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.     

Nutrient enrichment alters dynamics in experimental plant populations

Controlling weed populations requires an understanding of their underlying population dynamics which can be achieved through a combination of model development and long-term studies. In this paper, we develop models based on long-term data from experimental populations of the weedy annual plant Cardamine pensylvanica. Four replicate populations of C. pensylvanica were grown in growth chambers under three different nutrient levels but with all other environmental conditions held constant. We analyze the resulting time series using generalized additive models and perform stability analyses using Lyapunov exponents. Further, we test whether the proposed mechanism, delayed density dependence caused by maternal effects, is operating in our system by experimentally manipulating maternal density and assessing the resulting offspring quality. Our results show that that increasing the frequency of nutrients causes plant population dynamics to shift from stable to damped 2-point oscillations to longer cycles. This shift in population dynamics is due to a shift at high nutrients from populations being regulated by first order density feedbacks to being regulated by both first order and second order density feedbacks. A consequence of these first order and second order feedbacks was an increase in cycle lengths as demonstrated by the presence of complex eigenvalues. A short-term experiment confirmed that when grown under high nutrients, the density of maternal plants strongly affected offspring size, providing a mechanism whereby these second order density feedbacks could operate. Our results demonstrate that increasing nutrient frequency results in a qualitative shift in dynamics from stable to longer cycles.     

Experimental evidence that livestock grazing intensity affects cyclic vole population regulation processes

Grazing by domestic ungulates may limit the densities of small herbivorous mammals that act as key prey in ecosystems. Whether this also influences density dependence and the regulation of small herbivore populations, hence their propensity to exhibit multi-annual population cycles, is unknown. Here, we combine time series analysis with a large-scale grazing experiment on upland grasslands to examine the effects of livestock grazing intensity on the population dynamics of field voles (Microtus agrestis). Using log-linear modelling of replicated time series under different grazing treatments, we show that increased sheep densities weaken delayed density dependent regulation of vole population growth, hence reducing the cyclicity in vole population dynamics. While population regulation is commonly attributed to both top-down and bottom up processes, our results suggest that regulation of cyclic vole populations can be disrupted by the influence of another grazer in the same trophic level. These results support the view that ongoing changes in domestic grazing intensity, by affecting small mammal dynamics, can potentially have cascading impacts on higher trophic levels, and strongly influence the dynamics of upland grassland systems.     

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.     

Variation in plant quality and the population dynamics of herbivores: there is nothing average about aphids

In the attempt to use results from small-scale studies to make large-scale predictions, it is critical that we take into account the greater spatial heterogeneity encountered at larger spatial scales. An important component of this heterogeneity is variation in plant quality, which can have a profound influence on herbivore population dynamics. This influence is particularly relevant when we consider that the strength of density dependence can vary among host plants and that the strength of density dependence determines the difference between exponential and density- dependent growth. Here, we present some simple models and analyses designed to examine the impact of variable plant quality on the dynamics of insect herbivore populations, and specifically the consequences of variation in the strength of density dependence among host plants. We show that average values of herbivore population growth parameters, calculated from plants that vary in quality, do not predict overall population growth. Furthermore, we illustrate that the quality of a few individual plants within a larger plant population can dominate herbivore population growth. Our results demonstrate that ignoring spatial heterogeneity that exists in herbivore population growth on plants that differ in quality can lead to a misunderstanding of the mechanisms that underlie population dynamics.     

Cycles, stochasticity and density dependence in pink salmon population dynamics

Complex dynamics of animal populations often involve deterministic and stochastic components. A fascinating example is the variation in magnitude of 2-year cycles in abundances of pink salmon (Oncorhynchus gorbuscha) stocks along the North Pacific rim. Pink salmon have a 2-year anadromous and semelparous life cycle, resulting in odd- and even-year lineages that occupy the same habitats but are reproductively isolated in time. One lineage is often much more abundant than the other in a given river, and there are phase switches in dominance between odd- and even-year lines. In some regions, the weak line is absent and in others both lines are abundant. Our analysis of 33 stocks indicates that these patterns probably result from stochastic perturbations of damped oscillations owing to density-dependent mortality caused by interactions between lineages. Possible mechanisms are cannibalism, disease transmission, food depletion and habitat degradation by which one lineage affects the other, although no mechanism has been well-studied. Our results provide comprehensive empirical estimates of lagged density-dependent mortality in salmon populations and suggest that a combination of stochasticity and density dependence drives cyclical dynamics of pink salmon stocks.     

