Overcompensatory population dynamic responses to environmental stochasticity

1. To quantify the interactions between density-dependent, population regulation and density-independent limitation, we studied the time-series dynamics of an experimental laboratory insect microcosm system in which both environmental noise and resource limitation were manipulated. 2. A hierarchical Bayesian state-space approach is presented through which it is feasible to capture all sources of uncertainty, including observation error to accurately quantify the density dependence operating on the dynamics. 3. The regulatory processes underpinning the dynamics of two different bruchid beetles (Callosobruchus maculatus and Callosobruchus chinensis) are principally determined by environmental conditions, with fluctuations in abundance explained in terms of changes in overcompensatory dynamics and stochastic processes. 4. A general, stochastic population model is developed to explore the link between abundance fluctuations and the interaction between density dependence and noise. Taking account of time-lags in population regulation can substantially increase predicted population fluctuations resulting from underlying noise processes.     

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

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

Density-dependent demography in a Japanese temperate broad-leaved forest

A method of detecting the density-dependent dynamics of a size-structured population is developed. The method is applied to a Japanese broad-leaved forest and the density-dependent and-independent projection matrix models are constructed based on the data of the forest. Then, the difference between the density-independent and density-dependent dynamics is compared in terms of several statistical quantities obtained from the matrices. Three kinds of sensitivity matrices are proposed for the density-dependent matrix model. At earlier stages, the sensitivity when the population density is low are higher than at the equilibrium. On the other hand, the inverse result is obtained at later stages. Moreover, the responses of the forest is analyzed to a decrease in survival rate and to an increase in the probability of gap formation. The decrease in survival rate leads to an extreme decrease in the density of the forest. However, the decrease in recruitment rate gives little effect on it because the effect of density-dependence in recruitment of new individuals is strong. The forest has the optimal rate of gap formation such that leads to the maximum population density.     

Importance of endogenous feedback controlling the long-term abundance of tropical mosquito species

Mosquitoes are a major vector for tropical diseases, so understanding aspects that modify their population dynamics is vital for their control and protecting human health. Maximising the efficiency of control strategies for reducing transmission risk requires as a first step the understanding of the intrinsic population dynamics of vectors. We fitted a set of density-dependent and density-independent models to the long-term time series of six tropical mosquito species from northern Australia. The models’ strength of evidence was assessed using Akaike’s Information Criterion (AIC _c ), Bayesian Information Criterion (BIC) and jack-knifed cross-validation (C-V). Density dependence accounted for more than 99% of the model weight in all model-selection methods, with the Gompertz-logistic (Cushing model) being the best-supported model for all mosquito species (negative density feedback expressed even at low densities). The second-most abundant species, Aedes vigilax (a saline breeder), showed no spatial heterogeneity in its density-dependent response, but the remaining five species had different intrinsic growth rates across 11 study sites. Population densities of saline species were high only during the late dry to early wet season following the highest tides of the month or early flood rains when swamps were mostly saline, whereas those of freshwater species were highest during the mid-wet and mid-dry seasons. These findings demonstrate remarkably strong density dependence in mosquito populations, but also suggest that environmental drivers, such as rainfall and tides, are important in modifying seasonal densities. Neglecting to account for strong density feedback in tropical mosquito populations will clearly result in less effective control.     

A new demographic function maximized by life-history evolution

A goal of life-history theory has been to understand what combination of demographic traits is maximized by natural selection. In practice, researchers usually choose either density-independent population growth rate, lambda, or lifetime reproductive success, R0 (expected number of offspring produced in a lifetime). Others have shown that the maxima of density-independent lambda and R0 are evolutionarily stable strategies under specific density-dependent conditions: population regulation by equal density dependence among all age classes for lambda and by density dependence on a single age class for R0. Here I extend these connections between density-independent optimization models and density-dependent invasion function models in two ways. First, I derive a new demographic function for which a maximum corresponds to attainability of the equilibrium strategy or stability of the mean rather than stability of the variance of the strategy distribution. Second, I show explicitly a continuous range of cases with maxima between those for the lambda and R0. Graphical and biological interpretations are given for an example model. Finally, exceptions to a putative life-history generality (from lambda and R0 models), that high early-life mortality selects for high iteroparity, are shown.     

Density-dependent migration and synchronism in metapopulations

A spatially explicit metapopulation model with density-dependent dispersal is proposed in order to study the stability of synchronous dynamics. A stability criterion is obtained based on the computation of the transversal Liapunov number of attractors on the synchronous invariant manifold. We examine in detail a special case of density-dependent dispersal rule where migration does not occur if the patch density is below a certain critical density, while the fraction of individuals that migrate to other patches is kept constant if the patch density is above the threshold level. Comparisons with density-independent migration models indicate that this simple density-dependent dispersal mechanism reduces the stability of synchronous dynamics. We were able to quantify exactly this loss of stability through the frequency that synchronous trajectories are above the critical density.     

