Protecting haploid polymorphisms in temporally variable environments

Analysis of a continuous-time model shows that a protected polymorphism can arise in a haploid population subject to temporal fluctuations in selection. The requirements are that population size is regulated in a density-dependent manner and that an allele's arithmetic mean relative growth rate is greater than one when rare and that its harmonic mean relative growth rate is less than one when common. There is no requirement that relative growth rate be frequency dependent. Comparisons with discrete-time models show that the standard formalism used by population genetics ignores forced changes in generation time as rare advantageous alleles sweep into a population. In temporally variable environments, frequency-dependent changes in generation times tend to counteract these invasions. Such changes can prevent fixation and protect polymorphisms.     

Parental investment in temporally varying environments

Summary Using a model that allows the mean and variance of investment by parents in offspring to evolve in response to change in degree of temporal environmental variation, this paper shows that both parental investment parameters should increase with increases in temporal variation. If offspring receiving greater parental investment are viable over a broader range of environmental conditions, then increased temporal environmental variation can select for increases in parental investment. The variance in parental investment also may increase with increases in temporal variation, but there is a threshold level of temporal variation that must be exceeded before variance in parental investment is adaptive. Thus phenotypic variance in parental investment is not adaptive in all temporally varying environments. Further, increased overlap among generations reduces the expected effects of temporal variation on the mean and variance in parental investment. Thus a negative correlation between length of reproductive life and both measures of investment is expected. There is support for the predictions of this model in some animal groups, but not among plants. Possible reasons for the lack of support among plants are discussed and directions for future research aimed at distinguishing adaptive and maladaptive phenotypic variance in parental investment are suggested.     

Site fidelity in temporally correlated environments enhances population persistence

Site fidelity, the phenomenon of remaining faithful to sites, often where an individual has bred successfully in the past, has important consequences for population dynamics. Previous results have shown that site fidelity results in a positive correlation between population density and fitness. Here, I build on this theme by incorporating site fidelity using the win‐stay : lose‐switch rule often seen among birds, i.e. individuals return to sites were they bred successfully in the past and vacate those where they have not. Results demonstrate that the combination of site fidelity and temporal autocorrelation in site quality can enhance the persistence of population networks, whereas either factor acting alone has little or no influence. Moreover, there is an abrupt threshold at moderate levels of temporal autocorrelation, ρ_time > 0.35–0.4, beyond which persistence time and the probability of surviving >500 years is greatly accelerated. These results suggest that temporal autocorrelation combined with appropriate behavioural responses may enhance population persistence.     

Habitat selection and population regulation in temporally fluctuating environments

Understanding and predicting the distribution of organisms in heterogeneous environments lies at the heart of ecology, and the theory of density-dependent habitat selection (DDHS) provides ecologists with an inferential framework linking evolution and population dynamics. Current theory does not allow for temporal variation in habitat quality, a serious limitation when confronted with real ecological systems. We develop both a stochastic equivalent of the ideal free distribution to study how spatial patterns of habitat use depend on the magnitude and spatial correlation of environmental stochasticity and also a stochastic habitat selection rule. The emerging patterns are confronted with deterministic predictions based on isodar analysis, an established empirical approach to the analysis of habitat selection patterns. Our simulations highlight some consistent patterns of habitat use, indicating that it is possible to make inferences about the habitat selection process based on observed patterns of habitat use. However, isodar analysis gives results that are contingent on the magnitude and spatial correlation of environmental stochasticity. Hence, DDHS is better revealed by a measure of habitat selectivity than by empirical isodars. The detection of DDHS is but a small component of isodar theory, which remains an important conceptual framework for linking evolutionary strategies in behavior and population dynamics.     

Fish species richness in spring‐fed ponds: effects of habitat size versus isolation in temporally variable environments

1. Species richness in a habitat patch is determined by immigration (regional) and extinction (local) processes, and understanding their relative importance is crucial for conservation of biodiversity. In this study, we applied the Island Biogeography concept to spring ponds connected to a river in southwestern Japan to examine how immigration and extinction processes interact to determine fish species richness in temporally variable environments. 2. Fish censuses were conducted 15 times in 13 study ponds at 1–4 month intervals from August 1998 through October 2000. Effects of habitat size (pond area), isolation (distance from the river) and temporal environmental variability (water level fluctuation) on (i) species richness, (ii) immigration and extinction rates and (iii) population size and persistence of each fish species were assessed. 3. The results revealed predominant effects of distance on species richness, immigration/extinction rates and population size and persistence. Species richness decreased with increasing distance but was not related to either pond area or water level fluctuation. A negative effect of distance on immigration rate was detected, while neither pond area nor water level fluctuation had significant effects on extinction rate. Further, population size and persistence of four species increased with decreasing distance, suggesting that, in ponds close to the river, immigrants from the river reduce the probability of extinction (i.e. provide a rescue effect), contributing to the maintenance of high species richness. 4. Overall results emphasise the importance of immigration processes, rather than extinction, in shaping patterns of species richness in our system. The predominant importance of immigration was probably because of (i) high temporal variability that negates habitat‐size effects and (ii) continuous immigration that easily compensates for local extinctions. Our results suggest that consideration of regional factors (e.g. connectivity, locations of source populations and barriers to colonisation) is crucial for conservation and restoration of local habitats.     

