Individual variability and population regulation: an individual-based model

To study the influence of individual variability on population dynamics an individual-based model of the dynamics of a single population consisting of different individuals is constructed. The model is based on differences in individual assimilation rates due to intraspecific competition and variability of initial weights. The model exhibits "imperfect regulation", i.e., the number of individuals in the population oscillates and sooner or later the population becomes extinct. When individual variability is included, the model produces longer population extinction times than without individual variability. The average extinction time is not however a monotonic function of the degree of individual variability.     

Patterns and processes of population dynamics with fluctuating habitat size: a case study of a marine copepod inhabiting tide pools

The logistic model is a fundamental population model often used as the basis for analyzing wildlife population dynamics. In the classic logistic model, however, population dynamics may be difficult to characterize if habitat size is temporally variable because population density can vary at a constant abundance, which results in variable strength of density‐dependent feedback for a given population size. To incorporate habitat size variability, we developed a general population model in which changes in population abundance, density, and habitat size are taken into account. From this model, we deduced several predictions for patterns and processes of population dynamics: 1) patterns of fluctuation in population abundance and density can diverge, with respect of their correlation and relative variability; and 2) along with density dependence, habitat size fluctuation can affect population growth with a time lag because changes in habitat size result in changes in population density. In order to test these predictions, we applied our model to population dynamics data of 36 populations of Tigriopus japonicus, a marine copepod inhabiting tide pools of variable sizes caused by weather processes. As expected, we found a significant difference in the fluctuation patterns of population abundance and density of T. japonicus populations with respect to the correlation between abundance and density and their relative variability, which correlates positively with the variability of habitat size. In addition, we found direct and lagged‐indirect effects of weather processes on population growth, which were associated with density dependence and impose regulatory forces on local and regional population dynamics. These results illustrate how changes in habitat size can have an impact on patterns and processes of wildlife population dynamics. We suggest that without knowledge of habitat size fluctuation, measures of population size and its variability as well as inferences about the processes of population dynamics may be misleading.     

Beyond average: an experimental test of temperature variability on the population dynamics of <Emphasis Type="Italic">Tribolium confusum</Emphasis>

The relationship between ectotherm ecology and climatic conditions has been mainly evaluated in terms of average conditions. Average temperature is the more common climatic variable used in physiological and population studies, and its effect on individual and population-level processes is well understood. However, the intrinsic variability of thermal conditions calls attention to the potential effects that this variability could have in ecological systems. Regarding this point, two hypotheses are proposed. From the allocation principle, it may be inferred that if temperature variability is high enough to induce stress in the organisms, then this extra-cost should reduce the energetic budget for reproduction, which will be reflected in population parameters. Moreover, a mathematical property of non-linear functions, Jensen’s inequality, indicates that, in concave functions, like the temperature–reproduction performance function, variability reduces the expected value of the output variable, and again modifies population parameters. To test these hypotheses, experimental cultures of Tribolium confusum under two different thermal variability regimens were carried out. With these data, we fitted a simple population dynamics model to evaluate the predictions of our hypothesis. The results show that thermal variability reduces the maximum reproductive rate of the population but no other parameters such as carrying capacity or the nonlinear factor in a nonlinear version of the Ricker model, which confirms our hypotheses. This result has important consequences, such as the paradoxical increase in population variability under a decrease in thermal variability and the necessary incorporation of climatic variability to evaluate the net effect of climate change on the dynamics of natural populations.     

Quantifying Inter- and Intra-Population Niche Variability Using Hierarchical Bayesian Stable Isotope Mixing Models

Variability in resource use defines the width of a trophic niche occupied by a population. Intra-population variability in resource use may occur across hierarchical levels of population structure from individuals to subpopulations. Understanding how levels of population organization contribute to population niche width is critical to ecology and evolution. Here we describe a hierarchical stable isotope mixing model that can simultaneously estimate both the prey composition of a consumer diet and the diet variability among individuals and across levels of population organization. By explicitly estimating variance components for multiple scales, the model can deconstruct the niche width of a consumer population into relevant levels of population structure. We apply this new approach to stable isotope data from a population of gray wolves from coastal British Columbia, and show support for extensive intra-population niche variability among individuals, social groups, and geographically isolated subpopulations. The analytic method we describe improves mixing models by accounting for diet variability, and improves isotope niche width analysis by quantitatively assessing the contribution of levels of organization to the niche width of a population.     

