Models In Evolutionary Ecology Research Articles

Rate-induced collapse in evolutionary systems.

Recent work has highlighted the possibility of 'rate-induced tipping', in which a system undergoes an abrupt transition when a perturbation exceeds a critical rate of change. Here, we argue that this is widely applicable to evolutionary systems: collapse, or extinction, may occur when external changes occur too fast for evolutionary adaptation to keep up. To bridge existing theoretical frameworks, we develop a minimal evolutionary-ecological model showing that rate-induced extinction and the established notion of 'evolutionary rescue' are fundamentally two sides of the same coin: the failure of one implies the other, and vice versa. We compare the minimal model's behaviour with that of a more complex model in which the large-scale dynamics emerge from the interactions of many individual agents; in both cases, there is a well-defined threshold rate to induce extinction, and a consistent scaling law for that rate as a function of timescale. Due to the fundamental nature of the underlying mechanism, we suggest that a vast range of evolutionary systems should in principle be susceptible to rate-induced collapse. This would include ecosystems on all scales as well as human societies; further research is warranted.

Evolutionary Ecological Model of Defence Activation Disorders Via the Marginal Value Theorem.

ObjectiveExcessive activation of defence modules leads to some dysfunctional outcomes, which can be broadly classified to defence activation disorders. Defence activation disorders have high mortality, low fertility, high prevalence and high heritability. In this study, agent-based simulation model is formulated for solving this evolutionary paradox. MethodsThe emotional system is considered as a superordinate cognitive module for grasping the average resource amount and the average diminishing returns of resources, based on the Marginal Value Theorem. Under the assumption, the evolutionary ecological model was proposed and analysed. ResultsIndividuals utilising suboptimal strategies can be stably maintained in agent-based evolutionary simulation environments. Individuals were adapted to have different d-values according to the local niche. The simulation runs stably within the calibrated range of the variables for a long time. Agents establish locally optimal strategies based on their given d-values, and the relative proportion of subpopulation maintained stably in the heterogeneous habitat with the resource gradient. ConclusionThis study verifies the evolutionary mechanism of defence activation disorders in computer-simulated environments by using agent-based modelling with the Marginal Value Theorem. Balancing selection appears to be a plausible evolutionary mechanism that makes the suboptimal levels of defence activation the evolutionarily stable strategies.

Mathematical Models of Fertilization—An Eco-Evolutionary Perspective

AbstractMathematical models of fertilization have been developed for many taxa, for both external and internal fertilizers. They estimate the proportion or number of fertilized gametes based on gam...

The evolution of ecosystem ascendency in a complex systems based model

General patterns in ecosystem development can shed light on driving forces behind ecosystem formation and recovery and have been of long interest. In recent years, the need for integrative and process oriented approaches to capture ecosystem growth, development and organisation, as well as the scope of information theory as a descriptive tool has been addressed from various sides. However data collection of ecological network flows is difficult and tedious and comprehensive models are lacking. We use a hierarchical version of the Tangled Nature Model of evolutionary ecology to study the relationship between structure, flow and organisation in model ecosystems, their development over evolutionary time scales and their relation to ecosystem stability. Our findings support the validity of ecosystem ascendency as a meaningful measure of ecosystem organisation, which increases over evolutionary time scales and significantly drops during periods of disturbance. The results suggest a general trend towards both higher integrity and increased stability driven by functional and structural ecosystem coadaptation.

Tangent map intermittency as an approximate analysis of intermittency in a high dimensional fully stochastic dynamical system: The Tangled Nature model.

