Variation strategies of plants in heterogeneous environments

Plant structures exhibit five principal classes of variation in heterogeneous environments, namely uniformity, continuous lability, genetic specialization (polymorphism), environmentally- or statuscued alternatives (conditional choices) and multiple strategies—the simultaneous operation by one plant of distinct types of structures that perform the same function. Multiple strategies are a diverse but neglected class that includes simultaneous cosexuality (hermaphroditism and other monomorphic sex conditions), facultative cleistogamy, heteromorphic diaspores, and reproduction by both seeds and ramets. An analysis of seven functions in the angiosperm flora of New Zealand shows that uniform and labile strategies considered jointly are most common, and multiple strategies are more common than either polymorphisms or conditional choices. Phenotypic models of the natural selection of structural variation are presented. They predict the general conditions under which multiple, conditional and uniform strategies are selected when the environment is spatially heterogeneous for either parents or their offspring. The models can explain many features of variation strategies, including why multiple strategies are a plant speciality, why conditional strategies such as sex choosing are rare and random choices are even more rare (unknown?), and why some self-fertilizing plants have distinct cleistogamous flowers. The models also suggest further avenues of research.     

Evolutionarily stable strategies of migration in heterogeneous environments

By means of a simulation model we are showing that the rates of migration can be related to avoidance of competition between relatives, especially in clonal organisms. This could result in a strong selective pressure for migration, even at a high cost. In addition, if the habitat is fragmented, migration can strongly affect local dynamics and result in a dramatic decrease of the densities in some places. In parthenogenetically reproducing organisms like aphids, the level of relatedness in local populations is expected to be very high and therefore they can serve as a good model group for testing these hypotheses. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling optimal treatment strategies in a heterogeneous mixing model

Background

Many mathematical models assume random or homogeneous mixing for various infectious diseases. Homogeneous mixing can be generalized to mathematical models with multi-patches or age structure by incorporating contact matrices to capture the dynamics of the heterogeneously mixing populations. Contact or mixing patterns are difficult to measure in many infectious diseases including influenza. Mixing patterns are considered to be one of the critical factors for infectious disease modeling.

Methods

A two-group influenza model is considered to evaluate the impact of heterogeneous mixing on the influenza transmission dynamics. Heterogeneous mixing between two groups with two different activity levels includes proportionate mixing, preferred mixing and like-with-like mixing. Furthermore, the optimal control problem is formulated in this two-group influenza model to identify the group-specific optimal treatment strategies at a minimal cost. We investigate group-specific optimal treatment strategies under various mixing scenarios.

Results

The characteristics of the two-group influenza dynamics have been investigated in terms of the basic reproduction number and the final epidemic size under various mixing scenarios. As the mixing patterns become proportionate mixing, the basic reproduction number becomes smaller; however, the final epidemic size becomes larger. This is due to the fact that the number of infected people increases only slightly in the higher activity level group, while the number of infected people increases more significantly in the lower activity level group. Our results indicate that more intensive treatment of both groups at the early stage is the most effective treatment regardless of the mixing scenario. However, proportionate mixing requires more treated cases for all combinations of different group activity levels and group population sizes.

Conclusions

Mixing patterns can play a critical role in the effectiveness of optimal treatments. As the mixing becomes more like-with-like mixing, treating the higher activity group in the population is almost as effective as treating the entire populations since it reduces the number of disease cases effectively but only requires similar treatments. The gain becomes more pronounced as the basic reproduction number increases. This can be a critical issue which must be considered for future pandemic influenza interventions, especially when there are limited resources available.

     

Cultural niche construction of repertoire size and learning strategies in songbirds

Birdsong is a complex cultural and biological system, and the selective forces driving evolutionary changes in aspects of song learning vary considerably among species. The extent to which repertoire size, the number of syllables or song types sung by a bird, is subject to sexual selection is unknown, and studies to date have provided inconsistent evidence. Here, we propose that selection pressure on the size and complexity of birdsong repertoires may facilitate the construction of a niche in which learning, sexual selection, and song-based homophily may co-evolve. We show, using a review of the birdsong literature and mathematical modeling, that learning mode (open-ended or closed-ended learning) is correlated with the size of birdsong repertoires. Underpinning this correlation may be a form of cultural niche construction in which a costly biological trait (for example, open-ended learning) can spread in a population (or be lost) as a result of direct selection on an associated cultural trait (for example, song repertoire size).     

