Predator-prey dynamics in P systems ruled by metabolic algorithm

P systems are used to compute predator-prey dynamics expressed in the traditional formulation by Lotka and Volterra. By governing the action of the transition rules in such systems using the regulatory features of the metabolic algorithm we come up with simulations of the Lotka-Volterra equations, whose robustness is comparable to that obtained using Runge-Kutta schemes and Gillespie's Stochastic Simulation Algorithm. Besides their reliability, the results obtained using the metabolic algorithm on top of P systems have a clear biochemical interpretation concerning the role, of reactants or promoters, of the species involved.     

Specific non-monotonous interactions increase persistence of ecological networks

The relationship between stability and biodiversity has long been debated in ecology due to opposing empirical observations and theoretical predictions. Species interaction strength is often assumed to be monotonically related to population density, but the effects on stability of ecological networks of non-monotonous interactions that change signs have not been investigated previously. We demonstrate that for four kinds of non-monotonous interactions, shifting signs to negative or neutral interactions at high population density increases persistence (a measure of stability) of ecological networks, while for the other two kinds of non-monotonous interactions shifting signs to positive interactions at high population density decreases persistence of networks. Our results reveal a novel mechanism of network stabilization caused by specific non-monotonous interaction types through either increasing stable equilibrium points or reducing unstable equilibrium points (or both). These specific non-monotonous interactions may be important in maintaining stable and complex ecological networks, as well as other networks such as genes, neurons, the internet and human societies.     

Evolutionary dynamics of predator-prey systems: an ecological perspective

 Evolution takes place in an ecological setting that typically involves interactions with other organisms. To describe such evolution, a structure is needed which incorporates the simultaneous evolution of interacting species. Here a formal framework for this purpose is suggested, extending from the microscopic interactions between individuals – the immediate cause of natural selection, through the mesoscopic population dynamics responsible for driving the replacement of one mutant phenotype by another, to the macroscopic process of phenotypic evolution arising from many such substitutions. The process of coevolution that results from this is illustrated in the context of predator–prey systems. With no more than qualitative information about the evolutionary dynamics, some basic properties of predator–prey coevolution become evident. More detailed understanding requires specification of an evolutionary dynamic; two models for this purpose are outlined, one from our own research on a stochastic process of mutation and selection and the other from quantitative genetics. Much of the interest in coevolution has been to characterize the properties of fixed points at which there is no further phenotypic evolution. Stability analysis of the fixed points of evolutionary dynamical systems is reviewed and leads to conclusions about the asymptotic states of evolution rather different from those of game-theoretic methods. These differences become especially important when evolution involves more than one species. Received 10 November 1993; received in revised form 25 July 1994     

The effects of connectivity on metapopulation persistence: network symmetry and degree correlations

A spatial metapopulation is a mosaic of interconnected patch populations. The complex routes of colonization between the patches are governed by the metapopulation''s dispersal network. Over the past two decades, there has been considerable interest in uncovering the effects of dispersal network topology and its symmetry on metapopulation persistence. While most studies find that the level of symmetry in dispersal pattern enhances persistence, some have reached the conclusion that symmetry has at most a minor effect. In this work, we present a new perspective on the debate. We study properties of the in- and out-degree distribution of patches in the metapopulation which define the number of dispersal routes into and out of a particular patch, respectively. By analysing the spectral radius of the dispersal matrices, we confirm that a higher level of symmetry has only a marginal impact on persistence. We continue to analyse different properties of the in–out degree distribution, namely the ‘in–out degree correlation’ (IODC) and degree heterogeneity, and find their relationship to metapopulation persistence. Our analysis shows that, in contrast to symmetry, the in–out degree distribution and particularly, the IODC are dominant factors controlling persistence.     

Test systems to determine the ecological risks posed by toxin release from Bacillus thuringiensis genes in crop plants

Procedures for the selection of species for ecotoxicological risk assessment of Bacillus thuringiensis (Bt) gene products in the epigeal and hypogeal environments are proposed. Although species can be selected on the basis of ecological realism and functional importance, the number of organisms requiring testing and the nature of the test procedures remain uncertain with such a selectively toxic material. The heterogeneity of the soil environment, the stratification of plant material at different stages of breakdown and decomposition and the aggregation and patterns of movement of the soil fauna and flora impose problems for the design of ecologically relevant test methods. Similarly, the impact upon beneficial invertebrates, if toxic effects are detected, will be mediated by the scale and pattern of transgenic plant release in the fragmented agricultural landscape. To properly assess the ecological risks posed by a widely released toxin with a narrow spectrum of effects, a combination of laboratory tests, field experiments and longer-term monitoring will be required.     