Elasticity analysis of density-dependent matrix population models: the invasion exponent and its substitutes

In density-independent models, the population growth rate lambda measures population performance, and the perturbation analysis of lambda (its sensitivity and elasticity) plays an important role in demography. In density-dependent models, the invasion exponent lambdaI replaces lambda as a measure of population performance. The perturbation analysis of lambdaI reveals the effects of environmental changes and management actions, gives the direction and intensity of density-dependent natural selection on life history traits, and permits calculation of the sampling variance of the invasion exponent. Because density-dependent models require more data than density-independent models, it is tempting to look for substitutes for the invasion exponent, the sensitivity and elasticity of which can be calculated from a density-independent model. Here we examine the accuracy of two such substitutes: the dominant eigenvalue of the projection matrix evaluated at equilibrium (An) and the dominant eigenvalue of the matrix averaged over the attractor (A). Using a two-stage model that represents a wide range of life history types, we find that the elasticities of An or A often agree to within less than 5% error with those of the invasion exponent, even when population dynamics are chaotic. The exceptions are for semelparous life histories, especially when density-dependence affects fertility. This suggests that the elasticity analysis of density-independent models near equilibrium, or averaged over the attractor, provides useful information about the elasticity of the invasion exponent in density-dependent models.     

Bayesian population dynamics of interacting species: great gerbils and fleas in Kazakhstan

We propose a discrete-time Bayesian hierarchical model for the population dynamics of the great gerbil-flea ecological system. The model accounts for the sampling variability arising from data originally collected for other purposes. The prior for the unknown population densities incorporates specific biological hypotheses regarding the interacting dynamics of the two species, as well as their life cycles, where density-dependent effects are included. Posterior estimates are obtained via Markov chain Monte Carlo. The variance of the observed density estimates is a quadratic function of the unknown density. Our study indicates the presence of a density-dependent growth rate for the gerbil population. For the flea population there is clear evidence of density-dependent over-summer net growth, which is dependent on the flea-to-gerbil ratio at the beginning of the reproductive summer. Over-winter net growth is favored by high density. We estimate that on average 35% of the gerbil population survives the winter. Our study shows that hierarchical Bayesian models can be useful in extracting ecobiological information from observational data.     

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

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

Density-Dependent Harvest Modeling for the Eastern Wild Turkey

Abstract Many current wild turkey (Meleagris gallopavo) harvest models assume density-independent population dynamics. We developed an alternative model incorporating both nonlinear density-dependence and stochastic density-independent effects on wild turkey populations. We examined model sensitivity to parameter changes in 5% increments and determined mean spring and fall harvests and their variability in the short term (3 yr) and long term (10 yr) from proportional harvesting under these conditions. In the long term, population growth rates were most sensitive to poult:female ratios and the form of density dependence. The nonlinear density-dependent effect produced a population that maximized yield at 40% carrying capacity. The model indicated that a spring or fall proportional harvest could be maximized for fall harvest rates between 0% and 13% of the population, assuming a 15% spring male harvest and 5% spring illegal female kill. Combined spring and fall harvests could be maximized at a 9% fall harvest, under the same assumptions. Variability in population growth and harvest rates increased uncertainty in spring and fall harvests and the probability of overharvesting annual yield, with growth rate variation having the strongest effect. Model simulations suggested fall harvest rates should be conservative (≤9%) for most management strategies.     

Population extinction and quasi-stationary behavior in stochastic density-dependent structured models

Density-independent and density-dependent, stochastic and deterministic, discrete-time, structured models are formulated, analysed and numerically simulated. A special case of the deterministic, density-independent, structured model is the well-known Leslie age-structured model. The stochastic, density-independent model is a multitype branching process. A review of linear, density-independent models is given first, then nonlinear, density-dependent models are discussed. In the linear, density-independent structured models, transitions between states are independent of time and state. Population extinction is determined by the dominant eigenvalue λ of the transition matrix. If λ ≤ 1, then extinction occurs with probability one in the stochastic and deterministic models. However, if λ > 1, then the deterministic model has exponential growth, but in the stochastic model there is a positive probability of extinction which depends on the fixed point of the system of probability generating functions. The linear, density-independent, stochastic model is generalized to a nonlinear, density-dependent one. The dependence on state is in terms of a weighted total population size. It is shown for small initial population sizes that the density-dependent, stochastic model can be approximated by the density-independent, stochastic model and thus, the extinction behavior exhibited by the linear model occurs in the nonlinear model. In the deterministic models there is a unique stable equilibrium. Given the population does not go extinct, it is shown that the stochastic model has a quasi-stationary distribution with mean close to the stable equilibrium, provided the population size is sufficiently large. For small values of the population size, complete extinction can be observed in the simulations. However, the persistence time increases rapidly with the population size. This author received partial support by the National Science Foundation grant # DMS-9626417.     

