density dependence, consistent with the disappearance of large periodic multi‐annual fluctuations. Food‐addition resulted in higher densities whereas the effect on the seasonal density‐dependent structure was negligible. Stability analysis of the deduced population dynamics model suggests that the dynamics were not affected by food addition. Variation in food resources is therefore unlikely to be a direct cause for multi‐annual fluctuations in the studied system. Future studies should aim at linking the seasonal structure in the variation of vital rates to the seasonal structure in population dynamics.

Contrasting alternative hypotheses about rodent cycles by translating them into parameterized models

Ecologists working on population cycles of arvicoline (microtine) rodents consider three ecological mechanisms as the most likely explanations of this long‐standing puzzle in population ecology: maternal effects, interaction with specialist predators, and interaction with the food supply. Each of these hypotheses has now been translated into parameterized models, and has been shown to be capable of generating second‐order oscillations (that is, population cycles driven by delayed density dependence). This development places us in a unique situation for population ecology. We can now practice “strong inference” by explicitly and quantitatively comparing the predictions of the three rival hypotheses with data. In this review, we contrast the ability of each hypothesis to explain various empirically observed features of rodent cycles, with a particular emphasis on the well‐studied case of Microtus agrestis and other small rodents in Fennoscandia (Finland, Sweden and Norway). Our conclusion is that the current evidence best supports the predation hypothesis.

CHANGES IN PANDORA MOTH OUTBREAK DYNAMICS DURING THE PAST 622 YEARS

Episodic outbreaks of pandora moth (Coloradia pandora Blake), a forest insect that defoliates ponderosa pine (Pinus ponderosa Dougl. ex Laws.) and other pine species in the western United States, have recurred several times during the 20th century in forests of south-central Oregon. We collected and analyzed tree-ring samples from stands affected by recent outbreaks of pandora moth to develop a long-term record of outbreaks. Outbreaks were evident in tree-ring series as a characteristic ''signature'' of sharply reduced latewood width within a ring, followed by reduced ring widths lasting 4-20 yr. We verified that this tree-ring signature was unrelated to drought or other climatic fluctuations by comparing the timing of known and inferred outbreaks with independent climatic data. Using the pandora moth tree-ring signature, we reconstructed a 622-year record of 22 individual outbreaks in 14 old-growth ponderosa pine stands. This is currently the longest regional reconstruction of forest insect outbreak history in North America. Intervals between pandora moth outbreaks were highly variable within individual forest stands, ranging from 9 yr to 156 yr. Spectral analyses of a composite time series from all stands, however, showed more consistent intervals between outbreaks, suggesting quasicyclical population dynamics at regional and decadal scales. Waveforms extracted from the regional outbreak time series had periods ranging over ;18-24 yr (39.7% variance explained) and ;37-41 yr (37.3% variance explained). The periods and strengths of these cycles varied across the centuries, with the largest outbreaks occurring when relatively high-amplitude periods of the dominant cycles were in phase. Twentieth-century outbreaks were not more synchronous (extensive), severe, or longer in duration than outbreaks in previous centuries, but there was an unusual 60-yr reduction in regional activity during ;1920-1980. The changing dynamical behavior of pandora moth populations highlights the need to evaluate historical factors that may have influenced this system, such as climatic variations, forest fires, and human land uses. Although cyclical dynamics in animal populations have most commonly been attributed to endogenous, ecological processes (e.g., ''delayed density dependence,'' predators, patho- gens, and parasites) our findings suggest that exogenous processes (e.g., climatic oscilla- tions) may also be involved.

A Critical Evaluation of Research Techniques in Animal Ecology

A Critical Evaluation of Research Techniques in Animal Ecology

Reinterpreting space, time lags, and functional responses in ecological models.

Natural enemy-victim interactions are of major applied importance and of fundamental interest to ecologists. A key question is what stabilizes these interactions, allowing the long-term coexistence of the two species. Three main theoretical explanations have been proposed: behavioral responses, time-dependent factors such as delayed density dependence, and spatial heterogeneity. Here, using the powerful moment-closure technique, we show a fundamental equivalence between these three elements. Limited movement by organisms is a ubiquitous feature of ecological systems, allowing spatial structure to develop; we show that the effects of this can be naturally described in terms of time lags or within-generation functional responses.

Complex emergence patterns in a bark beetle predator

Abstract1 The emergence pattern of Thanasimus dubius (F.) (Coleoptera: Cleridae), a common predator of the southern pine beetle, Dendroctonus frontalis Zimmermann (Coleoptera: Scolytidae), was studied under field conditions across different seasons. A simple statistical model was then developed to characterize the emergence data, using the truncated geometric distribution. Data are also presented on the mortality of T. dubius eggs at various temperatures and humidities in an effort to explain certain aspects of emergence behaviour.2 Emergence of T. dubius from a given tree usually occurred in several discrete episodes across a two‐year period, with most individuals emerging in spring or autumn. Almost no emergence occurred in July and August, which may be an adaptation to avoid high temperature mortality. Emergence patterns appeared similar across seasons, with the time of year serving mainly to shift the pattern through time.3 Cycles in D. frontalis abundance may be the result of delayed density dependence generated by its natural enemy complex. The predator T. dubius is likely to be an important component of this delayed density dependence, because of its lengthy development time and apparent impact on D. frontalis.

Population dynamics of two marine polychaetes: the relative role of density dependence, predation, and winter conditions

Van der Meer, J., Beukema, J. J., and Dekker, R. 2000. Population dynamics of two marine polychaetes: the relative role of density dependence, predation, and winter conditions. – ICES Journal of Marine Science, 57: 1488–1494. We modelled the population dynamics of two polychaete species, a prey (Scoloplos armiger) and its predator (Nephtys hombergii) by simple linear and non-linear time–series models using a 29 year data series of population abundance and winter conditions. The log reproductive rate (i.e., the difference in log density between two succeeding years) of the prey population was density dependent and negatively related to the density of the predator. The log reproductive rate of the predator was also density dependent, but was to a greater extent determined by winter temperature, a density-independent factor. Log reproductive rate of the predator was not related to the density of the prey, nor could delayed density dependence be detected. Apparently, the feedback mechanism between predator and prey was weak, perhaps because the predator is a generalist. Predator density can therefore be categorized as a densityindependent factor with respect to the dynamics of the prey species. In neither of the two species was density dependence strong enough to generate complex or chaotic behaviour, as indicated by the weakly negative slope of the reproduction curve at the equilibrium, the apparent lack of a non-linear component in the reproduction curve, and the negative Lyapunov exponent.