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.     

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.     

Incorporating environmental stochasticity within a biological population model

The birth and death transition rates for a population are modelled as functions of both the population size and the environmental condition. An assortment of important theoretical results and techniques that can be utilized to analyze such a population’s behaviour is covered. Consequently, these results and techniques are used to study two examples. Firstly, we study a population with a stable equilibrium state, whose per capita birth and death rates are linearly related to the environmental condition. (The environmental condition in turn is modelled as an Ornstein–Uhlenbeck process.) Secondly, we study a population affected by two interdependent environmental factors.     

Pathogen interactions, population cycles, and phase shifts

Interspecific pathogen interactions can profoundly affect pathogen population dynamics and the efficacy of control strategies. However, many pathogens exhibit cyclic abundance patterns (e.g., seasonality), and temporal asynchrony between interacting pathogens could reduce the impact of those interactions. Here we use an extension of our previously published model to investigate the effects of cycles on pathogen interaction. We demonstrate that host immune memory can maintain the impact of an interaction, even when the effector pathogen abundance is low or the pathogen is absent. Paradoxically, immune memory can result in pathogens interacting more strongly when temporally out of phase. We find that interactions between species can result in changes to the temporal pattern of the affected species. We further demonstrate that this may be observed in a natural host-pathogen system. Given the continuing debate regarding the relevance of pathogen interactions in natural systems and increasing concern about treatment strategies for coinfections, both the discovery of a shift in cycle in empirical data and the mechanism by which we identified it are important. Finally, because the model structure used here is analogous to models of a simple predator-prey system, we also consider the consequences of these findings in the context of that system.     

Collapsing population cycles

During the past two decades population cycles in voles, grouse and insects have been fading out in Europe. Here, we discuss the cause and implication of these changes. Several lines of evidence now point to climate forcing as the general underlying cause. However, how climate interacts with demography to induce regime shifts in population dynamics is likely to differ among species and ecosystems. Herbivores with high-amplitude population cycles, such as voles, lemmings, snowshoe hares and forest Lepidoptera, form the heart of terrestrial food web dynamics. Thus, collapses of these cycles are also expected to imply collapses of important ecosystem functions, such as the pulsed flows of resources and disturbances.     

Correctly estimating how environmental stochasticity influences fitness and population growth

Increased temporal variance in life-history traits is generally predicted to decrease individual fitness and population growth. We show that a widely used result of stochastic sensitivity analysis that bolsters this generality is flawed because it ignores the effects of correlations between vital rates. Considering the effects of these correlations (although ignoring autocorrelations), we show that the apparently simple relationship between vital rate variance and fitness can be considerably more complex than previously thought. In particular, the previously estimated negative sensitivities of fitness or population growth to variance in a vital rate can be either enhanced by positive correlations between rates or reversed by negative correlations, even to the point that variability in a rate can increase fitness or population growth. We apply this new sensitivity calculation to data from the desert tortoise and discuss its interpretation in light of the factors generating vital rate correlations.     

The synergistic effects of stochasticity and dispersal on population densities

Using laboratory experiments, simulation models, and analytical techniques, we examined the impact of dispersal on the mean densities of patchily distributed populations. Even when dispersal leads to no net additions or removals of individuals from a population, it may nonetheless increase mean population densities if the net immigration rate is positive when populations are growing and negative when they are declining. As a model system for exploring this phenomenon, we used the yeastlike fungus Aureobasidium pullulans. In a laboratory experiment, we showed that dispersal can both ensure persistence and increase mean population densities even when dispersal among populations causes no direct addition or loss of fungal cells. From the laboratory data, we constructed a plausible model of A. pullulans dynamics among apple leaves within an orchard. This simulation model demonstrated that the effect of dispersal on mean densities is enhanced by three factors: weak density dependence of the dynamics within populations, high environmental variability affecting population growth rates, and lack of synchrony among the fluctuations of populations. Using an analytical model, we showed that the underlying mechanisms for this phenomenon are general, suggesting that a large effect of dispersal on mean population densities is possible in many natural systems.     

The follicular automaton model: effect of stochasticity and of synchronization of hair cycles