Seasonally limited host supply generates microparasite population cycles

Cycles in biological populations have been shown to arise from enemy-victim systems, delayed density dependence, andmaternal 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.     

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.     

Characterizing population vulnerability for 758 species

We investigate relationships between life history traits and the character of population dynamics as revealed by time series data. Our classification of time series is according to 'extinction category,' where we identify three classes of populations: (i) weakly varying populations with such high growth rates that long-term persistence is likely (unless some extreme catastrophe occurs); (ii) populations with such low growth rates that average population size must be large to buffer them against extinction in a variable environment; and (iii) highly variable populations that fluctuate so dramatically that dispersal or some other refuge mechanism is likely to be key to their avoidance of extinction. Using 1941 time series representing 758 species from the Global Population Dynamics Database, we find that, depending on the form of density dependence one assumes, between 46 and 90% of species exhibit dynamics that are so variable that even large carrying capacities could not buffer them against extinction on a 100-year time horizon. The fact that such a large proportion of population dynamics are so locally variable vindicates the growing realization that dispersal, habitat connectedness, and large-scale processes are key to local persistence. Furthermore, for mammals, simply by knowing body size, age at first reproduction, and average number of offspring we could correctly predict extinction categories for 83% of species (60 of 72).     

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

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

The collapse of cycles in the dynamics of North American grouse populations

Cyclic dynamics of bird and mammal populations are commonly reported in northern latitudes throughout the world, and recent European observations on rodents and grouse suggest that cycle periods decline towards southern latitudes. To investigate latitudinal patterns of cyclic dynamics in North America, we assembled 27 long‐term data sets collected between 1939 and 2001 for three grouse species. By fitting the data with autoregressive models to measure direct and delayed density dependence, we show that, in contrast to European studies, North American grouse exhibit period increases from north to south, with cycles collapsing via period lengthening. This occurs because delayed density dependence decreases in southern latitudes, whereas direct density dependence increases. These results show that cyclic dynamics can dissipate by period lengthening as well as the period shortening postulated for European grouse and rodents.     

Intrinsic and extrinsic determinants of mountain pine beetle population growth

1 Mountain pine beetle Dendroctonus ponderosae populations have large, economically significant outbreaks. Density dependence and environmental variability are expected to have important effects on their dynamics. We analysed time series data from an outbreak in the 1930s to determine the relative importance of population density and environmental variability on local population growth rates.
2 Resource depletion occurred rapidly at the scale of 0.4 ha and population growth rates were strongly density dependent. Annual environmental changes did not have detectable effects on population growth rates, leading to the conclusion that intrinsic processes influenced local population density more than extrinsic factors during this outbreak.
3 Our calculated value of r _max (1.16) does not suggest intrinsically cyclic population dynamics. Our estimate of r _max and density dependence will be useful in developing applied models of mountain pine beetle outbreaks, and the subsequent evaluation of management strategies.     

Comparative population dynamics of large and small mammals in the Northern Hemisphere: deterministic and stochastic forces

Deterministic feedbacks within populations interact with extrinsic, stochastic processes to generate complex patterns of animal abundance over time and space. Animals inherently differ in their responses to fluctuating environments due to differences in body sizes and life history traits. However, controversy remains about the relative importance of deterministic and stochastic forces in shaping population dynamics of large and small mammals. We hypothesized that effects of environmental stochasticity and density dependence are stronger in small mammal populations relative to their effects in large mammal populations and thus differentiate the patterns of population dynamics between them. We conducted an extensive, comparative analysis of population dynamics in large and small mammals to test our hypothesis, using seven population parameters to describe general dynamic patterns for 23 (14 species) time series of observations of abundance of large mammals and 38 (21 species) time series for small mammals. We used state‐space models to estimate the strength of direct and delayed density dependence as well as the strength of environmental stochasticity. We further used phylogenetic comparative analysis to detect differences in population dynamic patterns and individual population parameters, respectively, between large and small mammals. General population dynamic patterns differed between large and small mammals. However, the strength of direct and delayed density dependence was comparable between large and small mammals. Moreover, the variances of population growth rates and environmental stochasticity were greater in small mammals than in large mammals. Therefore, differences in population response to stochastic forces and strength of environmental stochasticity are the primary factor that differentiates population dynamic patterns between large and small mammal species.     

