Density‐dependent mortality in Pacific salmon: the ghost of impacts past?

Conservation biologists often ignore density dependence because at‐risk populations are typically small relative to historical levels. However, if populations are reduced as a result of impacts that lower carrying capacity, then density‐dependent mortality may exist at low population abundances. Here, we explore this issue in threatened populations of juvenile chinook salmon (Oncorhynchus tshawytscha). We followed the fate of more than 50 000 juvenile chinook in the Snake River Basin, USA to test the hypothesis that their survival was inversely associated with juvenile density. We also tested the hypotheses that non‐indigenous brook trout and habitat quality affect the presence or strength of density dependence. Our results indicate that juvenile chinook suffer density‐dependent mortality and the strength of density dependence was greater in streams in which brook trout were absent. We were unable to detect an effect of habitat quality on the strength of density dependence. Historical impacts of humans have greatly reduced population sizes of salmon, and the density dependence we report may stem from a shortage of nutrients normally derived from decomposing salmon carcasses. Cohorts of juvenile salmon may experience density‐dependent mortality at population sizes far below historical levels and recovery of imperiled populations may be much slower than currently expected.     

The Role of Density Regulation in Extinction Processes and Population Viability Analysis

We review the role of density dependence in the stochastic extinction of populations and the role density dependence has played in population viability analysis (PVA) case studies. In total, 32 approaches have been used to model density regulation in theoretical or applied extinction models, 29 of them are mathematical functions of density dependence, and one approach uses empirical relationships between density and survival, reproduction, or growth rates. In addition, quasi-extinction levels are sometimes applied as a substitute for density dependence at low population size. Density dependence further has been modelled via explicit individual spacing behaviour and/or dispersal. We briefly summarise the features of density dependence available in standard PVA software, provide summary statistics about the use of density dependence in PVA case studies, and discuss the effects of density dependence on extinction probability. The introduction of an upper limit for population size has the effect that the probability of ultimate extinction becomes 1. Mean time to extinction increases with carrying capacity if populations start at high density, but carrying capacity often does not have any effect if populations start at low numbers. In contrast, the Allee effect is usually strong when populations start at low densities but has only a limited influence on persistence when populations start at high numbers. Contrary to previous opinions, other forms of density dependence may lead to increased or decreased persistence, depending on the type and strength of density dependence, the degree of environmental variability, and the growth rate. Furthermore, effects may be reversed for different quasi-extinction levels, making the use of arbitrary quasi-extinction levels problematic. Few systematic comparisons of the effects on persistence between different models of density dependence are available. These effects can be strikingly different among models. Our understanding of the effects of density dependence on extinction of metapopulations is rudimentary, but even opposite effects of density dependence can occur when metapopulations and single populations are contrasted. We argue that spatially explicit models hold particular promise for analysing the effects of density dependence on population viability provided a good knowledge of the biology of the species under consideration exists. Since the results of PVAs may critically depend on the way density dependence is modelled, combined efforts to advance statistical methods, field sampling, and modelling are urgently needed to elucidate the relationships between density, vital rates, and extinction probability.     

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.     

Predators reverse the direction of density dependence for juvenile salmon mortality

The effect of predators on prey populations depends on how predator-caused mortality changes with prey population density. Predators can enforce density-dependent prey mortality and contribute to population stability, but only if they have a positive numerical or behavioral response to increased prey density. Otherwise, predator saturation can result in inversely density-dependent mortality, destabilizing prey populations and increasing extinction risk. Juvenile salmon and trout provide some of the clearest empirical examples of density-dependent mortality in animal populations. However, although juvenile salmon are very vulnerable to predators, the demographic effects of predators on juvenile salmon are unknown. We tested the interactive effects of predators and population density on the mortality of juvenile Atlantic salmon (Salmo salar) using controlled releases of salmon in natural streams. We introduced newly hatched juvenile salmon at three population density treatments in six study streams, half of which contained slimy sculpin (Cottus cognatus), a common generalist predator (18 release sites in total, repeated over two summers). Sculpin reversed the direction of density dependence for juvenile salmon mortality. Salmon mortality was density dependent in streams with no sculpin, but inversely density dependent in streams where sculpin were abundant. Such predator-mediated inverse density dependence is especially problematic for prey populations suppressed by other factors, thereby presenting a fundamental challenge to persistence of rare populations and restoration of extirpated populations.     

