Population dynamics in variable environments. VI. Cyclical environments

This paper studies the dynamics of an age-structured population which experiences cyclical variation in vital rates. The principal features of population behavior are found to be contained in an explicitly calculable response function. Three distinct regimes of qualitative behavior are described when cycle period is respectively much less than, of the order of, and much greater than the average generation length. These results make explicit the way in which transient properties corresponding to average vital rates determine population response to cycles.     

Population dynamics in variable environments. III. Evolutionary dynamics of r-selection

The boundary dynamics of a genetic model for an age-structured population in a temporally fluctuating environment are analyzed. The condition for invasion by a new allele identifies the logarithmic growth rate a of each life history phenotype as the fitness measure relevant to “r-selection.” An analytical formula is obtained for fitness a when temporal variance in life history characters is small. This formula reveals the major qualitative and quantitative effects of the average life history, fluctuations, and temporal autocorrelation on fitness. A similar approximation is obtained for the log-variance of population number so that the statistical distribution of population size can be estimated.     

Population dynamics in variable environments I. Long-run growth rates and extinction

A model of population growth is studied in which the Leslie matrix for each time interval is chosen according to a Markov process. It is shown analytically that the distribution of total population number is lognormal at long times. Measures of population growth are compared and it is shown that a mean logarithmic growth rate and a logarithmic variance effectively describe growth and extinction at long times. Numerical simulations are used to explore the convergence to lognormality and the effects of environmental variance and autocorrelation. The results given apply to other geometric growth models which involve nonnegative growth matrices.     

Population dynamics in variable environments. IV. Weak ergodicity in the Lotka equation

The Hilbert projective metric is applied to the continuous-time Lotka equation in demography to establish weak ergodicity: populations with the same time-varying fecundity and mortality schedules ultimately have the same age composition. The analysis displays clearly the dynamic content of Lotka's equation and identifies a contraction operator which forces convergence of birth sequences over time. The relationship between primitivity in the discrete (Leslie) and continuous (Lotka) demographic models is made clear.     

Population and prehistory III: Food-dependent demography in variable environments

The population dynamics of preindustrial societies depend intimately on their surroundings, and food is a primary means through which environment influences population size and individual well-being. Food production requires labor; thus, dependence of survival and fertility on food involves dependence of a population’s future on its current state. We use a perturbation approach to analyze the effects of random environmental variation on this nonlinear, age-structured system. We show that in expanding populations, direct environmental effects dominate induced population fluctuations, so environmental variability has little effect on mean hunger levels, although it does decrease population growth. The growth rate determines the time until population is limited by space. This limitation introduces a tradeoff between population density and well-being, so population effects become more important than the direct effects of the environment: environmental fluctuation increases mortality, releasing density dependence and raising average well-being for survivors. We discuss the social implications of these findings for the long-term fate of populations as they transition from expansion into limitation, given that conditions leading to high well-being during growth depress well-being during limitation.     

Age- and density-dependent population dynamics in static and variable environments

We consider a general model of a single-species population with age- and density-dependent per capita birth and death rates. In a static environment we show that if the per capita death rate is independent of age, then the local stability of any stationary state is guaranteed by the requirement that, in the region of the steady state, the density dependence of the birth rate should be negative and that of the death rate positive. In a variable environment we show that, provided the system is locally stable, small environmental fluctuations will give rise to small age structure and population fluctuations which are related to the driving environmental fluctuations by a simple “transfer function.” We illustrate our general theory by examining a model with a per capita death rate which is age and density independent and a per capita birth rate which is zero up to some threshold age a₀, adopts a finite density-dependent value up to a maximum age a_o + α, and is zero thereafter. We conclude from this model that resonance due specifically to single-species age-structure effects will only be of practical importance in populations whose members have a life cycle consisting of a long immature phase followed by a short burst of intense reproductive effort (α a_o).     

