Asymptotic states and topological structure of an activation-deactivation chemical network

The influence of the topology on the asymptotic states of a network of interacting chemical species has been studied by simulating its time evolution. Random and scale-free networks have been designed to support relevant features of activation-deactivation reactions networks (mapping signal transduction networks) and the system of ordinary differential equations associated to the dynamics has been numerically solved. We analysed stationary states of the dynamics as a function of the network's connectivity and of the distribution of the chemical species on the network; we found important differences between the two topologies in the regime of low connectivity. In particular, only for low connected scale-free networks it is possible to find zero activity patterns as stationary states of the dynamics which work as signal off-states. Asymptotic features of random and scale-free networks become similar as the connectivity increases.     

The influence of predator--prey population dynamics on the long-term evolution of food web structure

We develop a set of equations to describe the population dynamics of many interacting species in food webs. Predator-prey interactions are nonlinear, and are based on ratio-dependent functional responses. The equations account for competition for resources between members of the same species, and between members of different species. Predators divide their total hunting/foraging effort between the available prey species according to an evolutionarily stable strategy (ESS). The ESS foraging behaviour does not correspond to the predictions of optimal foraging theory. We use the population dynamics equations in simulations of the Webworld model of evolving ecosystems. New species are added to an existing food web due to speciation events, whilst species become extinct due to coevolution and competition. We study the dynamics of species-diversity in Webworld on a macro-evolutionary time-scale. Coevolutionary interactions are strong enough to cause continuous overturn of species, in contrast to our previous Webworld simulations with simpler population dynamics. Although there are significant fluctuations in species diversity because of speciation and extinction, very large-scale extinction avalanches appear to be absent from the dynamics, and we find no evidence for self-organized criticality.     

The risk of extinction—the mutational meltdown or the overpopulation

The phase diagrams survival-extinction for the Penna model with parameters: (mutations rate)-(birth rate), (mutation rate)-(harmful mutations threshold), (harmful mutation threshold)-(minimal reproduction age) are presented. The extinction phase may be caused by either mutational meltdown or overpopulation. When the Verhulst factor is responsible for removing only newly born babies and does not act on adults the overpopulation is avoided and only genetic factors may lead to species extinction.     

Small population effects in stochastic population dynamics

The discreteness of units of small populations can produce large fluctuations from a classical continuous representation, especially when null populations play a crucial role. These belong to what are here referred to as emergent and evanescent species. A few model biological systems are introduced in which this is the case, as well as a toy model that suggests a path to avoid the associated mathematical complexities. The corresponding division into null and non-null population sectors is carried out to leading order for the model systems, with promising results. Supported in part by DOE Office of Basic Science, Chemical Division. Reported at SMB03, the August 2003 meeting of the Society for Mathematical Biology.     

Numerical investigation of spatial pattern in a vegetation model with feedback function

The vegetative cover in semi-arid lands typically occurs as patches of individual species more or less separated from one another by bare ground. Klausmeier [1999. Regular and irregular patterns in semiarid vegetation. Science 284 (5421), 1826-1828] reported that the vegetation striped patterns can grow lying along the contours of gentle slopes. He has proposed a model of vegetation stripes based on competition for water. In this paper, our main aim is to study the positive feedback effects between the water and biomass on the vegetation spatial pattern formation within a nonsaturated soil, which arises from the suction of water by the roots and processes of water resource redistribution. According to the dispersion relation formula, we discuss the changes of the wavelength, wave speed, as well as the conditions of the spatial pattern formation. Our numerical results show that trees are more sensitive than grasses to the positive feedback function to format the spatial heterogenous pattern, and the stronger positive feedback increases the parameters region where vegetation bands occur, which indicates that the positive feedback raises the possibility of shift from green to desert states in semi-arid areas for the long term. Our numerical results also show that the positive feedback can increase the migration velocity of the vegetation stripes.     

Plankton population dynamics: food web interactions and abiotic constraints

1. In this introduction, I try to follow some developments in plankton ecology, how they have led to current research topics, and how the contributions in this issue of Freshwater Biology are related to these fields of research.
2. Due to several favourable features, such as small size, short generation time and a relatively homogeneous habitat, planktonic organisms remain ideal subjects for theoretical and experimental population ecology.
3. Important current research topics involve: (1) the control of plankton communities by external abiotic factors; (2) bottom-up (limitation by resources) and top-down (control by predators) effects in the food web; (3) the importance of dormant resting stages and benthic–pelagic coupling in plankton dynamics; (4) costs and benefits of the mixotrophic strategy, i.e. the ability to combine a phototrophic and a phagotrophic mode of nutrition.     

