Tracking a changing environment: optimal sampling, adaptive memory and overnight effects

Foraging in a variable environment presents a classic problem of decision making with incomplete information. Animals must track the changing environment, remember the best options and make choices accordingly. While several experimental studies have explored the idea that sampling behavior reflects the amount of environmental change, we take the next logical step in asking how change influences memory. We explore the hypothesis that memory length should be tied to the ecological relevance and the value of the information learned, and that environmental change is a key determinant of the value of memory. We use a dynamic programming model to confirm our predictions and then test memory length in a factorial experiment. In our experimental situation we manipulate rates of change in a simple foraging task for blue jays over a 36 h period. After jays experienced an experimentally determined change regime, we tested them at a range of retention intervals, from 1 to 72 h. Manipulated rates of change influenced learning and sampling rates: subjects sampled more and learned more quickly in the high change condition. Tests of retention revealed significant interactions between retention interval and the experienced rate of change. We observed a striking and surprising difference between the high and low change treatments at the 24 h retention interval. In agreement with earlier work we find that a circadian retention interval is special, but we find that the extent of this ‘specialness’ depends on the subject's prior experience of environmental change. Specifically, experienced rates of change seem to influence how subjects balance recent information against past experience in a way that interacts with the passage of time.     

Advantage of storage in a fluctuating environment

We will elaborate the evolutionary course of an ecosystem consisting of a population in a chemostat environment with periodically fluctuating nutrient supply. The organisms that make up the population consist of structural biomass and energy storage compartments. In a constant chemostat environment a species without energy storage always out-competes a species with energy reserves. This hinders evolution of species with storage from those without storage. Using the adaptive dynamics approach for non-equilibrium ecological systems we will show that in a fluctuating environment there are multiple stable evolutionary singular strategies (ss's): one for a species without, and one for a species with energy storage. The evolutionary end-point depends on the initial evolutionary state. We will formulate the invasion fitness in terms of Floquet multipliers for the oscillating non-autonomous system. Bifurcation theory is used to study points where due to evolutionary development by mutational steps, the long-term dynamics of the ecological system changes qualitatively. To that end, at the ecological time scale, the trait value at which invasion of a mutant into a resident population becomes possible can be calculated using numerical bifurcation analysis where the trait is used as the free parameter, because it is just a bifurcation point. In a constant environment there is a unique stable equilibrium for one species following the "competitive exclusion" principle. In contrast, due to the oscillatory dynamics on the ecological time scale two species may coexist. That is, non-equilibrium dynamics enhances biodiversity. However, we will show that this coexistence is not stable on the evolutionary time scale and always one single species survives.     

Problems of sampling and inference in the study of fluctuating dental asymmetry

Randomly distributed or “fluctuating” dental asymmetry has been accorded evolutionary meaning and interpreted as a result of environmental stress. However, except for congenital malformation syndromes, the determinants of human crown size asymmetry are still equivocal. Both a computer simulated sampling experiment using a combined sample size of N = 3000, and the requirements of adequate statistical power show that sample sizes of several hundred are needed to detect population differences in dental asymmetry. Using the largest available sample of children with defined prenatal stresses, we are unable to find systematic increases in crown size asymmetry. Given sampling limitations and the current inability to link increased human dental asymmetry to defined prenatal stresses, we suggest that fluctuating dental asymmetry is not yet established as a useful and reliable measure of general stress in human populations.     

Fitness consequences of avian personalities in a fluctuating environment

Individual animals differ in the way they cope with challenges in their environment, comparable with variation in human personalities. The proximate basis of variation in personality traits has received considerable attention, and one general finding is that personality traits have a substantial genetic basis. This poses the question of how variation in personality is maintained in natural populations. We show that selection on a personality trait with high heritability fluctuates across years within a natural bird population. Annual adult survival was related to this personality trait (behaviour in novel environments) but the effects were always opposite for males and females, and reversed between years. The number of offspring surviving to breeding was also related to their parents' personalities, and again selection changed between years. The observed annual changes in selection pressures coincided with changes in environmental conditions (masting of beeches) that affect the competitive regimes of the birds. We expect that the observed fluctuations in environmental factors lead to fluctuations in competition for space and food, and these, in association with variations in population density, lead to a variation in selection pressure, which maintains genetic variation in personalities.     