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.     

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.     

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     

Estimating Sustainable Harvest in Wolverine Populations Using Logistic Regression

Abstract: Population viability analysis (PVA) is a common tool to evaluate population vulnerability. However, most techniques require reliable estimates of underlying population parameters, which are often difficult to obtain and PVA are, therefore, best used in a qualitative context. Logistic regression is a powerful alternative to traditional PVA methods but has received surprisingly limited attention. Logistic regression fits regression equations to binary output from PVA models at a specific point in time to predict probability of a binary response over a range of parameter values. We used logistic regression on output from stochastic population models to evaluate the relative importance of demographic parameters for wolverine (Gulo gulo) populations and to estimate sustainable harvest in a wolverine population in Alaska. Our analysis indicated that adult survival is the most important demographic parameter to reliably estimate in wolverine populations because it had a greater effect on population persistence than did both fecundity and subadult survival. In accordance with this, harvest rate had a greater effect on population persistence than did any of the other harvest- and migration-related variables we tested. Furthermore, a high proportion of harvested females strengthened the effect of harvest. Hypothetical wolverine populations suffered high probabilities of both extinction and population decline over a range of realistic population sizes and harvest regimes. We suggest that harvested wolverine populations must be regarded as sink populations and that source populations in combination with sufficient dispersal corridors must be secured for any wolverine harvest to be sustainable.     

Effects of experimental population extinction for the spatial population dynamics of the butterfly Parnassius smintheus

While many studies have examined factors potentially impacting the rate of local population extinction, few experimental studies have examined the consequences of extinction for spatial population dynamics. Here we report results from a large‐scale, long‐term experiment examining the effects of local population extinction for the dynamics of surrounding populations. From 2001–2008 we removed all adult butterflies from two large, neighboring populations within a system of 17 subpopulations of the Rocky Mountain Apollo butterfly, Parnassius smintheus. Surrounding populations were monitored using individual, mark–recapture methods. We found that population removal decreased immigration to surrounding populations in proportion to their connectivity to the removed populations. Correspondingly, within‐generation population abundance declined. Despite these effects, we saw little consistent impact between generations. The extinction rates of surrounding populations were unaffected and local population growth was not consistently reduced by the lack of immigration. The broader results show that immigration affects local abundance within generations, but dynamics are mediated by density‐dependence within populations and by broader density‐independent factors acting between generations. The loss of immigrants resulting from extinction has little impact on the persistence of local populations in this system.     

Recruitment limitation: A theoretical perspective

Abstract A theoretical analysis of the concept of recruitment limitation leads to the conclusion that most populations should he regarded as jointly limited by recruitment and interactions between individuals after recruitment. The open nature of local marine systems does not permit avoidance of density-dependent interactions; it simply may make them more difficult to detect. Local populations consisting of settled organisms may not experience density-dependent interactions under some circumstances, but the entire species population consisting of the collection of local populations and their planktonic larvae must have density-dependent dynamics. Any local population of settled individuals can escape density dependence if sufficient density dependence occurs among planktonic larvae or within other local populations. Common conceptions of density dependence are too narrow, leading too often to the conclusion that it is absent from a system. It is equally wrong to expect that density-dependent interactions after settlement determine local population densities independently of recruitment. Special circumstances allowing density dependence to act strongly and quickly are needed before density dependence can neutralize the effects of recruitment. Recruitment limitation and density-dependent interactions therefore should not be regarded as alternatives but as jointly acting to determine the densities of marine benthic populations. Moreover, the interaction between fluctuating recruitment and density dependence is potentially the most interesting feature of recruitment limitation. For example, this interaction may be an important diversity-maintaining mechanism for marine systems.     