Comparative population dynamics of <Emphasis Type="Italic">Peromyscus leucopus</Emphasis> in North America: influences of climate,food, and density dependence

Temporal variation in population size is regulated by both exogenous forces and density-dependent feedbacks. Furthermore, accumulating evidence indicates that temporal and spatial variation in climate and resources can modify the strength of density dependence in animal populations. We analyzed six long-term time series estimates of Peromyscus leucopus (white-footed mouse) abundance from Kansas, Ohio, Pennsylvania, Virginia, Vermont, and Maine, USA, using the Kalman filter. Model-averaged estimates of the strength of delayed density dependence increased from west to east and from south to north. The strength of direct and delayed density dependence was positively related to the annual number of days with minimum temperature below −17.8°C. Annual population growth rates of P. leucopus at the Maine site were positively related to acorn abundance and P. leucopus populations tracked the changes in red-oak acorn abundance. The populations of P. leucopus living in northern latitudes might be more dependent on northern red oak (Quercus rubra) acorns for winter food than P. leucopus in southern latitudes. Furthermore, northern red oak trees mast every 4–5 years. Thus, longer, colder winters in northerly latitudes might result in stronger delayed density dependence in mouse populations with a shortage of winter food. Mice might simply track the acorn fluctuations in a delayed autocorrelated manner; however, delayed density dependence remained in our models for the Maine mouse populations after accounting for acorns, suggesting additional sources for delayed density dependence. Our results suggest that, in seed-eating Peromyscus, cyclicity may be regulated, in part, from low to high trophic levels. Deceased: Jerry O. Wolff     

Linking climate change to population cycles of hares and lynx

The classic 10‐year population cycle of snowshoe hares (Lepus americanus, Erxleben 1777) and Canada lynx (Lynx canadensis, Kerr 1792) in the boreal forests of North America has drawn much attention from both population and community ecologists worldwide; however, the ecological mechanisms driving the 10‐year cyclic dynamic pattern are not fully revealed yet. In this study, by the use of historic fur harvest data, we constructed a series of generalized additive models to study the effects of density dependence, predation, and climate (both global climate indices of North Atlantic Oscillation index (NAO), Southern Oscillation index (SOI) and northern hemispheric temperature (NHT) and local weather data including temperature, rainfall, and snow). We identified several key pathways from global and local climate to lynx with various time lags: rainfall shows a negative, and snow shows a positive effect on lynx; NHT and NAO negatively affect lynx through their positive effect on rainfall and negative effect on snow; SOI positively affects lynx through its negative effect on rainfall. Direct or delayed density dependency effects, the prey effect of hare on lynx and a 2‐year delayed negative effect of lynx on hare (defined as asymmetric predation) were found. The simulated population dynamics is well fitted to the observed long‐term fluctuations of hare and lynx populations. Through simulation, we find density dependency and asymmetric predation, only producing damped oscillation, are necessary but not sufficient factors in causing the observed 10‐year cycles; while extrinsic climate factors are important in producing and modifying the sustained cycles. Two recent population declines of lynx (1940–1955 and after 1980) were likely caused by ongoing climate warming indirectly. Our results provide an alternative explanation to the mechanism of the 10‐year cycles, and there is a need for further investigation on links between disappearance of population cycles and global warming in hare–lynx system.     