Rhythms of gene expression in a fluctuating intertidal environment

The physiological strategies that enable organisms to thrive in habitats where environmental factors vary dramatically on a daily basis are poorly understood. One of the most variable and unpredictable habitats on earth is the marine rocky intertidal zone located at the boundary between the terrestrial and marine environments. Mussels dominate rocky intertidal habitats throughout the world and, being sessile, endure wide variations in temperature, salinity, oxygen, and food availability due to diurnal, tidal, and climatic cycles. Analysis of gene-expression changes in the California ribbed mussel (Mytilus californianus) at different phases in the tidal cycle reveals that intertidal mussels exist in at least four distinct physiological states, corresponding to a metabolism and respiration phase, a cell-division phase, and two stress-response signatures linked to moderate and severe heat-stress events. The metabolism and cell-division phases appear to be functionally linked and are anticorrelated in time. The magnitudes and timings of these states varied by vertical position on the shore and appear to be driven by microhabitat conditions. The results provide new insights into the strategies that allow life to flourish in fluctuating environments and demonstrate the importance of time course data collected from field animals in situ in understanding organism-environment interactions.     

The Chitty effect: a consequence of dynamic energy allocation in a fluctuating environment

An important biological feature of cyclic populations of voles and lemmings is phase-related changes in average body mass, with adults in high-density phases being 20-30% heavier than those in low-density phases of a cycle. This observation, called the "Chitty effect," is considered to be a ubiquitous feature of cyclic populations. It has been argued that understanding the Chitty effect is fundamental to unraveling the enigma of population cycles. However, there exists no agreement among biologists regarding the causes of the Chitty effect. Here, I propose a simple hypothesis to explain the Chitty effect, based on phase-related, dynamic allocation of energy between reproductive and somatic effort. The essence of the hypothesis is that: (1) reproduction is suppressed in animals born or raised in the later part of the increase phase by environmental factors, including social influences; (2) suppression of reproduction limits the amount of energy that is diverted for reproductive effort, and forces a disproportionately greater amount of surplus power (the energy left after the energetic costs of standard and active metabolism are met) to be allocated for somatic effort; (3) the surplus energy, above and beyond what is required for routine biological activities, will allow continuous growth and deposition of additional body mass, which causes an increase in body mass; and (4) animals grow to a larger size as a population enters the peak density phase, causing an increase in the average body mass. The Chitty effect is predicted to be most pronounced at the late increase or peak phase of a population cycle. Possible causes of reproductive suppression include direct or indirect influences of the environmental factors. The Chitty effect may be a consequence, not a cause, of population cycles in small mammals.     

Adaptive diversification of a plastic trait in a predictably fluctuating environment

There is substantial evidence that evolutionary diversification can occur in allopatric conditions through reduction in the degree of phenotypic plasticity when an isolated population encounters a novel, more stable environment. Plasticity is no longer favored in the new environment, either because it carries an inherent physiological cost or because it leads to production of suboptimal phenotypes. In order to explore the role of phenotypic plasticity in sympatric diversification, we modeled the ecological and evolutionary dynamics of Escherichia coli bacteria in batch cultures. Our results describe an evolutionary pathway leading to metabolic diversification in a sympatric environment without spatial structure. In an environment that fluctuates widely and predictably, evolutionary branching leads to diversification and stable coexistence of generalist and specialist ecotypes for some combinations of parameters. Diversification and stable coexistence occur when reaction norms are steep and trade-offs between metabolic pathways are convex. We conclude that, in principle, diversification due to reduced plasticity can occur without allopatric isolation, reduced environmental variability, or an explicit cost of plasticity.     