Flexible cognitive strategies during motor learning

Visuomotor rotation tasks have proven to be a powerful tool to study adaptation of the motor system. While adaptation in such tasks is seemingly automatic and incremental, participants may gain knowledge of the perturbation and invoke a compensatory strategy. When provided with an explicit strategy to counteract a rotation, participants are initially very accurate, even without on-line feedback. Surprisingly, with further testing, the angle of their reaching movements drifts in the direction of the strategy, producing an increase in endpoint errors. This drift is attributed to the gradual adaptation of an internal model that operates independently from the strategy, even at the cost of task accuracy. Here we identify constraints that influence this process, allowing us to explore models of the interaction between strategic and implicit changes during visuomotor adaptation. When the adaptation phase was extended, participants eventually modified their strategy to offset the rise in endpoint errors. Moreover, when we removed visual markers that provided external landmarks to support a strategy, the degree of drift was sharply attenuated. These effects are accounted for by a setpoint state-space model in which a strategy is flexibly adjusted to offset performance errors arising from the implicit adaptation of an internal model. More generally, these results suggest that strategic processes may operate in many studies of visuomotor adaptation, with participants arriving at a synergy between a strategic plan and the effects of sensorimotor adaptation.     

Effects of algal diversity on the production of biomass in homogeneous and heterogeneous nutrient environments: a microcosm experiment

Background

One of the most common questions addressed by ecologists over the past decade has been-how does species richness impact the production of community biomass? Recent summaries of experiments have shown that species richness tends to enhance the production of biomass across a wide range of trophic groups and ecosystems; however, the biomass of diverse polycultures only rarely exceeds that of the single most productive species in a community (a phenomenon called ‘transgressive overyielding’). Some have hypothesized that the lack of transgressive overyielding is because experiments have generally been performed in overly-simplified, homogeneous environments where species have little opportunity to express the niche differences that lead to ‘complementary’ use of resources that can enhance biomass production. We tested this hypothesis in a laboratory experiment where we manipulated the richness of freshwater algae in homogeneous and heterogeneous nutrient environments.

Methodology/Principal Findings

Experimental units were comprised of patches containing either homogeneous nutrient ratios (16∶1 nitrogen to phosphorus (N∶P) in all patches) or heterogeneous nutrient ratios (ranging from 4∶1 to 64∶1 N∶P across patches). After allowing 6–10 generations of algal growth, we found that algal species richness had similar impacts on biomass production in both homo- and heterogeneous environments. Although four of the five algal species showed a strong response to nutrient heterogeneity, a single species dominated algal communities in both types of environments. As a result, a ‘selection effect’–where diversity maximizes the chance that a competitively superior species will be included in, and dominate the biomass of a community–was the primary mechanism by which richness influenced biomass in both homo- and heterogeneous environments.

Conclusions/Significance

Our study suggests that spatial heterogeneity, by itself, is not sufficient to generate strong effects of biodiversity on productivity. Rather, heterogeneity must be coupled with variation in the relative fitness of species across patches in order for spatial niche differentiation to generate complementary resource use.     

Towards a cognitive niche: divergent foraging strategies resulting from limited cognitive ability of foraging herbivores in a spatially complex environment.

A model was developed to explain one mechanism whereby differential optimal foraging strategies can occur between species as a result of selection for competition avoidance. This is the primary requirement for niche differentiation to evolve without a difference in the underlying foraging ability or morphology. The model used an individual-based patch choice mechanism, whereby herbivores move from patch to patch seeking food with the highest nutrient intake characteristics. The choice of patch was governed by a parameter, mu, which determined to what extent information in the landscape at different distances from the herbivore was used by it to make foraging decisions. A genetic algorithm was used to optimise the value, mu, in a complex landscape. The value of mu quickly converged to a single value with stabilising selection occurring when there was only a single species foraging. When there was a competing species with a fixed value of mu, the value of mu evolved to be above or below the mean for the single species mean depending on whether the value of mu for the competitor was below, or above the single-species mean, respectively. This was indicative of niche segregation. However mu tended to vary unstably over time when allowed to vary simultaneously in both species, although there was evidence for interaction between the two values. These results indicate that there can be a competitive advantage in choosing a cognitive strategy that is complementary to that used by other species.     