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.

     

Predictive models in spatially and temporally variable freshwater systems

Abstract This paper discusses the relationships between scaling and predictability in ecosystems. The logical basis of ecosystem modelling is explored using ideas first developed in complexity theory and analogies with the behaviour of complex adaptive systems. Any ecological model is a scale-dependent entity and both empirical and dynamic models of freshwater systems have their strengths and weaknesses. The logical basis of modelling using functional groups is explored. I conclude that such an approach can be justified and that such models have predictive power. Any predictive model of freshwater systems must take the major scales of external (atmospheric and catchment) forcing into account as well as the scales of key processes in the ecosystem itself. The importance of so-called ‘pink noise’ spectra, which arise both from external forcing and the internal dynamics of dynamic systems, is noted. The key scales of pattern and process in freshwater ecosystems are discussed in relation to the properties of the major functional groups. In order to have predictive power, I conclude that models of freshwater systems must include sediment exchanges and the properties of aquatic macrophytes as well as water column interactions and the pelagic components. When viewed at the scale of functional groups and the major biogeochemical processes, freshwater ecosystems may not be as complex as is often assumed.     

Timing of diapause in relation to temporally variable catastrophes

This paper analyses the response of the distribution of diapause switching times in an arthropod population with respect to variation in a catastrophe, which kills nondiapause individuals. For concreteness, the catastrophe will be taken to the onset of winter. The relationship between an individual's switching time and the decision whether to diapause is defined as follows: If she passes through the end of the sensitive period, during which the diapause decision is made, before her switching time, she will complete development and reproduce rather than diapause. If she passes through the sensitive period on or after her switching time, she will diapause. The model follows the evolution of the distribution of switching times for a population over a sequence of years. Random variation in the end of the season is created by sampling from a normal distribution of times at the end of the growing season. The model is for a haploid population in which the distribution of switching times that a female passes to her offspring is normally distributed having her switching time as its mean. This approximates a sexual population with strong positive assortative mating and heritability near 1. This mode of inheritance permits a rapid response to yearly changes in the end of the season as a contrast to earlier models, which incorporated a slow response. Patterns of temporal change in the median switching time are analyzed. The influences of three parameters are considered: the mean and standard deviation of the end of the season, and standard deviation of the offspring distribution. The main conclusion differs from the results of earlier models in that the end of the season must be extremely variable before the median of the distribution of switching times displays conservative behavior, i. e., before it becomes significantly earlier than the median expected when the end of the season is constant and equal to the mean of the normal distribution for the end of the season used in the simulation. Previous models predicted a conservative response even in moderately variable environments.     

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 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.     

Trophic network structure emerges through antagonistic coevolution in temporally varying environments

Understanding the mechanisms underlying ecological specialization is central to our understanding of community ecology and evolution. Although theoretical work has investigated how variable environments may affect specialization in single species, little is known about how such variation impacts bipartite network structure in antagonistically coevolving systems. Here, we develop and analyse a general model of victim-enemy coevolution that explicitly includes resource and population dynamics. We investigate how temporal environmental heterogeneity affects the evolution of specialization and associated community structure. Environmental productivity influences victim investment in resistance, which will shape patterns of specialization through its regulating effect on enemy investment in infectivity. We also investigate the epidemiological consequences of environmental variability and show that enemy population density is maximized for intermediate lengths of productive seasons, which corresponds to situations where enemies can evolve higher infectivity than victims can evolve defence. We discuss our results in the light of empirical studies, and further highlight ways in which our model applies to a range of natural systems.     

Reproductive strategy of insects as adaptation to temporally varying environments

Diversity of oviposition curve observed in 125 insects was analysed using the ratio of the length of period for development to that for reproduction. On the basis of this empirical data, two extreme reproductive patterns were selected: prolonged reproduction with early maturity and concentrated reproduction with late maturity. Population growth of the species with each reproductive pattern was calculated usingLeslie Matrix under some simulated fluctuating environments where the length of time during which the environments change is short compared with the time required to stabilize age structure. These simulation studies show that there is an optimal ratio of the length of period for development to that for reproduction in achieving high population densities and this ratio varies depending on the favorableness of environment for reproductive success: as the environmental favorableness decreases, the optimal ratio becomes larger.     

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.     