Human scalp hair consists of a set of about 10(5)follicles which progress independently through developmental cycles. Each hair follicle successively goes through the anagen (A), catagen (C), telogen (T) and latency (L) phases that correspond, respectively, to growth, arrest and hair shedding before a new anagen phase is initiated. Long-term experimental observations in a group of ten male, alopecic and non-alopecic volunteers allowed determination of the characteristics of hair follicle cycles. On the basis of these observations, we previously proposed a follicular automaton model to simulate the dynamics of human hair cycles and the development of different patterns of alopecia [Halloy et al. (2000) Proc. Natl Acad. Sci. U.S.A.97, 8328-8333]. The automaton model is defined by a set of rules that govern the stochastic transitions of each follicle between the successive states A, T, L and the subsequent return to A. These transitions occur independently for each follicle, after time intervals given stochastically by a distribution characterized by a mean and a standard deviation. The follicular automaton model was shown to account both for the dynamical transitions observed in a single follicle, and for the behaviour of an ensemble of independently cycling follicles. Here, we extend these results and investigate additional properties of the model. We present a deterministic version of the follicular automaton. We show that numerical simulations of the stochastic version of the automaton yield steady-state level of follicles in the different phases which approach the levels predicted by the deterministic equations as the number of follicles progressively increases. Only the stochastic version can successfully reproduce the fluctuations of the fractions of follicles in each of the three phases, observed in small follicle populations. When the standard deviation is reduced or when the follicles become otherwise synchronized, e.g. by a periodic external signal inducing the transition of anagen follicles into telogen phase, large-amplitude oscillations occur in the fractions of follicles in the three phases. These oscillations are not observed in humans but are reminiscent of the phenomenon of moulting observed in a number of mammalian species.     

Seasonality,population dynamics and production of planktonic rotifers in Lough Neagh,Northern Ireland

The abundances, population dynamics and production of the rotifer community of Lough Neagh were examined for a three year period. Keratella cochlearis was the most abundant species accounting for over 40% of biomass followed by Polyarthra dolichoptera and Notholca acuminata. The mean standing crop for the rotiferan zooplankton increased in successive years (41, 51, 75 mg dwt m^–2) as did production (1037, 1322, 1417 mg dwt m^–2 y^–1). The seasonal pattern of biomass expression and production varies markedly in different years. Instantaneous birth rates tend to be lower but more consistent for the more abundant species, instantaneous death rates show periods of negative mortality indicating an inadequacy of the model employed but explicable as hatching of resting eggs. K. cochlearis as the most successful species is explained as its perennial appearance and adaptation to the low annual temperature cycle found in the lough. The population succession and the annual occurrence of species differs in each year.     

Environmental stochasticity and extinction risk in a population of a small songbird, the great tit

Using a long-term demographic data set, we estimated the separate effects of demographic and environmental stochasticity in the growth rate of the great tit population in Wytham Wood, United Kingdom. Assuming logistic density regulation, both the demographic (sigma2d = 0.569) and environmental (sigma2e = 0.0793) variance, with interactions included, were significantly greater than zero. The estimates of the demographic variance seemed to be relatively insensitive to the length of the study period, whereas reliable estimates of the environmental variance required long time series (at least 15 yr of data). The demographic variance decreased significantly with increasing population density. These estimates are used in a quantitative analysis of the demographic factors affecting the risk of extinction of this population. The very long expected time to extinction of this population (approximately 10(19) yr) was related to a relatively large population size (>/=120 pairs during the study period). However, for a given population size, the expected time to extinction was sensitive to both variation in population growth rate and environmental stochasticity. Furthermore, the form of the density regulation strongly affected the expected time to extinction. Time to extinction decreased when the maximum density regulation approached K. This suggests that estimates of viability of small populations should be given both with and without inclusion of density dependence.     

Relative importance of density-dependent regulation and environmental stochasticity for butterfly population dynamics

The relative contribution of density-dependent regulation and environmental stochasticity to the temporal dynamics of animal populations is one of the central issues of ecology. In insects, the primary role of the latter factor, typically represented by weather patterns, is widely accepted. We have evaluated the impact of density dependence as well as density-independent factors, including weather and mowing regime, on annual fluctuations of butterfly populations. As model species, we used Maculinea alcon and M. teleius living in sympatry and, consequently, we also analysed the effect of their potential competition. Density dependence alone explained 62 and 42% of the variation in the year-to-year trends of M. alcon and M. teleius, respectively. The cumulative Akaike weight of models with density dependence, which can be interpreted as the probability that this factor should be contained in the most appropriate population dynamics model, exceeded 0.97 for both species. In contrast, the impacts of inter-specific competition, mowing regime and weather were much weaker, with their cumulative weights being in the range of 0.08–0.21; in addition, each of these factors explained only 2–5% of additional variation in Maculinea population trends. Our results provide strong evidence for density-dependent regulation in Maculinea, while the influence of environmental stochasticity is rather minor. In the light of several recent studies on other butterflies that detected significant density-dependent effects, it would appear that density-dependent regulation may be more widespread in this group than previously thought, while the role of environmental stochasticity has probably been overestimated. We suggest that this misconception is the result of deficiencies in the design of most butterfly population studies in the past, including (1) a strong focus on adults and a neglect of the larval stage in which density-dependent effects are most likely to occur; (2) an almost exclusive reliance on transect count results that may confound the impact of environmental stochasticity on butterfly numbers with its impact on adult longevity. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Seasonality of births and family characteristics in a Spanish population

The seasonality of births in the period 1871-1977 is studied in a rural north-western Spanish population. Based on a total sample of 11,695 birth registrations, temporal variation is analysed. For siblings, according to family reconstitution, the total family size, the legitimacy of the child, and birth order are considered. A coefficient of birth month dispersion is defined and estimated for each family. Intra-family variation is related to inter-family coefficients in order to determine whether the local seasonal pattern of births may be partly explained by family characteristics.     