Evolution in heterogeneous environments: between soft and hard selection

Since their first formulations about half a century ago, the soft and hard selection models have become classical frameworks to study selection in subdivided populations. These models differ in the timing of density regulation and represent two extreme types of selection: density- and frequency-dependent selection (soft) and density- and frequency-independent selection (hard). Yet only few attempts have been made so far to model intermediate scenarios. Here, we design a model where migration may happen twice during the life cycle: before density regulation with probability d(J) (juvenile migration) and after density regulation with probability d(A) (adult migration). In the first step, we analyze the conditions for the coexistence of two specialists. We find that coexistence is possible under a large range of selection types, even when environmental heterogeneity is low. Then, we investigate the different possible outcomes obtained through gradual evolution. We show that polymorphism is more likely to evolve when the trade-off is weak, environmental heterogeneity is high, migration is low, and in particular when juvenile migration is low relative to adult migration, because the timing of migration affects the magnitude of frequency-dependent selection relative to gene flow. This model may provide a more general theoretical framework to experimentally study evolution in heterogeneous environments.     

Functional redundancy in heterogeneous environments: implications for conservation

It has been argued that one of the best ways to conserve biological diversity is to maintain the integrity of functional processes within communities, and this can be accomplished by assessing how much ecological redundancy exists in communities. Evidence suggests, however, that the functional roles species play are subject to the influences of local environmental conditions. Species may appear to perform the same function (i.e. be redundant) under a restricted set of conditions, yet their functional roles may vary in naturally heterogeneous environments. Incorporating the environmental context into ecological experiments would provide a critical perspective for examining functional redundancy among species.     

Prey-predator models in spatially heterogeneous environments

The effects of environmental heterogeneity on models of prey-predator systems are investigated. Refuge behaviour is found in a continuous gradually varying environment. In this situation we do not necessarily get oscillating population cycles. The stabilizing effect observed depends on environmental variation and is not produced by diffusion alone. Our conclusions are fairly independent of the details of the model.     

Stochastic population growth in spatially heterogeneous environments: the density-dependent case

Journal of Mathematical Biology - This work is devoted to studying the dynamics of a structured population that is subject to the combined effects of environmental stochasticity, competition for...     

Swarming in homogeneous environments: A social interaction based framework

A great variety of biological groups form a self-organized swarming motion at some point during their life spans, which has two prominent collective features: common velocity and constant spacings among members. In this paper, we present a general individual-based motion framework to explain such collective motion of swarms in homogeneous environments. The motion framework utilizes the concept of social interactions that has been widely accepted throughout the literature. We assume that during the motion of the swarm, each member senses and interacts with its neighbors via virtual Attraction/Alignment/Repulsion (A/A/R) forces, while perceiving and following the gradient force of the environment. During the swarm's motion, the neighborhood and the interaction relations among members may dynamically change. To explicitly consider the effect of such dynamic change on the emergence of swarm's collective behavior, we use an algebraic graph to model the topology of the interaction and the neighborhood relations among the members.By using mathematical tools of nonsmooth analysis theory and Lyapunov stability theory, we analytically prove that if the A/A/R forces have limited ranges, and the attraction/repulsion forces are balanced at a certain range, the proposed framework leads to a parallel type of collective motion of the swarm. We mathematically show that the velocities of all swarm members asymptotically converge to a common value and the spacings among neighbors remain unchanging. In addition to the mathematical analysis, a few sets of simulation results are included to demonstrate the presented framework.The contributions of this paper are twofold: First, unlike most works in the literature that mainly use computer simulations to study the swarming phenomena, this paper provides an analytical methodology to investigate how the collective group behavior is self-organized by individual motions. Second, the presented motion framework works over a general range of A/A/R interactions. In other words, we analytically prove that the commonly used A/A/R model can lead to a collective motion of the swarm. In addition, we show that the alternative model in the literature that uses only attraction/repulsion (A/R) interactions is in fact a special case of the A/A/R model.     

Linked selected and neutral loci in heterogeneous environments

We analyze a system of ordinary differential equations modeling haplotype frequencies at a physically linked pair of loci, one selected and one neutral, in a population consisting of two demes with divergent selection regimes. The system is singularly perturbed, with the migration rate m between the demes serving as a small parameter. We use geometric singular perturbation theory to show that when m is sufficiently small, each solution not initially fixed for the same selected allele in both demes approaches one of a 1-dimensional continuum of equilibria. We then obtain asymptotic expansions of the solutions and show their validity on arbitrarily long finite time intervals. From these expansions we obtain formulas for the transient dynamics of F _ST (a measure of population structure) at both loci, as well as for the rate of genotyping error if the allelic state at the selected locus is inferred from that at the neutral (marker) locus. We examine two cases in detail, one modeling two populations in secondary contact after a period of evolution in allopatry, and the other modeling the origination and spread of a resistance allele.Electronic supplementary material Supplementary material is available in the online version of this article at http://dx.doi.org/10.1007/s00285-006-0038-6 and is accessible for authorized users.     