Estimation of a Nonlinear Density-Dependence Parameter for Wild Turkey

Abstract: Although previous research and theory has suggested that wild turkey (Meleagris gallopavo) populations may be subject to some form of density dependence, there has been no effort to estimate and incorporate a density-dependence parameter into wild turkey population models. To estimate a functional relationship for density dependence in wild turkey, we analyzed a set of harvest-index time series from 11 state wildlife agencies. We tested for lagged correlations between annual harvest indices using partial autocorrelation analysis. We assessed the ability of the density-dependent theta-Ricker model to explain harvest indices over time relative to exponential or random walk growth models. We tested the homogeneity of the density-dependence parameter estimates (θ) from 3 different harvest indices (spring harvest no. reported harvest/effort, survey harvest/effort) and calculated a weighted average based on each estimate's variance and its estimated covariance with the other indices. To estimate the potential bias in parameter estimates from measurement error, we conducted a simulation study using the theta-Ricker with known values and lognormally distributed measurement error. Partial autocorrelation function analysis indicated that harvest indices were significantly correlated only with their value at the previous time step. The theta-Ricker model performed better than the exponential growth or random walk models for all 3 indices. Simulation of known parameters and measurement error indicated a strong positive upward bias in the density-dependent parameter estimate, with increasing measurement error. The average density-dependence estimate, corrected for measurement error ranged 0.25 ≤ θC ≤ 0.49, depending on the amount of measurement error and assumed spring harvest rate. We infer that density dependence is nonlinear in wild turkey, where growth rates are maximized at 39-42% of carrying capacity. The annual yield produced by density-dependent population growth will tend to be less than that caused by extrinsic environmental factors. This study indicates that both density-dependent and density-independent processes are important to wild turkey population growth, and we make initial suggestions on incorporating both into harvest management strategies.     

Multiple sources of evidence for density dependence in the endangered Hawaiian stilt (Himantopus mexicanus knudseni)

Hawaiian stilts (Himantopus mexicanus knudseni) are an endangered subspecies of the Black-necked stilt endemic to the Hawaiian Islands. Despite long-term study, the main drivers of Hawaiian stilt population dynamics are poorly understood. We tested for density dependence using two sources of evidence: a 30-year time series of annual estimated range-wide abundance, and two 15+ year time series of reproductive success. Using separate methods with independent data, sources allowed us to make up for the potentially positive bias of one approach with the more conservative nature of the second. We compared nonlinear density-dependent and density-independent population model fits to our time-series data, using both frequentist and Bayesian state-space approaches. Across both approaches, density-dependent models best fit observed population dynamics, with lower AICc and cross-validation statistics compared to density-independent models. Among density-dependent models, a conditional model in which density-independent dynamics occur below a population size threshold (~850–1,000 birds), and then density-dependent dynamics occur above that threshold, performed best across Bayesian and frequentist model comparisons, with the Ricker model ranked next or equivalently. Our analysis of reproduction data revealed a strong negative effect of local adult density on nest success (proportion of nests hatching at least one chick) at Kealia National Wildlife Refuge on Maui, where few alternative breeding habitats are available, but no such effect at another site where many nearby alternative wetlands are available. These congruent results across independent datasets and analytical approaches support the hypothesis that Hawaiian stilts exhibit density dependence across their range.     

Mechanisms of density dependence in fluctuating vole populations: deducing annual density dependence from seasonal processes

Based on recent advances in time-series analyses of ecological dynamics using statistical and mathematical models, we summarise our recent results on the seasonal processes in the annual population dynamics of the grey-sided vole Clethrionomys rufocanus (Sundevall, 1846) in Hokkaido, Japan, and report additional analyses on annual and seasonal density dependence. Annual direct density dependence was strong in almost all populations. In contrast, delayed density dependence was generally weak, although clear delayed density dependence was detected in some of the studied populations. Although seasonal density dependence was observed both in winter and summer, direct density dependence was much more profound during winter; thus, winter density dependence contributed most to the overall annual direct density dependence. We found no correlation between the seasonal components of annual direct density dependence; however, the corresponding seasonal components for annual delayed density dependence were positively correlated. We conclude that winter conditions influence the strength of annual direct density dependence most profoundly. Moreover, we conclude that direct density dependence during summer and winter may be generated by different mechanisms, whereas delayed density dependence seems to be generated by a common mechanism. Candidate mechanisms are discussed in relation to general knowledge of northern rodent populations and to specific insights provided by earlier studies of grey-sided voles in Hokkaido.     

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.     