Bayesian Population Physiologically-Based Pharmacokinetic (PBPK) Approach for a Physiologically Realistic Characterization of Interindividual Variability in Clinically Relevant Populations

Interindividual variability in anatomical and physiological properties results in significant differences in drug pharmacokinetics. The consideration of such pharmacokinetic variability supports optimal drug efficacy and safety for each single individual, e.g. by identification of individual-specific dosings. One clear objective in clinical drug development is therefore a thorough characterization of the physiological sources of interindividual variability. In this work, we present a Bayesian population physiologically-based pharmacokinetic (PBPK) approach for the mechanistically and physiologically realistic identification of interindividual variability. The consideration of a generic and highly detailed mechanistic PBPK model structure enables the integration of large amounts of prior physiological knowledge, which is then updated with new experimental data in a Bayesian framework. A covariate model integrates known relationships of physiological parameters to age, gender and body height. We further provide a framework for estimation of the a posteriori parameter dependency structure at the population level. The approach is demonstrated considering a cohort of healthy individuals and theophylline as an application example. The variability and co-variability of physiological parameters are specified within the population; respectively. Significant correlations are identified between population parameters and are applied for individual- and population-specific visual predictive checks of the pharmacokinetic behavior, which leads to improved results compared to present population approaches. In the future, the integration of a generic PBPK model into an hierarchical approach allows for extrapolations to other populations or drugs, while the Bayesian paradigm allows for an iterative application of the approach and thereby a continuous updating of physiological knowledge with new data. This will facilitate decision making e.g. from preclinical to clinical development or extrapolation of PK behavior from healthy to clinically significant populations.     

Distinct cellular states determine calcium signaling response

The heterogeneity in mammalian cells signaling response is largely a result of pre‐existing cell‐to‐cell variability. It is unknown whether cell‐to‐cell variability rises from biochemical stochastic fluctuations or distinct cellular states. Here, we utilize calcium response to adenosine trisphosphate as a model for investigating the structure of heterogeneity within a population of cells and analyze whether distinct cellular response states coexist. We use a functional definition of cellular state that is based on a mechanistic dynamical systems model of calcium signaling. Using Bayesian parameter inference, we obtain high confidence parameter value distributions for several hundred cells, each fitted individually. Clustering the inferred parameter distributions revealed three major distinct cellular states within the population. The existence of distinct cellular states raises the possibility that the observed variability in response is a result of structured heterogeneity between cells. The inferred parameter distribution predicts, and experiments confirm that variability in IP3R response explains the majority of calcium heterogeneity. Our work shows how mechanistic models and single‐cell parameter fitting can uncover hidden population structure and demonstrate the need for parameter inference at the single‐cell level.     

Harvested populations are more variable only in more variable environments

The interaction between environmental variation and population dynamics is of major importance, particularly for managed and economically important species, and especially given contemporary changes in climate variability. Recent analyses of exploited animal populations contested whether exploitation or environmental variation has the greatest influence on the stability of population dynamics, with consequences for variation in yield and extinction risk. Theoretical studies however have shown that harvesting can increase or decrease population variability depending on environmental variation, and requested controlled empirical studies to test predictions. Here, we use an invertebrate model species in experimental microcosms to explore the interaction between selective harvesting and environmental variation in food availability in affecting the variability of stage‐structured animal populations over 20 generations. In a constant food environment, harvesting adults had negligible impact on population variability or population size, but in the variable food environments, harvesting adults increased population variability and reduced its size. The impact of harvesting on population variability differed between proportional and threshold harvesting, between randomly and periodically varying environments, and at different points of the time series. Our study suggests that predicting the responses to selective harvesting is sensitive to the demographic structures and processes that emerge in environments with different patterns of environmental variation.     

Population and life-history consequences of within-cohort individual variation

The consequences of within-cohort (i.e., among-individual) variation for population dynamics are poorly understood, in particular for the case where life history is density dependent. We develop a physiologically structured population model that incorporates individual variation among and within cohorts and allows us to explore the intertwined relationship between individual life history and population dynamics. Our model is parameterized for the lizard Zootoca vivipara and reproduces well the species' dynamics and life history. We explore two common mechanisms that generate within-cohort variation: variability in food intake and variability in birth date. Predicted population dynamics are inherently very stable and do not qualitatively change when either of these sources of individual variation is introduced. However, increased within-cohort variation in food intake leads to changes in morphology, with longer but skinnier individuals, even though mean food intake does not change. Morphological changes result from a seemingly universal nonlinear relationship between growth and resource availability but may become apparent only in environments with strongly fluctuating resources. Overall, our results highlight the importance of using a mechanistic framework to gain insights into how different sources of intraspecific variability translate into life-history and population-dynamic changes.     

Probabilistic methods for addressing uncertainty and variability in biological models: application to a toxicokinetic model

Population variability and uncertainty are important features of biological systems that must be considered when developing mathematical models for these systems. In this paper we present probability-based parameter estimation methods that account for such variability and uncertainty. Theoretical results that establish well-posedness and stability for these methods are discussed. A probabilistic parameter estimation technique is then applied to a toxicokinetic model for trichloroethylene using several types of simulated data. Comparison with results obtained using a standard, deterministic parameter estimation method suggests that the probabilistic methods are better able to capture population variability and uncertainty in model parameters.     