It is well known that low-dimensional nonlinear deterministic maps close to a tangent bifurcation exhibit intermittency and this circumstance has been exploited, e.g., by Procaccia and Schuster [Phys. Rev. A 28, 1210 (1983)], to develop a general theory of 1/f spectra. This suggests it is interesting to study the extent to which the behavior of a high-dimensional stochastic system can be described by such tangent maps. The Tangled Nature (TaNa) Model of evolutionary ecology is an ideal candidate for such a study, a significant model as it is capable of reproducing a broad range of the phenomenology of macroevolution and ecosystems. The TaNa model exhibits strong intermittency reminiscent of punctuated equilibrium and, like the fossil record of mass extinction, the intermittency in the model is found to be non-stationary, a feature typical of many complex systems. We derive a mean-field version for the evolution of the likelihood function controlling the reproduction of species and find a local map close to tangency. This mean-field map, by our own local approximation, is able to describe qualitatively only one episode of the intermittent dynamics of the full TaNa model. To complement this result, we construct a complete nonlinear dynamical system model consisting of successive tangent bifurcations that generates time evolution patterns resembling those of the full TaNa model in macroscopic scales. The switch from one tangent bifurcation to the next in the sequences produced in this model is stochastic in nature, based on criteria obtained from the local mean-field approximation, and capable of imitating the changing set of types of species and total population in the TaNa model. The model combines full deterministic dynamics with instantaneous parameter random jumps at stochastically drawn times. In spite of the limitations of our approach, which entails a drastic collapse of degrees of freedom, the description of a high-dimensional model system in terms of a low-dimensional one appears to be illuminating.

Linear stability theory as an early warning sign for transitions in high dimensional complex systems

We analyse in detail a new approach to the monitoring and forecasting of the onset of transitions in high dimensional complex systems by application to the Tangled Nature model of evolutionary ecology and high dimensional replicator systems with a stochastic element. A high dimensional stability matrix is derived in the mean field approximation to the stochastic dynamics. This allows us to determine the stability spectrum about the observed quasi-stable configurations. From overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean field approximation, we are able to construct a good early-warning indicator of the transitions occurring intermittently.

The Tangled Nature Model for organizational ecology

The Tangled Nature Model--a biologically inspired model of evolutionary ecology--is described, simulated, and analyzed to show its applicability in organization science and organizational ecology. It serves as a conceptual framework for understanding the dynamics in populations of organizations. A salient dynamical feature of this model is the spontaneous generation of a symbiotic group of core organizations. This core, consisting of several dominating species, introduces a mesoscopic level between that of the individual and the whole system. Despite prolonged periods of stability, this core is disrupted at random by parasitic interactions causing sudden core rearrangements. The size distribution of the core organizations is log-normal as predicted by theory and supported by empirical findings. As a simple application of the model, we study the adaptation of organizations to changes in resource availability in terms of population size, population diversity, and ecological efficiency. We find evidence that a temporary reduction in resources forces a consolidation resulting in a sustained increase in overall efficiency, suggesting that such reductions can be applied strategically to drive incremental improvements.

Forecasting systemic transitions in high dimensional stochastic complex systems

We briefly describe a new procedure to monitor and forecast transitions occurring in high dimensional complex systems. The method is illustrated by applications to two model systems: firstly to the Tangled Nature Model of evolutionary ecology and secondly to a stochastic replicator system. The quasi-stable configurations of the stochastic dynamics are taken as input for a stability analysis of the deterministic mean field approximation of the dynamics. We demonstrate that the largest overlap between the observed configuration and the unstable eigendirections serves as a precursor that allows us to forecast transitions with an efficiency of about 80% even if we only know the couplings matrix describing the dynamics to with 10% accuracy.

The Tangled Nature Model for Organizational Ecology

The Tangled Nature Model, a biologically inspired model of evolutionary ecology, is described, simulated and analyzed to show its applicability in organization science and organizational ecology, both as a conceptual framework and as a tool for qualitative prediction about real organizations. We find that a symbiotic group of core organizations is generated, with the core disrupted at random by parasitic interactions causing sudden core rearrangements. This core is a spontaneously generated mesoscopic level of structure between the individual and whole system level. As a simple application of the model, we study the adaptation of organizations to changes in resource availability in terms of population size, population diversity, and ecological efficiency. We find evidence that a temporary reduction in resources forces a consolidation resulting in a sustained increase in overall efficiency, suggesting that such reductions can be applied strategically to drive incremental improvements.