Population dynamics of animals in unpredictably-changing tropical environments

We studied population dynamics of a solitary phytophagous beetle,Epilachna viqintioctopunctata and a social stingless bee,Trigona minangkabau, in Sumatra, Indonesia for 5 years from 1981. Population increase ofEpilachna vigintioctopunctata was suppressed in months of normal rainfall (≥300mm) but was released in the 1982–1983 El Nino-Southern. Oscillation when rainfall dropped to 50% of the long-term average. Mechanisms might be direct; rainfall lowered egg hatchability and the time of adult’s residence on host plants. When dry weather continued for more than three generations, theEpilachna vigintioctopunctata population reached a density at which food shortage due to defoliation occurred. Although parasitism of immature stages was high, it was not a population-regulating factor. Thus, there were two types of ecological crunch: competition for food resources at the end of favourable dry periods and high mortality during heavy rainfall periods that usually followed El Nino-Southern Oscillation dry conditions. By an experimental addition of artificial nest sites, colony density ofTrigona minangkabau increased 2.5 times the original density of natural colonies. One-half of artificial nest sites were occupied by arboreal ants and thus competition for nest sites with ants suppressed further increase ofTrigona minangkabau. Intermediate rainfall was favourable forTrigona minangkabau because the rate of colony foundation decreased both during dry El Niño-Southern Oscillation months and months with heavy rain. Colony death was independent from rainfall. Many colonies that survived for 6 months persisted for >2 years and colony density was quite stable.Trigona minangkabau colonies could survive even under unfavourable periods, by hoarding resources in the nest. There was no significant ecological crunch during the study period and colony density almost always tracked the carrying capacity of the habitat, which was basically determined by nest-site abundance. Climatic conditions, especially rainfall, changed with various periodicities, 4–5 years for El Nino-Southern Oscillation, and 2 years for the monsoon and other shorter periods. The contribution of periodicities of 1 and 0.5 years, that were linked to movement of the sun, were weak, indicating that animals could not use seasonal changes of environments,e.g. daylength, to predict environmental changes. We discuss traits adaptive to such unpredictably-changing tropical environments. Separation of predictability of temporal environmental change and synchronous changes among patches improves our understanding. Low oviposition rate and resulting prolonged life-span ofEpilachna vigintioctopunctata, usually associated withK-selected traits of life history, seem to be adaptations for unpredictable environmental changes.     

Spatial and temporal synchrony in reptile population dynamics in variable environments

Resources are seldom distributed equally across space, but many species exhibit spatially synchronous population dynamics. Such synchrony suggests the operation of large-scale external drivers, such as rainfall or wildfire, or the influence of oasis sites that provide water, shelter, or other resources. However, testing the generality of these factors is not easy, especially in variable environments. Using a long-term dataset (13–22 years) from a large (8000 km²) study region in arid Central Australia, we tested firstly for regional synchrony in annual rainfall and the dynamics of six reptile species across nine widely separated sites. For species that showed synchronous spatial dynamics, we then used multivariate follow a multivariate auto-regressive state–space (MARSS) models to predict that regional rainfall would be positively associated with their populations. For asynchronous species, we used MARSS models to explore four other possible population structures: (1) populations were asynchronous, (2) differed between oasis and non-oasis sites, (3) differed between burnt and unburnt sites, or (4) differed between three sub-regions with different rainfall gradients. Only one species showed evidence of spatial population synchrony and our results provide little evidence that rainfall synchronizes reptile populations. The oasis or the wildfire hypotheses were the best-fitting models for the other five species. Thus, our six study species appear generally to be structured in space into one or two populations across the study region. Our findings suggest that for arid-dwelling reptile populations, spatial and temporal dynamics are structured by abiotic events, but individual responses to covariates at smaller spatial scales are complex and poorly understood.     

Population genetics study of hemoglobinopathies in Uzbekistan. II. Population dynamics of hemoglobinopathies

It was shown that on comparing variability of selective neutral genetic marker systems with that of the beta-thalassemia system for the populations of different hierarchical level, the relative importance of selection and genetic drift could be evaluated. The genetic differentiation of the beta-thalassemia gene frequencies in elementary populations (villages) could be solely explained by genetic drift. On the other hand, the differentiation of district populations (the sizes of the populations being 10(6] for beta-thalassemia gene frequencies could be explained by selection forces. This is supported by the fact that the genetic distances and FST values are only significant for the beta-thalassemia gene and not for the neutral genetic systems, when the district populations are compared.     

Population and prehistory II: space-limited human populations in constant environments

We present a population model to examine the forces that determined the quality and quantity of human life in early agricultural societies where cultivable area is limited. The model is driven by the non-linear and interdependent relationships between the age distribution of a population, its behavior and technology, and the nature of its environment. The common currency in the model is the production of food, on which age-specific rates of birth and death depend. There is a single non-trivial equilibrium population at which productivity balances caloric needs. One of the most powerful controls on equilibrium hunger level is fertility control. Gains against hunger are accompanied by decreases in population size. Increasing worker productivity does increase equilibrium population size but does not improve welfare at equilibrium. As a case study we apply the model to the population of a Polynesian valley before European contact.     