The dynamical consequences of developmental variability and demographic stochasticity for host-parasitoid interactions

Few age-structured models of species dynamics incorporate variability and uncertainty in population processes. Motivated by laboratory data for an insect and its parasitoid, we investigate whether such assumptions are appropriate when considering the population dynamics of a single species and its interaction with a natural enemy. Specifically, we examine the effects of developmental variability and demographic stochasticity on different types of cyclic dynamics predicted by traditional models. We show that predictions based on the deterministic fixed-development approach are differentially sensitive to variability and noise in key life stages. In particular, we find that the demonstration of half-generation cycles in the single-species model and the multigeneration cycles in the host-parasitoid model are sensitive to the introduction of developmental variability and noise, whereas generation cycles are robust to the intrinsic variability and uncertainty that may be found in nature.     

Factors affecting levels of genetic diversity in natural populations.

Genetic variability is the clay of evolution, providing the base material on which adaptation and speciation depend. It is often assumed that most interspecific differences in variability are due primarily to population size effects, with bottlenecked populations carrying less variability than those of stable size. However, we show that population bottlenecks are unlikely to be the only factor, even in classic case studies such as the northern elephant seal and the cheetah, where genetic polymorphism is virtually absent. Instead, we suggest that the low levels of variability observed in endangered populations are more likely to result from a combination of publication biases, which tend to inflate the level of variability which is considered ''normal'', and inbreeding effects, which may hasten loss of variability due to drift. To account for species with large population sizes but low variability we advance three hypotheses. First, it is known that certain metapopulation structures can result in effective population sizes far below the census size. Second, there is increasing evidence that heterozygous sites mutate more frequently than equivalent homozygous sites, plausibly because mismatch repair between homologous chromosomes during meiosis provides extra opportunities to mutate. Such a mechanism would undermine the simple relationship between heterozygosity and effective population size. Third, the fact that related species that differ greatly in variability implies that large amounts of variability can be gained or lost rapidly. We argue that such cases are best explained by rapid loss through a genome-wide selective sweep, and suggest a mechanism by which this could come about, based on forced changes to a control gene inducing coevolution in the genes it controls. Our model, based on meiotic drive in mammals, but easily extended to other systems, would tend to facilitate population isolation by generating molecular incompatabilities. Circumstances can even be envisioned in which the process could provide intrinsic impetus to speciation.     

Population Dynamics and Environmental Variability

SYNOPSIS. A model relating environmental variability and populationvariability is proposed and discussed. The model strongly emphasizesthe importance of the different consequences of erratic andregular environmental variability, which are discussed fromboth the theoretical and empirical viewpoints. Data on populationvariability for six species in three communities (temperateintertidal, subtropical intertidal, and oligotrophic lake benthic)are presented and discussed in the context of the model. Ingeneral, environmental variability and population variabilityare trongly correlated. The impact of erratic environmentalvariability is apparent in one community.     

Genetic analysis of ecologically relevant morphological variability in Plantago lanceolata L.

Summary Morphological variability was studied in two populations of Plantago lanceolata using diallel analysis. In each population, reciprocal crosses between all possible pairs of ten plants were made. In the greenhouse, six members of each family were grown and many characters were measured. Using the model of Cockerham and Weir, the contributions of the different genetic variance components were calculated. From earlier papers it was postulated in advance to what extent and by which effect the characters in both populations were genetically determined. The populations had been differentiated for life history and morphological characters, and varied also in the relative contribution of genetic components to variability. In the Merrevliet (Me) population, where strong biotic selection was assumed, low levels of additive-genetic variability were present and the relative dominance appeared to be high. The contrasting population, Westduinen (Wd), which is abiotically controlled and shows strong environmental variability, possessed higher levels of additive-genetic variability and lower levels of relative dominance. It is possible that differential natural selection has diminished additive-genetic variability to different extents in both populations: plasticity and environmental heterogeneity prevented the loss of additive-genetic variability in Wd, whereas in the stable population, Me, natural selection had the opportunity of not only changing the means of the characters but also of diminishing additive-genetic variability to a great extent.Grassland Species Research Group Publication No. 146     

Cell volume distributions reveal cell growth rates and division times

A population of cells in culture displays a range of phenotypic responses even when those cells are derived from a single cell and are exposed to a homogeneous environment. Phenotypic variability can have a number of sources including the variable rates at which individual cells within the population grow and divide. We have examined how such variations contribute to population responses by measuring cell volumes within genetically identical populations of cells where individual members of the population are continuously growing and dividing, and we have derived a function describing the stationary distribution of cell volumes that arises from these dynamics. The model includes stochastic parameters for the variability in cell cycle times and growth rates for individual cells in a proliferating cell line. We used the model to analyze the volume distributions obtained for two different cell lines and one cell line in the absence and presence of aphidicolin, a DNA polymerase inhibitor. The derivation and application of the model allows one to relate the stationary population distribution of cell volumes to extrinsic biological noise present in growing and dividing cell cultures.     