Paradoxical persistence through mixed-system dynamics: towards a unified perspective of reversal behaviours in evolutionary ecology

Counterintuitive dynamics of various biological phenomena occur when composite system dynamics differ qualitatively from that of their component systems. Such composite systems typically arise when modelling situations with time-varying biotic or abiotic conditions, and examples range from metapopulation dynamics to population genetic models. These biological, and related physical, phenomena can often be modelled as simple financial games, wherein capital is gained and lost through gambling. Such games have been developed and used as heuristic devices to elucidate the processes at work in generating seemingly paradoxical outcomes across a spectrum of disciplines, albeit in a field-specific, ad hoc fashion. Here, we propose that studying these simple games can provide a much deeper understanding of the fundamental principles governing paradoxical behaviours in models from a diversity of topics in evolution and ecology in which fluctuating environmental effects, whether deterministic or stochastic, are an essential aspect of the phenomenon of interest. Of particular note, we find that, for a broad class of models, the ecological concept of equilibrium reactivity provides an intuitive necessary condition that must be satisfied in order for environmental variability to promote population persistence. We contend that further investigations along these lines promise to unify aspects of the study of a range of topics, bringing questions from genetics, species persistence and coexistence and the evolution of bet-hedging strategies, under a common theoretical purview.     

Optimal patch use and metapopulation dynamics

Summary We compared the metapopulation dynamics of predator—prey systems with (1) adaptive global dispersal, (2) adaptive local dispersal, (3) fixed global dispersal and (4) fixed local dispersal by predators. Adaptive dispersal was modelled using the marginal value theorem, such that predators departed patches when the instantaneous rate of prey capture was less than the long-term rate of prey capture averaged over all patches, scaled to the movement time between patches. Adaptive dispersal tended to stabilize metapopulation dynamics in a similar manner to conventional fixed dispersal models, but the temporal dynamics of adaptive dispersal models were more unpredictable than the smooth oscillations of fixed dispersal models. Moreover, fixed and adaptive dispersal models responded differently to spatial variation in patch productivity and the degree of compartmentalization of the system. For both adaptive dispersal and fixed dispersal models, localized (stepping-stone) dispersal was more strongly stabilizing than global (island) dispersal. Variation among predators in the probability of dispersal in relation to local prey density had a strong stabilizing influence on both within-patch and metapopulation dynamics. These results suggest that adaptive space use strategies by predators could have important implications for the dynamics of spatially heterogeneous trophic systems.     

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.     

Discrete three-stage population model: persistence and global stability results

A general three-stage discrete-time population model is studied. The inherent net reproductive number for this model is derived. Global stability of the origin is established provided that the inherent net reproductive number is less than one. If it is larger than one the existence of a unique positive fixed point is proved and the persistence of the system is established. Finally, for certain parameter ranges global stability of the positive fixed point is proved.     

Density dependence and the control of helminth parasites

1. The transient dynamics and stability of a population are determined by the interplay between species density, its spatial distribution and the positive and negative density-dependent processes regulating population growth. 2. Using the human-helminth parasite system as an example, we propose that the life-stage upon which negative density dependence operates will influence the rate of host reinfection following anthelmintic chemotherapy, and the likely success of control programmes. 3. Simple deterministic models are developed which highlight how a parasite species whose population size is down-regulated by density-dependent establishment will reinfect a host population at a faster rate than a species with density-dependent parasite fecundity. 4. Different forms of density dependence can produce the same equilibrium behaviour but different transient dynamics. Under-representing the nature and magnitude of density-dependent mechanisms, and in particular those operating upon establishing life-stages, may cause the resilience of the parasite population to a control perturbation to be underestimated.     

Population persistence time under intermittent control in stochastic environments

If there exists a critical population size above which environmental degradation becomes serious, the population should be suppressed or reduced upon reaching that level. Since population size control is accompanied by costs, a reduction in control frequency may be preferable from an economic viewpoint. Although this can be realized by decreasing the population size drastically in each control, such management may result in increased population extinction probability according to environmental stochasticity. The effects of population management on both mean population persistence time and management cost were analyzed theoretically using a diffusion process. The model showed the functional forms of both mean persistence time and control frequency explicitly; these decreased with an increasing number of individuals removed from the population in each control operation. Based on the analysis, indices representing management costs are proposed. Mean persistence time is generally an increasing function of the cost indices. Nevertheless, if the cost of each control increases with the number of individuals removed, even the most conservative management practice (continuous control) may not be overly expensive.     