Coevolution in temporally variable environments

Many potentially mutualistic interactions are conditional, with selection that varies between mutualism and antagonism over space and time. We develop a genetic model of temporally variable coevolution that incorporates stochastic fluctuations between mutualism and antagonism. We use this model to determine conditions necessary for the coevolution of matching traits between a host and a conditional mutualist. Using an analytical approximation, we show that matching traits will coevolve when the geometric mean interaction is mutualistic. When this condition does not hold, polymorphism and trait mismatching are maintained, and coevolutionary cycles may result. Numerical simulations verify this prediction and suggest that it remains robust in the presence of temporal autocorrelation. These results are compared with those from spatial models with unrestricted movement. The comparisons demonstrate that gene flow is unnecessary for generating empirical patterns predicted by the geographic mosaic theory of coevolution.     

Adaptive management in variable environments

Adaptive management (AM) encourages land managers to modify plans for the future based on carefully evaluating what happened in the past. Extreme abiotic variation overwhelms effects of management, making AM extremely difficult to implement. We demonstrate how passive AM, involving monitoring over a few years and using data to inform future decisions, was used to determine seeding rates of native plants in a restoration experiment conducted in the Irvine Ranch National Landmark in Southern California. We found that seedling density depended more on the year in which seeding was conducted than on seeding rates. Analysis of longer term data, using weather as independent variables in analyses, can help managers tease apart the relative importance of management actions and of precipitation. Seeding in multiple years provided a bet hedging strategy for increasing success of the restoration project, given inter-annual variation in precipitation. Limitations of our seeding rate example could be resolved through active AM, in the form of controlled, manipulative experiments testing different seeding rates and replicated over many years. Effective AM requires a willingness to repeat management actions that failed due to abiotic conditions in a single year. What failed last year may work well in the future, and evaluating the role of environmental variation requires repetition across multiple years.

     

Survival and production in variable resource environments

A dynamic energy budget (DEB) model describes the rates at which organisms assimilate and utilize energy from food for maintenance, growth, reproduction and development. We study the dynamic behavior of one particular DEB model, Kooijman’s κ rule model, whose key assumption is that somatic and reproductive tissues are competing for energy. We assume an environment in which the food density fluctuates either periodically or stochastically (pink noise). Both types of fluctuations stimulate growth; the magnitude of the (average) increase in size depends on both the strength and duration of the fluctuations. In a stochastic environment, the risk of mortality due to starvation increases with increasing fluctuation intensity. The mean lifespan is also a function of the model parameter κ characterizing the partitioning of energy between somatic and reproductive tissues. Organisms committing a large fraction of resources to reproduction endure periods of food shortage relatively well. The effects of food fluctuations on reproduction are complex. With stochastic food, reproduction in survivors increases with increasing fluctuation intensities, but lifetime reproduction decreases. Periodic fluctuations may enhance reproduction, depending on the value of κ. Thus, a variable food supply stimulates growth, increases mortality and may enhance reproduction, depending on life history.     

Population dynamics of mitochondria II. Turnover and ageing of rat liver mitochondria

Membrane-bound multi-protein complexes in mitochondria are provisionally classified into four categories based on possible mechanism of their assembly and degradation. These mechanisms may be investigated by the use of pulse-labeled radioactive markers which are not re-utilizable. Age dependent assembly is defined as that mechanism by which one or more of the pulse-labeled subunits are assembled into a complex, only while this complex is assembled. If the labeled sub-units can be taken up by the complex randomly during its life-span, then the mechanism is called age-independent assembly. Age-dependent degradation was defined as that mechanism by which the labeled subunits are decomposed, only when the complex is being degraded as an entity. If the labeled subunits are decomposed randomly, the mechanism is called age-independent degradation. Four categories are made by combining each of the assembly and degradation mechanisms. A differential equation was obtained to describe the fate of labeled sub-units that follow the age-dependent assembly and age-dependent degradation. Also derived was an equation for the age-independent assembly and age-dependent degradation. The other two categories which involve the age-independent degradation after age-dependent or age-independent assembly are described by single exponential kinetics. Practical application of the equations is illustrated with the use of experimental data on mitochondrial turnover found in the literature which suggests that the pulse-labeled proteins in rat liver mitochondria may follow the age-dependent assembly and degradation. The present attempts to introduce the concept of ageing into multi-protein complexes in mitochondria are the extensions of the steady state theory of mutation by Eyring & Stover (1970).     

Correlated dynamics in egocentric communication networks

We investigate the communication sequences of millions of people through two different channels and analyse the fine grained temporal structure of correlated event trains induced by single individuals. By focusing on correlations between the heterogeneous dynamics and the topology of egocentric networks we find that the bursty trains usually evolve for pairs of individuals rather than for the ego and his/her several neighbours, thus burstiness is a property of the links rather than of the nodes. We compare the directional balance of calls and short messages within bursty trains to the average on the actual link and show that for the trains of voice calls the imbalance is significantly enhanced, while for short messages the balance within the trains increases. These effects can be partly traced back to the technological constraints (for short messages) and partly to the human behavioural features (voice calls). We define a model that is able to reproduce the empirical results and may help us to understand better the mechanisms driving technology mediated human communication dynamics.     