Comparative reproductive biology of sympatric species: nest and chick survival of American avocets and black‐necked stilts

Identifying differences in reproductive success rates of closely related and sympatrically breeding species can be useful for understanding limitations to population growth. We simultaneously examined the reproductive ecology of American avocets Recurvirostra americana and black‐necked stilts Himantopus mexicanus using 1274 monitored nests and 240 radio‐marked chicks in San Francisco Bay, California. Although there were 1.8 times more avocet nests than stilt nests, stilts nonetheless fledged 3.3 times more chicks. Greater production by stilts than avocets was the result of greater chick survival from hatching to fledging (avocet: 6%; stilt: 40%), and not because of differences in clutch size (avocet: 3.84; stilt: 3.77), nest survival (avocet: 44%; stilt: 35%), or egg hatching success (avocet: 90%; stilt: 92%). We reviewed the literature and confirmed that nest survival and hatching success are generally similar when avocets and stilts breed sympatrically. In addition to species, chick survival was strongly influenced by age, site, and year. In particular, daily survival rates increased rapidly with chick age, with 70% of mortalities occurring ≤ 1 week after hatch. California gulls Larus californicus caused 55% of avocet, but only 15% of stilt, chick deaths. Differential use of micro‐habitats likely reduced stilt chick's vulnerability to gull predation, particularly during the first week after hatch, because stilts nested in vegetation 2.7 times more often than avocets and vegetation height was 65% taller at stilt nests compared with avocet nests. Our results demonstrate that two co‐occurring and closely related species with similar life history strategies can differ markedly in reproductive success, and simultaneous studies of such species can identify differences that limit productivity.     

Impact of density and environmental factors on population fluctuations in a migratory passerine

1. Populations of plants and animals typically fluctuate because of the combined effects of density-dependent and density-independent processes. The study of these processes is complicated by the fact that population sizes are typically not known exactly, because population counts are subject to sampling variance. Although the existence of sampling variance is broadly acknowledged, relatively few studies on time-series data have accounted for it, which can result in wrong inferences about population processes. 2. To increase our understanding of population dynamics, we analysed time series from six Central European populations of the migratory red-backed shrike Lanius collurio by simultaneously assessing the strength of density dependence, process and sampling variance. In addition, we evaluated hypotheses predicting effects of factors presumed to operate on the breeding grounds, at stopover sites in eastern Africa during fall and spring migration and in the wintering grounds in southern Africa. We used both simple and state-space formulations of the Gompertz equation to model population size. 3. Across populations and modelling approaches, we found consistent evidence for negative density-dependent population regulation. Further, process variance contributed substantially to variation in population size, while sampling variance did not. Environmental conditions in eastern and southern Africa appear to influence breeding population size, as rainfall in the Sahel during fall migration and in the south African wintering areas were positively related to population size in the following spring in four of six populations. In contrast, environmental conditions in the breeding grounds were not related to population size. 4. Our findings suggest negative density-dependent regulation of red-backed shrike breeding populations and are consistent with the long-standing hypothesis that conditions in the African staging and wintering areas influence population numbers of species breeding in Europe. 5. This study highlights the importance of jointly investigating density-dependent and density-independent processes to improve our understanding of factors influencing population fluctuations in space and time.     

Density dependence and the control of helminth parasites

1. The transient dynamics and stability of a population are determined by the interplay between species density, its spatial distribution and the positive and negative density-dependent processes regulating population growth. 2. Using the human-helminth parasite system as an example, we propose that the life-stage upon which negative density dependence operates will influence the rate of host reinfection following anthelmintic chemotherapy, and the likely success of control programmes. 3. Simple deterministic models are developed which highlight how a parasite species whose population size is down-regulated by density-dependent establishment will reinfect a host population at a faster rate than a species with density-dependent parasite fecundity. 4. Different forms of density dependence can produce the same equilibrium behaviour but different transient dynamics. Under-representing the nature and magnitude of density-dependent mechanisms, and in particular those operating upon establishing life-stages, may cause the resilience of the parasite population to a control perturbation to be underestimated.     