Forecasting transitions in systems with high-dimensional stochastic complex dynamics: a linear stability analysis of the tangled nature model.

We propose a new procedure to monitor and forecast the onset of transitions in high-dimensional complex systems. We describe our procedure by an application to the tangled nature model of evolutionary ecology. The quasistable configurations of the full stochastic dynamics are taken as input for a stability analysis by means of the deterministic mean-field equations. Numerical analysis of the high-dimensional stability matrix allows us to identify unstable directions associated with eigenvalues with a positive real part. The overlap of the instantaneous configuration vector of the full stochastic system with the eigenvectors of the unstable directions of the deterministic mean-field approximation is found to be a good early warning of the transitions occurring intermittently.

An evolutionary model of social change in the Middle Ohio Valley: Was social complexity impossible during the late woodland but mandatory during the late prehistoric?

We present an evolutionary model of social change in the Middle Ohio Valley during the Fort Ancient period (AD 1000–1650), primarily relying on an application of Winterhalder’s (1986) and Kelly’s (1995) evolutionary ecology model of cultural responses to environmental variability. We predict changes in social organization, political complexity, and patterns of stylistic similarity. As the environmental background for our model we employ recently published moisture data. By iteratively applying the synchronic Winterhalder–Kelly model we are able to predict a sequence of general trends that agree with much current interpretation of Fort Ancient development. Specifically, the model leads us to expect increasing village size, the development of regional traditions, and the development of leadership roles and a region-wide style Horizon around AD 1400. However, our model provides the ability to make testable predictions that deviate from the accepted cultural history and predicts that the Middle Ohio Valley and the groups referred to as Fort Ancient were far from homogenous.

A predator–prey refuge system: Evolutionary stability in ecological systems

A refuge model is developed for a single predator species and either one or two prey species where no predators are present in the prey refuge. An individual’s fitness depends on its strategy choice or ecotype (predators decide which prey species to pursue and prey decide what proportion of their time to spend in the refuge) as well as on the population sizes of all three species. It is shown that, when there is a single prey species with a refuge or two prey species with no refuge compete only indirectly (i.e. there is only apparent competition between prey species), that stable resident systems where all individuals in each species have the same ecotype cannot be destabilized by the introduction of mutant ecotypes that are initially selectively neutral. In game-theoretic terms, this means that stable monomorphic resident systems, with ecotypes given by a Nash equilibrium, are both ecologically and evolutionarily stable. However, we show that this is no longer the case when the two indirectly-competing prey species have a refuge. This illustrates theoretically that two ecological factors, that are separately stabilizing (apparent competition and refuge use), may have a combined destabilizing effect from the evolutionary perspective. These results generalize the concept of an evolutionarily stable strategy (ESS) to models in evolutionary ecology. Several biological examples of predator–prey systems are discussed from this perspective.

Plant invasion phenomenon enhances reproduction performance in an endangered spider

Current models in evolutionary ecology predict life history alterations in response to habitat suitability to optimize fitness. Only few empirical studies have demonstrated how life history traits that are expected to trade off against each other differ among environments. In Europe, many salt marshes have been recently invaded by the grass Elymus athericus. Previous studies however showed higher densities of the endangered spider Arctosa fulvolineata (Araneae: Lycosidae) in invaded salt marshes compared to natural habitats, which suggests a lower habitat suitability in the latter. The aim of this study was to determine if this emerging habitat (1) affects the amount of resource acquisition and (2) alters the balance between life history traits that are expected to trade off against each other in this stenotopic salt marsh species. As suggested by theoretical studies, an optimization of fitness by increasing egg size at the cost of decreasing fecundity in unsuitable (i.e., natural) habitats was expected. Females presenting cocoon were then collected in close invaded and natural salt marsh areas within the Mont Saint-Michel Bay (France). By considering female mass as covariate, cocoon mass, number of eggs, and egg volume were compared between both habitats. Clutch mass was strongly determined by female mass in both habitats. Clutch mass was however significantly smaller in the natural habitat compared to the invaded habitat, indicating a higher resource acquisition in the latter. When correcting for female size, fecundity was additionally increased in the invaded habitat through a significant decrease in egg size. This phenotypic response can be explained by differences in habitat structure between invaded and natural habitats: the former offers a more complex litter favoring nocturnal wanderers like A. fulvolineata. The existence of such an adaptive reproduction strategy depending on habitat suitability constitutes an original case of an invasion that favors an endangered species.