Predicting availability to consumers of spatially and temporally variable resources

Ecological dynamics in many aquatic communities are strongly influenced by spatial and temporal variability of key limiting resources, and the extent to which consumers can locate and exploit concentrations of those resources. Intuitively, resource concentrations that are `close' and `long-lived' should typically be more available to consumers than `distant' and `ephemeral' resource concentrations. The speed and accuracy with which consumers can locate concentrations of their resources is in part determined by their movement characteristics and sensory constraints, which vary with taxon, life-history stage, physiological state, environmental conditions, and other factors. This has motivated detailed observation and modelling of individual-level foraging behaviors in a wide variety of taxa. However, our abilities to develop this intuitive concept of availability into empirically-based, quantitative predictions for consumer–resource interactions remain limited, largely due to the complexities of formulating and simulating spatially explicit models of consumer–resource interactions, and the difficulty of understanding how specific simulation results relate to broader ecological situations. This paper presents a non-dimensional index, the Frost number, that provides a simple prediction of availability to consumers of spatially and temporally varying resource concentrations. This index incorporates characteristics of both resource distributions and consumer movement behaviors. When Frost numbers characterizing consumer–resource interactions are much less than unity, resource concentrations are typically unavailable to consumers because travel time to reach them exceeds the longevity of the resource. Conversely, when Frost numbers are much greater than unity, resource longevity exceeds travel time so that resource concentrations are available. The Frost number may provide a preliminary identification of the length and time scales at which resources are available to consumers in complex ecological systems, even when detailed spatial observations and simulations are not available.     

Elasticities in variable environments: properties and implications

Elasticities in stochastic matrix models are used to understand both population and evolutionary dynamics. We examine three such elasticities: stochastic elasticity E(ij)(S) with respect to the (i, j) matrix element, the elasticity E(ij)(S mu) with respect to the mean mu(ij) of the matrix element, and the elasticity E(ij)(S sigma) with respect to the variability sigma(ij) of the matrix element. We show that the stochastic elasticity E(S) does not accurately describe the effect of variability; one should use E(S sigma) and E(S mu). We establish two general properties of these elasticities: a sum rule that connects them and a limit on the sum of the E(S sigma). We discuss the implications of these properties for the analysis of buffering and selection on the average rates versus the variability of rates.     

Coevolution drives temporal changes in fitness and diversity across environments in a bacteria-bacteriophage interaction.

Coevolutionary interactions are thought to play a crucial role in diversification of hosts and parasitoids. Furthermore, resource availability has been shown to be a fundamental driver of species diversity. Yet, we still do not have a clear understanding of how resource availability mediates the diversity generated by coevolution between hosts and parasitoids over time. We used experiments with bacteria and bacteriophage to test how resources affect variation in the competitive ability of resistant hosts and temporal patterns of diversity in the host and parasitoid as a result of antagonistic coevolution. Bacteria and bacteriophage coevolved for over 150 bacterial generations under high and low-resource conditions. We measured relative competitive ability of the resistant hosts and phenotypic diversity of hosts and parasitoids after the initial invasion of resistant mutants and again at the end of the experiment. Variation in relative competitive ability of the hosts was both time- and environment-dependent. The diversity of resistant hosts, and the abundance of host-range mutants attacking these phenotypes, differed among environments and changed over time, but the direction of these changes differed between the host and parasitoid. Our results demonstrate that patterns of fitness and diversity resulting from coevolutionary interactions can be highly dynamic.     

Diversification in temporally heterogeneous environments: effect of the grain in experimental bacterial populations

Although theory established the necessary conditions for diversification in temporally heterogeneous environments, empirical evidence remains controversial. One possible explanation is the difficulty of designing experiments including the relevant range of temporal grains and the appropriate environmental trade-offs. Here, we experimentally explore the impact of the grain on the diversification of the bacterium Pseudomonas fluorescens SBW25 in a temporally fluctuating environment by including 20 different pairs of environments and four temporal grains. In general, higher levels of diversity were observed at intermediate temporal grains. This resulted in part from the enhanced capacity of disruptive selection to generate negative genotypic correlations in performance at intermediate grains. However, the evolution of reciprocal specialization was an uncommon outcome. Although the temporal heterogeneity is in theory less powerful than the spatial heterogeneity to generate and maintain the diversity, our results show that diversification under temporal heterogeneity is possible provided appropriate environmental grains.     

Epibacterial community patterns on marine macroalgae are host-specific but temporally variable

Marine macroalgae are constantly exposed to epibacterial colonizers. The epiphytic bacterial patterns and their temporal and spatial variability on host algae are poorly understood. To investigate the interaction between marine macroalgae and epiphytic bacteria, this study tested if the composition of epibacterial communities on different macroalgae was specific and persisted under varying biotic and abiotic environmental conditions over a 2-year observation time frame. Epibacterial communities on the co-occurring macroalgae Fucus vesiculosus, Gracilaria vermiculophylla and Ulva intestinalis were repeatedly sampled in summer and winter of 2007 and 2008. The epibacterial community composition was analysed by denaturing gradient gel electrophoresis (DGGE) and 16S rRNA gene libraries. Epibacterial community profiles did not only differ significantly at each sampling interval among algal species, but also showed consistent seasonal differences on each algal species at a bacterial phylum level. These compositional patterns re-occurred at the same season of two consecutive years. Within replicates of the same algal species, the composition of bacterial phyla was subject to shifts at the bacterial species level, both within the same season but at different years and between different seasons. However, 7-16% of sequences were identified as species specific to the host alga. These findings demonstrate that marine macroalgae harbour species-specific and temporally adapted epiphytic bacterial biofilms on their surfaces. Since several algal host-specific bacteria were highly similar to other bacteria known to either avoid subsequent colonization by eukaryotic larvae or to exhibit potent antibacterial activities, algal host-specific bacterial associations are expected to play an important role for marine macroalgae.