Comment arising from a paper by Wolda and Dennis: using and interpreting the results of tests for density dependence

We argue that tests for density dependence are useful in analyses of population dynamics and suggest guide lines for their use and interpretation of results which avoid many of the problems discussed by Wolda and Dennis (1993). Processes other than density dependence per se can cause statistical tests to indicate the presence of density dependence (Wolda and Dennis 1993 and unpublished simulations). Tests for density dependence cannot reveal the mechanism of regulation, but they do indicate the nature of long-term population dynamics. Tests for density dependence give misleading results if sampling is not at generation intervals; however, this problem is avoided if we only use tests on data collected in each generation (Holyoak 1993a). Similarly, species should be semelparous. Non-delayed density dependence should not be considered without looking for delayed density dependence, since the presence of delayed density dependence can lead to over-detection of non-delayed density dependence (Woiwod and Hanski 1992; Holyoak 1993b). The partial autocorrelation function and knowledge of life-history are more useful than tests for density dependence for indicating whether any density dependence is delayed or not (Royama 1992; Holyoak 1993b). Estimation error with a constant upper size limit causes tests for density dependence to overestimate the frequency of delayed density dependence; however we do not know whether estimation error is bounded in real populations. Work in progress suggests that 20–40 generations (depending on the nature of population dynamics) gives a moderate level of accuracy with tests for density dependence, and >40 generations are necessary for tests to be accurate in their assessment of the strength of density dependence. We conclude that tests are useful indicators of whether density dependence, or other feedback mechanisms are likely to be acting.     

Changes over time in the spatiotemporal dynamics of cyclic populations of field voles (Microtus agrestis L.)

We demonstrate changes over time in the spatial and temporal dynamics of an herbivorous small rodent by analyzing time series of population densities obtained at 21 locations on clear cuts within a coniferous forest in Britain from 1984 to 2004. Changes had taken place in the amplitude, periodicity, and synchrony of cycles and density-dependent feedback on population growth rates. Evidence for the presence of a unidirectional traveling wave in rodent abundance was strong near the beginning of the study but had disappeared near the end. This study provides empirical support for the hypothesis that the temporal (such as delayed density dependence structure) and spatial (such as traveling waves) dynamics of cyclic populations are closely linked. The changes in dynamics were markedly season specific, and changes in overwintering dynamics were most pronounced. Climatic changes, resulting in a less seasonal environment with shorter winters near the end of the study, are likely to have caused the changes in vole dynamics. Similar changes in rodent dynamics and the climate as reported from Fennoscandia indicate the involvement of large-scale climatic variables.     

Comparing the consequences of induced and constitutive plant resistance for herbivore population dynamics

Although it has been suggested that induced and constitutive plant resistance should have different effects on insect herbivore population dynamics, there is little experimental evidence that plant resistance can influence herbivore populations longer than one season. We used a density-manipulation experiment and model fitting to examine the effects of constitutive and induced resistance on herbivore dynamics over both the short and long term. We used likelihood methods to fit population dynamic models to recruitment data for populations of Mexican bean beetles on soybean varieties with no resistance, constitutive resistance, or induced resistance. We compared model configurations that fit parameters for resistance types separately to models that did not account for resistance type. Models representing the hypothesis that the three resistance types differed in their effects on beetle dynamics received the most support. Induced resistance resulted in lower population growth rates and stronger density dependence than no resistance. Constitutive resistance resulted in lower population growth rates and stronger density dependence than induced resistance. Constitutive resistance had a stronger effect on both short-term beetle recruitment and predicted beetle population dynamics than induced resistance. The results of this study suggest that induced and constitutive resistance can differ in their effects on herbivore populations even in a relatively complex system.     

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.     

Floater dynamics can explain positive patterns of density-dependent fecundity in animal populations

After some 70 years of debate on density-dependent regulation of animal populations, there is still poor understanding of where spatial and temporal density dependence occurs. Clearly defining the portion of the population that shapes density-dependent patterns may help to solve some of the ambiguities that encircle density dependence and its patterns. In fact, individuals of the same species and population can show different dynamics and behaviors depending on their locations (e.g., breeding vs. dispersal areas). Considering this form of intrapopulation heterogeneity may improve our understanding of density dependence and population dynamics in general. We present the results of individual-based simulations on a metapopulation of the Spanish imperial eagle Aquila adalberti. Our results suggest that high rates of floater mortality within settlement areas can determine a shift in the classical relationship (from negative to positive) between the fecundity (i.e., fledglings per pair) and density (i.e., number of pairs) of the breeding population. Finally, we proved that different initial conditions affecting the breeder portion of the population can lead to the same values of fecundity. Our results can represent a starting point for new and more complex approaches studying the regulation of animal populations, where the forgotten and invisible component--the floater--is taken into account.