Environmental correlates of life history pattern in ground-beetles on Tenerife (Canary Islands)

The spatial and temporal structure of Carabus ( Nesaeocarabus) interruptus Dejean, 1831 populations and the independent effects of climate along altitudinal gradients in the island of Tenerife, especially whether environmental preferences constrains the species breeding patterns at local and regional scales were evaluated. Ground-beetles were sampled with twenty-one pitfall traps in each of the forty-one plots during one year study. Some sampled specimens were dissected and dried to determine sex, weight and ovarian maturation. The populations were restricted to the middle climatic zone (600–1700 m). There was a long adult activity period from October to June and the changes in the weekly capture success were strongly correlated with the rainfall and temperature. Overall the males during winter were more active than the females. The emergence of new adults occurred only in spring and the body dry weight peaked in April–May. From start of autumn the weight was recovered to the initial values of the cycle, increased and peaked in January. The females prolonged its oviposition period from mid-autumn to the starting of spring. The species showed a winter breeding pattern and the seasonal variations in multiple life history traits could correspond with the changing conditions of the microclimatic variables. An evolutionary ecological model could help explain the life history pattern variability among the Carabus species in South-western Europe. The species could tackle the geographic dispersion of their populations for the single purpose of seeking a suitable hydrothermal environment (high rainfall and mild temperatures) if the food was insured.

Dangerous nutrients: Evolution of phytoplankton resource uptake subject to virus attack

Phytoplankton need multiple resources to grow and reproduce (such as nitrogen, phosphorus, and iron), but the receptors through which they acquire resources are, in many cases, the same channels through which viruses attack. Therefore, phytoplankton can face a bottom-up vs. top-down tradeoff in receptor allocation: Optimize resource uptake or minimize virus attack? We investigate this top-down vs. bottom-up tradeoff using an evolutionary ecology model of multiple essential resources, specialist viruses that attack through the resource receptors, and a phytoplankton population that can evolve to alter the fraction of receptors used for each resource/virus type. Without viruses present the singular continuously stable strategy is to allocate receptors such that resources are co-limiting, which also minimizes the equilibrium concentrations of both resources. Only one virus type can be present at equilibrium (because phytoplankton, in this model, are a single resource for viruses), and when a virus type is present, it controls the equilibrium phytoplankton population size. Despite this top-down control on equilibrium densities, bottom-up control determines the evolutionary outcome. Regardless of which virus type is present, the allocation strategy that yields co-limitation between the two resources is continuously stable. This is true even when the virus type attacking through the limiting resource channel is present, even though selection for co-limitation in this case decreases the equilibrium phytoplankton population and does not decrease the equilibrium concentration of the limiting resource. Therefore, although moving toward co-limitation and decreasing the equilibrium concentration of the limiting resource often co-occur in models, it is co-limitation, and not necessarily the lowest equilibrium concentration of the limiting resource, that is the result of selection. This result adds to the growing body of literature suggesting that co-limitation at equilibrium is a winning strategy.