Phase switching in population cycles

Oscillatory populations may exhibit a phase change in which, for example, a high–low periodic pattern switches to a low–high pattern. We propose that phase shifts correspond to stochastic jumps between basins of attraction in an appropriate phase space which associates the different phases of a periodic cycle with distinct attractors. This mechanism accounts for two-cycle phase shifts and the occurrence of asynchronous replicates in experimental cultures of Tribolium.     

Circadian activity patterns,photoperiodic responses and population cycles in voles

Summary Patterns of above-ground activity were recorded in two free-ranging populations of Microtus agrestis (L.) and one population of M. arvalis (Pall.) over several years by means of passage counters. Long-term variations of the circadian patterns were observed, but did not repeat themselves in a 12-month cycle. Variations in all three populations could be described by a sinusoidal function of an 18-month period. Maxima and minima of the sine-function were connected to distinct photoperiods (equinoxes and solstices). In a cyclic North Swedish population, the sine-function was superimposed by a second function which shows saturation behaviour. The relevance of these findings is discussed with respect to vole population cycles.     

Consistency and fluctuation theorems for discrete time structured population models having demographic stochasticity

In this paper we prove a consistency theorem (law of large numbers) and a fluctuation theorem (central limit theorem) for structured population processes. The basic assumptions for these theorems are that the individuals have no statistically distinguishing features beyond their class and that the interaction between any two individuals is not too high. We apply these results to density dependent models of Leslie type and to a model for flour beetle dynamics. Received: 24 February 1999 / Revised version: 23 July 1999 / Published online: 14 September 2000     

Allee effect, sexual selection and demographic stochasticity

The negative frequency-dependent effect of reproductive success in animals on population growth refers to a category of phenomena termed the Allee effect. The mechanistic basis for this effect and hence an understanding of its consequences has been obscure. We suggest that sexual selection, in particular female mate preferences, is a previously neglected component giving rise to the Allee effect. Lack of breeding and reduced reproductive success of females at low population densities are commonly described in situations where females have little or no opportunity to choose a mate, consistent with this suggestion. We developed a demographic model that incorporated the effects of lack of female choice on rates of reproduction. Using either a mating system with incompatibility or a system with a directional mate preference, we show that commonly encountered levels of reproductive suppression in the absence of suitable mates in a population, where sexual selection still operates, may increase the effects of demographic stochasticity considerably.     

Stage,age and individual stochasticity in demography

Demography is the study of the population consequences of the fates of individuals. Individuals are differentiated on the basis of age or, in general, life cycle stages. The movement of an individual through its life cycle is a random process, and although the eventual destination (death) is certain, the pathways taken to that destination are stochastic and will differ even between identical individuals; this is individual stochasticity. A stage‐classified demographic model contains implicit age‐specific information, which can be analyzed using Markov chain methods. The living stages in the life cycles are transient states in an absorbing Markov chain; death is an absorbing state. This paper presents Markov chain methods for computing the mean and variance of the lifetime number of visits to any transient state, the mean and variance of longevity, the net reproductive rate R₀, and the cohort generation time. It presents the matrix calculus methods needed to calculate the sensitivity and elasticity of all these indices to any life history parameters. These sensitivities have many uses, including calculation of selection gradients. It is shown that the use of R₀ as a measure of fitness or an invasion exponent gives erroneous results except when R₀=λ=1. The Markov chain approach is then generalized to variable environments (deterministic environmental sequences, periodic environments, iid random environments, Markovian environments). Variable environments are analyzed using the vec‐permutation method to create a model that classifies individuals jointly by the stage and environmental condition. Throughout, examples are presented using the North Atlantic right whale (Eubaleana glacialis) and an endangered prairie plant (Lomatium bradshawii) in a stochastic fire environment.     

Floater survival affects population persistence. The role of prey availability and environmental stochasticity

We develop two individual-based models using a large and detailed data set (information gathered over more than a century) on a population of a longlived and territorial predator, the Spanish imperial eagle. We investigated the relationship between survival and predator pressure, prey behaviour and patch availability (i.e. settlement areas). Survival of dispersing individuals was highly dependent on the number of available settlement areas, mediated by prey availability. Changes in prey behaviour due to predation pressure (e.g. shifting from diurnal to nocturnal activity) can decrease their availability for predators even if the density significantly exceeds the predator needs. Environmental stochasticity had a strong influence on population viability when it occurred in a synchroneous way between breeding and settlement areas, and an increase in floater mortality negatively influenced stability and dynamics of the breeding segment of populations in reproductive areas. Our simulations demonstrated the link between the dynamics in settlement and breeding areas: factors affecting floater survival also influence whole population dynamics. Moreover, model outputs provided insights into the relationship between environmental stochasticity and population dynamics.