Finite metapopulation models with density-dependent migration and stochastic local dynamics

The effects of small density-dependent migration on the dynamics of a metapopulation are studied in a model with stochastic local dynamics. We use a diffusion approximation to study how changes in the migration rate and habitat occupancy affect the rates of local colonization and extinction. If the emigration rate increases or if the immigration rate decreases with local population size, a positive expected rate of change in habitat occupancy is found for a greater range of habitat occupancies than when the migration is density-independent. In contrast, the reverse patterns of density dependence in respective emigration and immigration reduce the range of habitat occupancies where the metapopulation will be viable. This occurs because density-dependent migration strongly influences both the establishment and rescue effects in the local dynamics of metapopulations.     

The evolution of density-dependent dispersal

Despite a large body of empirical evidence suggesting that the dispersal rates of many species depend on population density, most metapopulation models assume a density-independent rate of dispersal. Similarly, studies investigating the evolution of dispersal have concentrated almost exclusively on density-independent rates of dispersal. We develop a model that allows density-dependent dispersal strategies to evolve. Our results demonstrate that a density-dependent dispersal strategy almost always evolves and that the form of the relationship depends on reproductive rate, type of competition, size of subpopulation equilibrium densities and cost of dispersal. We suggest that future metapopulation models should account for density-dependent dispersal     

Long-term population trends of endangered Hawaiian waterbirds

We analyzed long-term winter survey data (1956–2007) for three endangered waterbirds endemic to the Hawaiian Islands, the Hawaiian moorhen (Gallinula chloropus sandvicensis), Hawaiian coot (Fulica alai), and Hawaiian stilt (Himantopus mexicanus knudseni). Time series were analyzed by species–island combinations using generalized additive models, with alternative models compared using Akaike information criterion (AIC). The best model included three smoothers, one for each species. Our analyses show that all three of the endangered Hawaiian waterbirds have increased in population size over the past three decades. The Hawaiian moorhen increase has been slower in more recent years than earlier in the survey period, but Hawaiian coot and stilt numbers still exhibit steep increases. The patterns of population size increase also varied by island, although this effect was less influential than that between species. In contrast to earlier studies, we found no evidence that rainfall affects counts of the target species. Significant population increases were found on islands where most wetland protection has occurred (Oahu, Kauai), while weak or no increases were found on islands with few wetlands or less protection (Hawaii, Maui). Increased protection and management, especially on Maui where potential is greatest, would likely result in continued population gains, increasing the potential for meeting population recovery goals.     

Density dependence, regulation and open-closed populations: insights from the wigeon, Anas penelope

We investigated whether the degree of exchange with other populations affects the occurrence of density-dependent regulation. We contrasted data from an Icelandic and a Finnish population of breeding wigeons ( Anas penelope ), the former population being more closed than the later. We looked for density dependence in time-series data and investigated whether breeding success is density dependent and plays a role in population dynamics and regulation. Time-series analysis did not reveal density-dependent regulation in either population. Nor did we find evidence of density-dependent breeding success in either population. However, population growth rate appeared to be strongly dependent on the breeding success in the previous year in the closed population but not in the open population. Our findings underline how important it is to link time-series analysis to the study of potential stabilizing mechanisms in order to understand population dynamics and regulation. We also suggest that it may be a difficult task to achieve sustainability in waterfowl harvesting, the theoretical basis of which is density-dependent population regulation.     

Temporal changes in the strength of density-dependent mortality and growth in intertidal barnacles

1. In demographically open marine systems, the extent to which density-dependent processes in the benthic adult phase are required for population persistence is unclear. At one extreme, represented by the recruitment limitation hypothesis, larval supply may be insufficient for the total population size to reach a carrying capacity and density-independent mortality predominates. At the opposite extreme, populations are saturated and density-dependent mortality is sufficiently strong to reshape patterns established at settlement. 2. We examined temporal variation in the way density-independent and density-dependent mortality interact in a typical sessile marine benthic invertebrate, the acorn barnacle Semibalanus balanoides (L.), over a 2-year period. 3. Recruitment was manipulated at two high recruitment sites in north Wales, UK to produce recruit densities covering the range naturally found in this species. Following manipulation, fixed quadrats were monitored using digital photography and temporal changes in mortality and growth rate were examined. 4. Over a 2-year period there was a clear, spatially consistent, over-compensatory relationship between the density of recruits and adult abundance indicating strong density-dependent mortality. The strength of density dependence intensified with increasing recruitment. 5. Density-dependent mortality did not operate consistently over the study period. It only operated in the early part of the benthic phase, but the pattern of adult abundance generated was maintained throughout the whole 2-year period. Thus, early life-history processes dictated adult population abundance and dynamics. 6. Examination of the natural recruitment regime in the area of study indicated that both positive and negative effects of recruitment will occur over scales varying from kilometres to metres.