Testing metapopulation dynamics using genetic, demographic and ecological data

The metapopulation concept is a cornerstone in the recent history of ecology and evolution. However, determining whether a natural system fits a metapopulation model is a complex issue. Extinction-colonization dynamics are indeed often difficult to quantify because species detectability is not always 100%, resulting in an imperfect record of extinctions. Here, we explore whether combining population genetics with demographic and ecological surveys can yield more realistic estimates of metapopulation dynamics. We apply this approach to the freshwater snail Drepanotrema depressissimum in a fragmented landscape of tropical ponds. In addition to studying correlations between genetic diversity and demographical or ecological characteristics, we undertake, for the first time, a detailed search for genetic signatures of extinction-recolonization events using temporal changes in allele frequencies within sites. Surprisingly, genetic data indicate that extinction is much rarer than suggested by demographic surveys. Consequently, this system is better described as a set of populations with different sizes and immigration rates than as a true metapopulation. We identify several cases of apparent extinction owing to nondetection of low-density populations, and of aestivating individuals in desiccated ponds. More generally, we observed a frequent mismatch between genetic and demographical/ecological information at small spatial and temporal scales. We discuss the causes of these discrepancies and show how these two types of data provide complementary information on population dynamics and history, especially when temporal genetic samples are available.     

Restoration options for potential persistence of submersed aquatic vegetation: combining ecological, hydrodynamic and sediment transport modelling

1. Restoration of shallow turbid lakes to promote growth of submersed aquatic vegetation (SAV) requires knowledge of the environmental factors affecting SAV growth and persistence, and a means to predict the success of SAV reestablishment under different management scenarios to improve these environmental conditions. We used a dynamic ecological modelling approach relating SAV responses to changes in physical and chemical conditions, with information on water level, flow and transparency being provided by hydrodynamic and sediment transport models. 2. The potential persistence of Vallisneria americana was similar under simulated environmental conditions in 1946 and in 1954, as was the potential persistence of Potamogeton pectinatus, indicating that the disappearance of V. americana from Peoria Lake (U.S.A.) previously attributed to an extended spring flood in 1954, may have been related to the combined effects of changes in water level, flow and water transparency as well as possibly other factors. 3. Recent environmental conditions (for 2000) proved not to be conducive for the colonization and persistence potential of V. americana, but would allow colonization by P. pectinatus. The construction of a hypothetical levee along the eastern descending line of the navigation channel in Upper Peoria Lake, which was expected to reduce fetch‐ and navigation‐related turbidity, did not improve the situation for V. americana and overall deteriorated the situation for P. pectinatus. Thus, such a hydraulic alteration, generally considered as beneficial for SAV restoration, may not always be successful. 4. The results of the simulations indicated that the environmental conditions for potential persistence in Peoria Lake were generally less favourable for V. americana than for P. pectinatus. Measures suggested to restore SAV communities in such a lake should aim at reducing concentrations of total suspended solids at the point of inflow by a factor of three to four and limiting fetch‐ and navigation‐related resuspension.     

How populations persist when asexuality requires sex: the spatial dynamics of coping with sperm parasites

The twofold cost of sex implies that sexual and asexual reproduction do not coexist easily. Asexual forms tend to outcompete sexuals but may eventually suffer higher extinction rates, creating tension between short- and long-term advantages of different reproductive modes. The 'short-sightedness' of asexual reproduction takes a particularly intriguing form in gynogenetic species complexes, in which an asexual species requires sperm from a related sexual host species to trigger embryogenesis. Asexuals are then predicted to outcompete their host, after which neither species can persist. We examine whether spatial structure can explain continued coexistence of the species complex, and assess the evidence based on data on the Amazon molly (Poecilia formosa). A modification of the Levins metapopulation model creates two regions of good prospects for coexistence, connected by a region of poorer patch occupancy levels. In the first case, mate discrimination and/or niche differentiation keep local extinction rates low, and most patches contain both species; the other possibility resembles host-parasite dynamics where parasites frequently drive the host locally extinct. Several dynamical features are counterintuitive and relate to the parasitic nature of interactions in the species complex: for example, high local extinction rates of the asexual species can be beneficial for its own persistence. This creates a link from the evolution of sexual reproduction to that of prudent predation.