Syntrophic growth on formate: a new microbial niche in anoxic environments

Anaerobic syntrophic associations of fermentative bacteria and methanogenic archaea operate at the thermodynamic limits of life. The interspecies transfer of electrons from formate or hydrogen as a substrate for the methanogens is key. Contrary requirements of syntrophs and methanogens for growth-sustaining product and substrate concentrations keep the formate and hydrogen concentrations low and within a narrow range. Since formate is a direct substrate for methanogens, a niche for microorganisms that grow by the conversion of formate to hydrogen plus bicarbonate--or vice versa--may seem unlikely. Here we report experimental evidence for growth on formate by syntrophic communities of (i) Moorella sp. strain AMP in coculture with a thermophilic hydrogen-consuming Methanothermobacter species and of (ii) Desulfovibrio sp. strain G11 in coculture with a mesophilic hydrogen consumer, Methanobrevibacter arboriphilus AZ. In pure culture, neither Moorella sp. strain AMP, nor Desulfovibrio sp. strain G11, nor the methanogens grow on formate alone. These results imply the existence of a previously unrecognized microbial niche in anoxic environments.     

Evolution of a single niche specialist in variable environments

The pattern (space versus time) and scale (relative to the lifetime of individuals) of environmental variation is thought to play a central role in governing the evolution of the ecological niche and the maintenance of genetic variance in fitness. To evaluate this idea, we serially propagated an initially genetically uniform population of the bacterium Pseudomonas fluorescens for a few hundred generations in environments that differed in both the pattern and scale at which two highly contrasted carbon substrates were experienced. We found that, contrary to expectations, populations often evolved into a single niche specialist adapted to the less-productive substrate in variable environments and that the genetic variance in fitness across different components of the environment was not generally higher in variable environments when compared with constant environments. We provide evidence to suggest that our results reflect a novel constraint on niche evolution imposed by the supply of beneficial mutations available to selection in variable environments.     

Clonal plants as cooperative systems: Benefits in heterogeneous environments

All natural environments are spatially and temporally heterogeneous. Consequently, their ability to provide essential resources for the growth of plants is variable. Modular plant species produce repeated basic structures which, in the case of clonal species, are called ramets. Ramets belonging to the same clone are distributed throughout the environment in space and time, and therefore they may be located in sites which differ in resource-providing quality. The connections between ramets may allow resources to be shared, enabling the clone to behave as a cooperative system. As a result of such physiological integration, ramets can survive in conditions where there is lethal shortage of a resource because they are connected to, and supported by, ramets located in conditions where there is ample supply of the same resource. Physiological integration between connected ramets presents opportunities for heterogeneous environments to be exploited to an extent that is only just becoming apparent. As heterogeneity is ubiquitous in natural environments, it may be expected that plants, as relatively immobile organisms, will have evolved the capacity to cope with it by making appropriate localized morphological and/or physiological plastic responses. Recent studies suggest that such responses not only enable clonal species to cope with environmental heterogeneity, but that under some circumstances they can benefit more from environments which are heterogeneous rather than homogeneous, even when both types of environment contain the same amount of resources. Studies on Glechoma hederacea (Lamiaceae) that illustrate this phenomenon are described.     

Understanding foraging behaviour in spatially heterogeneous environments

The role of stochasticity and spatial heterogeneity in foraging systems is investigated. We formulate a spatially explicit model which describes the behaviour of grazing animals in response to local information using simple stochastic rules. In particular the model reflects the biology in that decisions to move to a new location are based on visual assessment of the sward height in a surrounding neighbourhood, whilst the decision to graze the current location is based on the residual sward height and olfactory assessment of local faecal contamination. It is assumed that animals do not interact directly, but do so through modification of, and response to a common environment. Spatial heterogeneity is shown to have significant effects including reducing the equilibrium intake rate and increasing the optimal stocking density, and must therefore be taken into account by resource managers. We demonstrate the relationship between the stochastic spatial model and its non-spatial deterministic counterpart, and in the process derive a moment-closure approximation to the full process, which can be regarded as an intermediate, or pseudo-spatial model. The role of spatial heterogeneity is emphasized, and better understood by comparing the results obtained from each approach. The relative efficiency of random and directed searching behaviour in spatially heterogeneous environments is explored for both clean and contaminated pastures, and the impact of faecal avoidance behaviour assessed.