Non-linear biological responses to environmental noise affect population extinction risk

Non-linearities are commonly observed in the responses of organisms to environment. They potentially modify the qualitative and quantitative properties of population dynamics. We studied how non-linear responses to environment, or "noise filters", influence population variability and extinction risk by introducing coloured noise to the growth rate in the Hassell single-species model. The consequences of noise filtering were analysed by comparing the model dynamics with linearly filtered and non-linearly filtered noise that have the same mean. Three biologically plausible filters we used: saturating, unimodal optimum type, and sigmoid responses.
Filtering can either decrease or increase population variability when compared to linear noise response. The effect of noise filtering on variability is most pronounced with stable population dynamics and the outcome depends on the filter type, population growth rate, and noise colour.
Non-linear noise filtering predominantly increases extinction risks when population growth rate is low (R<5). As an exception, saturating filter has a window of decreased risk at very low growth rate and reddened environment. In the unstable range of the dynamics (15These results suggest that accounting for the non-linear responses to environment should be considered when estimating extinction risks and population variability. Moreover, the non-linear responses make noise colour a more important factor in these analyses.     

Environmental Uncertainty and Variable Diapause

We analyze a stage-structured model of a population that displays variable diapause in a randomly varying environment. The ruggedness of the environment is measured by the extent of random variation in per-capita reproductive success. We show how variable diapause and environmental characteristics affect the population′s stochastic growth rate. In rugged unpredictable environments, phenotypes that show some tendency to diapause are found to have a higher growth rate than nondiapausing phenotypes. In harsh rugged environments, some tendency to diapause may be all that permits population persistence. Positive serial autocorrelation causes the optimal diapause fraction to decrease, while negative autocorrelation causes that fraction to increase. The structured model behaves very differently from a scalar model for large diapause fractions even in uncorrelated environments, and in many cases predicts a broad optimum. The difference between models is due to the extreme variability of stage structure in populations subject to even small variability when diapause tendency is high.     

Is assemblage variability related to environmental variability? An answer for riverine fish

We examine the variability of riverine fish assemblages in terms of assemblage stability (i.e. variability of numbers of individuals within species over time and variability of assemblage total density), assemblage persistence, and assemblage species richness using data from a 9-yr survey of 27 sites within 18 coastal streams of North-western France. To do so, we test a hypothesized directional model for the expected relationships between environmental variability, assemblage variability, assemblage persistence, and assemblage species richness: 1) environmental variability within a given system is likely to generate variable local population size within this system, thus increasing local assemblages variability; 2) environmental variability should increase extinction rates (or, under constant colonization rates, decrease persistence), because the more population sizes vary within an assemblage, the more likely they are to become zero in some period of time; 3) assemblage variability should reduce assemblage species richness by increasing extinction rates within populations composing these assemblages. Results are compatible with our starting hypotheses and show that assemblage variability increased with environmental variability (i.e. discharge variability), that assemblage persistence decreased with environmental variability, and that species richness decreased with assemblage variability after environmental factors were controlled for. Thus, disturbance regimes, in our case, can alter the stability properties of assemblages and extrinsic determinants of assemblage variability may be an important determinant of assemblage species richness. These results have important conservation and management implications, due to the strong impact of river regulation on flow regimes.     

Transients and tradeoffs of phenotypic switching in a fluctuating limited environment

Phenotypic variability in a microorganism population is thought to be advantageous in fluctuating environments, however much remains unknown about the precise conditions for this advantage to hold. In particular competition for a growth-limiting resource and the dynamics of that resource in the environment modify the tradeoff between different effects of variability. Here we investigate theoretically a model system for variable populations under competition for a flowing resource that governs growth (chemostat model) and changes with time. This environment generally induces density-dependent selection among competing sub-populations. We characterize quantitatively the transient dynamics in this system, and find that equilibration between total population density and environment can occur separately and with a distinct timescale from equilibration between competing sub-populations. We analyze quantitatively the two opposing effects of heterogeneity-transient response to change, and fitness at equilibrium-and find the optimal strategy in a fluctuating environment. We characterize the phase diagram of the system in term of its optimal strategy and find it to be strongly dependent on the typical timescale of the environment and weakly dependent on the internal parameters of the population.