The threshold of survival for systems in a fluctuating environment

Thresholds for survival and extinction are important for assessing the risk of mortality in systems exposed to exogeneous stress. For generic, rudimentary population models and the classical resource-consumer models of Leslie and Gallopin, we demonstrate the existence of a survival threshold for situations where demographic parameters are fluctuating, generally, in a nonperiodic manner. The fluctuations are assumed, to be generated by exogenous, anthropogenic stresses such as toxic chemical exposures. In general, the survival threshold is determined by a relationship between mean stress measure in organisms to the ratio of the population intrinsic growth rate and stress response rate. Research supported by the fund of Chinese Natural Science. Research supported in part by the U.S. Enviromental Protection Agency under cooperative agreement CR-813353-01-0.     

Prebiotic nucleotide oligomerization in a fluctuating environment: Effects of kaolinite and cyanamide

Summary The clay kaolinite was tested for its ability to promote nucleotide oligomerization in model prebiotic systems. Heterogeneous mixtures of clay, water and nucleotide were repeatedly evaporated to dryness at 60°C and redissolved in water in cyclic fashion in the presence or absence of cyanamide and/ or ammonium chloride. With or without cycling, kaolinite alone did not promote the oligomerization of nucleotides at detectable levels. Cycling of clay in combination with cyanamide, however, promoted high levels of condensation to a mixture of oligonucleotides and dinucleotide pyrophosphate without requiring ammonium chloride. Although cycling with clay favored synthesis of dinucleotide pyrophosphate, cycling without clay enhanced formation of oligonucleotides. These results support the hypothesis that the presence of clays in fluctuating environments would have influenced the course of prebiotic condensation reactions.     

Periodic solutions of population models in a periodically fluctuating environment.

A periodically fluctuating environment is assumed in a population-modeling process that generates nonautonomous difference equations. The existence and uniqueness of periodic solutions are studied. A sufficient condition for existence and a necessary condition for uniqueness are obtained. Stability of the periodic solutions is investigated. Several numerical examples are given to illustrate the basic results, and a brief discussion is presented.     

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.     

Evolution of size-dependent flowering in a variable environment: partitioning the effects of fluctuating selection

In a stochastic environment, two distinct processes, namely nonlinear averaging and non-equilibrium dynamics, influence fitness. We develop methods for decomposing the effects of temporal variation in demography into contributions from nonlinear averaging and non-equilibrium dynamics. We illustrate the approach using Carlina vulgaris, a monocarpic species in which recruitment, growth and survival all vary from year to year. In Carlina the absolute effect of temporal variation on the evolutionarily stable flowering strategy is substantial (ca. 50% of the evolutionarily stable flowering size) but the net effect is much smaller (ca. 10%) because the effects of temporal variation do not influence the evolutionarily stable strategy in the same direction.     

Coexistence in a fluctuating environment by the effect of relative nonlinearity: A minimal model

The minimal model of the “relative nonlinearity” type fluctuation-maintained coexistence is investigated. The competing populations are affected by an environmental white noise. With quadratic density dependence, the long-term growth rates of the populations are determined by the average and the variance of the (fluctuating) total density. At most two species can coexist on these two “regulating” variables; competitive exclusion would ensue in a constant environment. A numerical study of the expected time until extinction of any of the two species reveals that the criterion of mutual invasibility predicts the parameter range of long-term coexistence correctly in the limit of zero extinction threshold. However, any extinction threshold consistent with a realistic population size will allow only short-term coexistence. Therefore, our simulations question the biological relevance of mutual invasibility, as a sufficient condition of coexistence, for large density fluctuations. We calculate the average and the variance of the fluctuating density of the coexisting populations analytically via the moment-closure approximation; the results are reasonably close to the simulated behavior. Based on this treatment, robustness of coexistence is studied in the limit of infinite population size. We interpret the results of this analysis in the context of necessity of niche segregation with respect to the regulating variables using a framework theory published earlier.     