Correlation, selection and the evolution of species networks

We use a generalised version of the individual-based Tangled Nature model of evolutionary ecology to study the relationship between ecosystem structure and evolutionary history. Our evolved model ecosystems typically exhibit interaction networks with exponential degree distributions and an inverse dependence between connectance and species richness. We use a simplified network evolution model to demonstrate that the observed degree distributions can occur as a consequence of partial correlations in the inheritance process. Further to this, in the limit of low connectance and maximal correlation, distributions of power-law form, P ( k ) ∝ 1 / k , can be achieved. We also show that a hyperbolic relationship between connectance and species richness, C ∼ 1 / D can arise as a consequence of probabilistic constraints on the evolutionary search process.

The Tangled Nature model with inheritance and constraint: Evolutionary ecology restricted by a conserved resource

We study a version of the Tangled Nature model of evolutionary ecology redefined in a phenotype space where mutants have properties correlated to their parents. The model has individual-based dynamics whilst incorporating species scale competitive constraints and a system scale resource constraint. Multiple species arise that coexist in a species interaction network with evolving global properties. Both the mean interaction strength and the network connectance increase relative to the null system as mutualism becomes more extensive. From a study of the dependence of average degree on the resource level we extract the diversity-connectance relationship which conforms to the hyperbolic form seen in field data. This is adjudged to arise as a consequence of the evolutionary pressure to achieve positive interactions. The network degree distributions conform more strongly to exponential than to the null binomial distributions in all cases. This effect is believed to be caused by correlations in the reproductive process. We also study how resource availability influences the phenotypical lifetime distribution which is approximately of power law form. We observe that the mean lifetime is inversely related to the resource level.

Coevolutionary arms races between bacteria and bacteriophage

We propose a computational and theoretical framework for analyzing rapid coevolutionary dynamics of bacteriophage and bacteria in their ecological context. Bacteriophage enter host cells via membrane-bound surface receptors often responsible for nutrient uptake. As such, a selective pressure will exist for the bacteria to modify its receptor configuration and, in turn, for the phage to modify its tail fiber. A mathematical model of these trait adaptations is developed by using the framework of adaptive dynamics. Host strains differ in their efficiency of resource uptake and resistance to phage, whereas phage strains differ in their host preference for adsorption. We solve the evolutionary ecology model and find the conditions for coevolutionary branching and relevant dimensionless parameters leading to distinct quasispecies. We confirm these calculations using stochastic Monte Carlo simulations of populations evolving in a chemostat with fixed washout rate and inflow resource density. We find that multiple quasispecies of bacteria and phage can coexist in a homogeneous medium with a single resource. When diversification occurs, quasispecies of phage adsorb effectively to only a limited subset of the total number of quasispecies of bacteria, i.e., functional differences between quasispecies arise endogenously within the evolutionary ecology framework. Finally, we discuss means to relate predictions of this model to experimental studies in the chemostat, using the model organisms Escherichia coli and the virulent strain of lambda phage.

EVOLUTION OF SPATIALLY INHOMOGENEOUS ECOSYSTEMS: AN UNIFIED MODEL BASED APPROACH

Recently, we have extended our "unified" model of evolutionary ecology to incorporate the spatial inhomogeneities of the ecosystem and the migration of individual organisms from one patch to another within the same ecosystem. In this paper, an extension of our recent model is investigated so as to describe the migration and speciation in a more realistic way.

Network properties, species abundance and evolution in a model of evolutionary ecology

We study the evolution of the network properties of a populated network embedded in a genotype space characterized by either a low or a high number of potential links, with particular emphasis on the connectivity and clustering. Evolution produces two distinct types of network. When a specific genotype is only able to influence a few other genotypes, the ecosystem consists of separate non-interacting clusters (i.e. isolated compartments) in genotype space. When different types may influence a large number of other sites, the network becomes one large interconnected cluster. The distribution of interaction strengths—but not the number of connections—changes significantly with time. We find that the species abundance is only realistic for a high level of species connectivity. This suggests that real ecosystems form one interconnected whole in which selection leads to stronger interactions between the different types. Analogies with niche and neutral theory and assembly models are also considered.