Clupeoid life-history styles in variable environments

Synopsis Marine fish species with planktonic larval stages experience high and variable pre-adult mortality, and in accordance with general life-history theory have evolved iteroparity to reduce the uncertainty in reproductive success of individuals. In this paper we use a Monte Carlo model to explore the influence of spawning style and adult survival of clupeoids on the spawning success of individual fish during their life span, when early stage survival is determined according to different spectra of environmental variability. In these simulations the variation in reproductive success was governed first by the number of batches of eggs spawned by each adult fish over its lifespan (as determined by its pattern of spawning and the adult survival rate), and secondly by the patterning of environmental variability affecting early stage survival. We consider that the life history styles of the clupeoids are based on co-evolved traits in which the different patterns of iteroparity represent different solutions for coping with the variable nature of early-stage survival. When these life history traits are compared on time scales appropriate to each species, they are therefore unlikely to provide the correlation between brood strength variation and the life span of adults proposed in Murphy's (1968) contribution to this aspect of life history theory.     

Population growth in random environments

This paper reviews some recent advances in single population stochastic differential equation growth models. They are a natural way to model population growth in a randomly varying environment. The question of which calculus, Itô or Stratonovich, is preferable is addressed. The two calculi coincide when the noise term is linear, if we take into account the differences in the interpretation of the parameters. This clarifies, among other things, the controversy on the theory of niche limiting similarity proposed by May and MacArthur. The effects of correlations in the environmental fluctuations and statistical methods for estimating parameters and for prediction based on a single population trajectory are mentioned. Applications to fisheries, wildlife management and particularly to environmental impact assessment are now becoming possible and are proposed in this paper.     

Population dynamics within a microbial consortium during growth on diesel fuel in saline environments

The diversity and dynamics of a bacterial community extracted from an exploited oil field with high natural soil salinity near Comodoro Rivadavia in Patagonia (Argentina) were investigated. Community shifts during long-term incubation with diesel fuel at four salinities between 0 and 20% NaCl were monitored by single-strand conformation polymorphism community fingerprinting of the PCR-amplified V4-V5 region of the 16S rRNA genes. Information obtained by this qualitative approach was extended by flow cytometric analysis to follow quantitatively the dynamics of community structures at different salinities. Dominant and newly developing clusters of individuals visualized via their DNA patterns versus cell sizes were used to identify the subcommunities primarily involved in the degradation process. To determine the most active species, subcommunities were separated physically by high-resolution cell sorting and subsequent phylogenetic identification by 16S rRNA gene sequencing. Reduced salinity favored the dominance of Sphingomonas spp., whereas at elevated salinities, Ralstonia spp. and a number of halophilic genera, including Halomonas, Dietzia, and Alcanivorax, were identified. The combination of cytometric sorting with molecular characterization allowed us to monitor community adaptation and to identify active and proliferating subcommunities.     

Population dynamics in two-patch environments: Some anomalous consequences of an optimal habitat distribution

The effect of dispersal on population size and stability is explored for a population that disperses passively between two discrete habitat patches. Two basic models are considered. In the first model, a single population experiences density-dependent growth in both patches. A graphical construction is presented which allows one to determine the spatial pattern of abundance at equilibrium for most reasonable growth models and rates of dispersal. It is shown under rather general conditions that this equilibrium is unique and globally stable. In the second model, the dispersing population is a food-limited predator that occurs in both a source habitat (which contains a prey population) and a sink habitat (which does not). Passive dispersal between source and sink habitats can stabilize an otherwise unstable predator-prey interaction. The conditions allowing this are explored in some detail. The theory of optimal habitat selection predicts the evolutionarily stable distribution of a population, given that individuals can freely move among habitats so as to maximize individual fitness. This theory is used to develop a heuristic argument for why passive dispersal should always be selectively disadvantageous (ignoring kin effects) in a spatially heterogeneous but temporally constant environment. For both the models considered here, passive dispersal may lead to a greater number of individuals in both habitats combined than if there were no dispersal. This implies that the evolution of an optimal habitat distribution may lead to a reduction in population size; in the case of the predator-prey model, it may have the additional effect of destabilizing the interaction. The paper concludes with a discussion of the disparate effects habitat selection might have on the geographical range occupied by a species.