Catalysis of peptide bond formation by histidyl-histidine in a fluctuating clay environment

Summary The condensation of glycine to form oligoglycines during wet-dry fluctuations on clay surfaces was enhanced up to threefold or greater by small amounts of histidyl-histidine. In addition, higher relative yields of the longer oligomers were produced. Other specific dipeptides tested gave no enhancement, and imidazole, histidine, and N-acetylhistidine gave only slight enhancements. Histidyl-histidine apparently acts as a true catalyst (in the sense of repeatedly catalyzing the reaction), since up to 52 nmol of additional glycine were incorporated into oligoglycine for each nmol of catalyst added. This is the first known instance of a peptide or similar molecule demonstrating a catalytic turnover number greater than unity in a prebiotic oligomer synthesis reaction, and suggests that histidyl-histidine is a model for a primitive prebiotic protoenzyme. Catalysis of peptide bond synthesis by a molecule which is itself a peptide implies that related systems may be capable of exhibiting autocatalytic growth.     

The effects of a fluctuating environment on the water relations of larval Lepidoptera

Abstract. New techniques for haemolymph analysis under field conditions have permitted studies of short-term changes in the body fluid concentrations of insects, in association with ambient conditions.
The haemolymph of four species of caterpillar changes in relation to the prevailing relative humidity, but the magnitude of these changes was correlated with the degree of exposure to the environment characteristic of each species and instar. In larvae habitually fully exposed to ambient conditions, haemolymph concentrations normally changed predictably through a day in relation to the humidity. However, osmoregulatory mechanisms operated to keep the increments in osmolality within acceptable limits. For those larvae which inhabit protected microenvironments with constant high humidity, either in association with plants or in conspecific aggregations, ambient humidity had little effect on the blood when this was sampled in situ. But when removed from such habitats, blood osmolality increases were large and rapid, and the larvae often succumbed to desiccation.
The role of biochemical, physiological, behavioural and ecological strategies in establishing the water balance of an insect in its natural surroundings are considered in the light of these findings.     

Phytoplankton blooms in a fluctuating environment: the roles of plankton response time scales and grazing

Our new view of planktonic ecosystems states that the picoplanktoncan outcompete the netplankton for nutrients, but are held toa relatively constant biomass because of the short responsetime scales of their protist grazers. The long response timeof the mesozooplankton grazing the netphytoplankton allows theselarger phytoplankton to respond to environmental fluctuationswith large changes in biomass. There is some ambiguity in theliterature, however, over the relative importance of ‘responsetime scales’ versus grazing in controlling the phytoplanktonbiomass. To address this issue, a simple model including explicitresponse time scales and grazing was formulated. The model wasused to explore the influence of these two dynamics in controllingthe response of phytoplankton to sudden changes in the carryingcapacity of the environment. It was applied to the IronEx IIdata to explore the implications of the two types of control.The model supports the hypothesis that the short response timescale of the protists limits the picoplankton biomass. However,it also shows that the zooplankton grazing rate (here representedby a clearance rate a) has a much stronger effect in determiningthe phytoplankton biomass than the response time scale.     

An evolutionary maximum principle for density-dependent population dynamics in a fluctuating environment

The evolution of population dynamics in a stochastic environment is analysed under a general form of density-dependence with genetic variation in r and K, the intrinsic rate of increase and carrying capacity in the average environment, and in σ_e², the environmental variance of population growth rate. The continuous-time model assumes a large population size and a stationary distribution of environments with no autocorrelation. For a given population density, N, and genotype frequency, p, the expected selection gradient is always towards an increased population growth rate, and the expected fitness of a genotype is its Malthusian fitness in the average environment minus the covariance of its growth rate with that of the population. Long-term evolution maximizes the expected value of the density-dependence function, averaged over the stationary distribution of N. In the θ-logistic model, where density dependence of population growth is a function of N^θ, long-term evolution maximizes E[N^θ]=[1−σ_e²/(2r)]K^θ. While σ_e² is always selected to decrease, r and K are always selected to increase, implying a genetic trade-off among them. By contrast, given the other parameters, θ has an intermediate optimum between 1.781 and 2 corresponding to the limits of high or low stochasticity.