Shifting trends: detecting environmentally mediated regulation in long-lived marine vertebrates using time-series data

Assessing the status and trends in animal populations is essential for effective species conservation and management practices. However, unless time-series abundance data demonstrate rapid and reliable fluctuations, objective appraisal of directionality of trends is problematic. We adopted a multiple-working hypotheses approach based on information-theoretic and Bayesian multi-model inference to examine the population trends and form of intrinsic regulation demonstrated by a long-lived species, the southern elephant seal. We also determined the evidence for density dependence in 11 other well-studied marine mammal species. (1) We tested the type of population regulation for elephant seals from Marion Island (1986–2004) and from 11 other marine mammal species, and (2) we described the trends and behavior of the 19-year population time series at Marion Island to identify changes in population trends. We contrasted five plausible trend models using information-theoretic and Bayesian-inference estimates of model parsimony. Our analyses identified two distinct phases of population growth for this population with the inflexion occurring in 1998. Thus, the population decreased between 1986 and 1997 (−3.7% per annum) and increased between 1997 and 2004 (1.9% per annum). An index of environmental stochasticity, the Southern Oscillation Index, explained some of the variance in r and N. We determined analytically that there was good evidence for density dependence in the Marion Island population and that density dependence was widespread among marine mammal species (67% of species showed evidence for population regulation). This approach demonstrates the potential functionality of a relatively simple technique that can be applied to short time series to identify the type of regulation, and the uncertainty associated with the phenomenon, operating in populations of large mammals.     

The role of age of first breeding in modeling raptor reintroductions

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The role of predation in the decline and extirpation of woodland caribou

To select appropriate recovery strategies for endangered populations, we must understand the dynamics of small populations and distinguish between the possible causes that drive such populations to low numbers. It has been suggested that the pattern of population decline may be inversely density-dependent with population growth rates decreasing as populations become very small; however, empirical evidence of such accelerated declines at low densities is rare. Here we analyzed the pattern of decline of a threatened population of woodland caribou (Rangifer tarandus caribou) in British Columbia, Canada. Using information on the instantaneous rate of increase relative to caribou density in suitable winter foraging habitat, as well as on pregnancy rates and on causes and temporal distribution of mortalities from a sample of 349 radiocollared animals from 15 subpopulations, we tested 3 hypothesized causes of decline: (a) food regulation caused by loss of suitable winter foraging habitat, (b) predation-sensitive foraging caused by loss of suitable winter foraging habitat and (c) predation with caribou being secondary prey. Population sizes of caribou subpopulations ranged from <5 to >500 individuals. Our results showed that the rates of increase of these subpopulations varied from −0.1871 to 0.0496 with smaller subpopulations declining faster than larger subpopulations. Rates of increase were positively related to the density of caribou in suitable winter foraging habitat. Pregnancy rates averaged 92.4% ±2.24 and did not differ among subpopulations. In addition, we found predation to be the primary cause of mortality in 11 of 13 subpopulations with known causes of mortality and predation predominantly occurred during summer. These results are consistent with predictions that caribou subpopulations are declining as a consequence of increased predation. Recovery of these woodland caribou will thus require a multispecies perspective and an appreciation for the influence of inverse density dependence on population trajectories.     

Individual‐based modelling of resource competition to predict density‐dependent population dynamics: a case study with white storks

Density regulation influences population dynamics through its effects on demographic rates and consequently constitutes a key mechanism explaining the response of organisms to environmental changes. Yet, it is difficult to establish the exact form of density dependence from empirical data. Here, we developed an individual‐based model to explore how resource limitation and behavioural processes determine the spatial structure of white stork Ciconia ciconia populations and regulate reproductive rates. We found that the form of density dependence differed considerably between landscapes with the same overall resource availability and between home range selection strategies, highlighting the importance of fine‐scale resource distribution in interaction with behaviour. In accordance with theories of density dependence, breeding output generally decreased with density but this effect was highly variable and strongly affected by optimal foraging strategy, resource detection probability and colonial behaviour. Moreover, our results uncovered an overlooked consequence of density dependence by showing that high early nestling mortality in storks, assumed to be the outcome of harsh weather, may actually result from density dependent effects on food provision. Our findings emphasize that accounting for interactive effects of individual behaviour and local environmental factors is crucial for understanding density‐dependent processes within spatially structured populations. Enhanced understanding of the ways animal populations are regulated in general, and how habitat conditions and behaviour may dictate spatial population structure and demographic rates is critically needed for predicting the dynamics of populations, communities and ecosystems under changing environmental conditions.     

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.