Triadic conceptual structure of the maximum entropy approach to evolution

Many problems in evolutionary theory are cast in dyadic terms, such as the polar oppositions of organism and environment. We argue that a triadic conceptual structure offers an alternative perspective under which the information generating role of evolution as a physical process can be analyzed, and propose a new diagrammatic approach. Peirce's natural philosophy was deeply influenced by his reception of both Darwin's theory and thermodynamics. Thus, we elaborate on a new synthesis which puts together his theory of signs and modern Maximum Entropy approaches to evolution in a process discourse. Following recent contributions to the naturalization of Peircean semiosis, pointing towards ‘physiosemiosis’ or ‘pansemiosis’, we show that triadic structures involve the conjunction of three different kinds of causality, efficient, formal and final. In this, we accommodate the state-centered thermodynamic framework to a process approach. We apply this on Ulanowicz's analysis of autocatalytic cycles as primordial patterns of life. This paves the way for a semiotic view of thermodynamics which is built on the idea that Peircean interpretants are systems of physical inference devices evolving under natural selection. In this view, the principles of Maximum Entropy, Maximum Power, and Maximum Entropy Production work together to drive the emergence of information carrying structures, which at the same time maximize information capacity as well as the gradients of energy flows, such that ultimately, contrary to Schrödinger's seminal contribution, the evolutionary process is seen to be a physical expression of the Second Law.     

Biological vs. physical mixing effects on benthic food web dynamics

Biological particle mixing (bioturbation) and solute transfer (bio-irrigation) contribute extensively to ecosystem functioning in sediments where physical mixing is low. Macrobenthos transports oxygen and organic matter deeper into the sediment, thereby likely providing favourable niches to lower trophic levels (i.e., smaller benthic animals such as meiofauna and bacteria) and thus stimulating mineralisation. Whether this biological transport facilitates fresh organic matter assimilation by the metazoan lower part of the food web through niche establishment (i.e., ecosystem engineering) or rather deprives them from food sources, is so far unclear. We investigated the effects of the ecosystem engineers Lanice conchilega (bio-irrigator) and Abra alba (bioturbator) compared to abiotic physical mixing events on survival and food uptake of nematodes after a simulated phytoplankton bloom. The (13)C labelled diatom Skeletonema costatum was added to 4 treatments: (1) microcosms containing the bioturbator, (2) microcosms containing the bio-irrigator, (3) control microcosms and (4) microcosms with abiotic manual surface mixing. Nematode survival and subsurface peaks in nematode density profiles were most pronounced in the bio-irrigator treatment. However, nematode specific uptake (Δδ(13)C) of the added diatoms was highest in the physical mixing treatment, where macrobenthos was absent and the diatom (13)C was homogenised. Overall, nematodes fed preferentially on bulk sedimentary organic material rather than the added diatoms. The total C budget (μg C m(-2)), which included TO(13)C remaining in the sediment, respiration, nematode and macrobenthic uptake, highlighted the limited assimilation by the metazoan benthos and the major role of bacterial respiration. In summary, bioturbation and especially bio-irrigation facilitated the lower trophic levels mainly over the long-term through niche establishment. Since the freshly added diatoms represented only a limited food source for nematodes, the macrobenthic effect was more pronounced in niche establishment than the negative structuring effects such as competition.     

The structure of a plant-pollinator food web

The pollination biology literature is dominated by examples of specialization between plants and their pollinators. However, a recent review shows that it is generalization that prevails in the field, with most plants having a number of pollinators and most pollinators visiting a number of plants. Consequently, the vast majority of plant–pollinator interactions are embedded in a complex web of plant–pollinator interactions. These plant-pollinator webs can be studied in the manner of conventional food webs and the aim of this paper is to illustrate how contemporary methods of web construction and analysis can be applied to plant-pollinator communities.     

Rich dynamics in a predator–prey model with both noise and periodic force

A spatial version of the predator–prey model with Holling III functional response, which includes some important factors such as external periodic forces, noise, and diffusion processes is investigated. For the model only with diffusion, it exhibits spiral waves in the two-dimensional space. However, combined with noise, it has the feature of chaotic patterns. Moreover, the oscillations become more obvious when the noise intensity is increased. Furthermore, the spatially extended system with external periodic forces and noise exhibits a resonant pattern and frequency-locking phenomena. These results may help us to understand the effects arising from the undeniable susceptibility to random fluctuations in the real ecosystems.     

The effects of mixotrophy on the stability and dynamics of a simple planktonic food web model

Recognition of the microbial loop as an important part of aquatic ecosystems disrupted the notion of simple linear food chains. However, current research suggests that even the microbial loop paradigm is a gross simplification of microbial interactions due to the presence of mixotrophs-organisms that both photosynthesize and graze. We present a simple food web model with four trophic species, three of them arranged in a food chain (nutrients-autotrophs-herbivores) and the fourth as a mixotroph with links to both the nutrients and the autotrophs. This model is used to study the general implications of inclusion of the mixotrophic link in microbial food webs and the specific predictions for a parameterization that describes open ocean mixed layer plankton dynamics. The analysis indicates that the system parameters reside in a region of the parameter space where the dynamics converge to a stable equilibrium rather than displaying periodic or chaotic solutions. However, convergence requires weeks to months, suggesting that the system would never reach equilibrium in the ocean due to alteration of the physical forcing regime. Most importantly, the mixotrophic grazing link seems to stabilize the system in this region of the parameter space, particularly when nutrient recycling feedback loops are included.     

Prey preference,intraguild predation and population dynamics of an arthropod food web on plants

The theory of intraguild predation (IGP) largely studies effects on equilibrium densities of predators and prey, while experiments mostly concern transient dynamics. We studied the effects of an intraguild (IG) predator, the bug Orius laevigatus, on the population dynamics of IG-prey, the predatory mite Phytoseiulus persimilis, and a shared prey, the phytophagous two-spotted spider mite Tetranychus urticae, as well as on the performance of cucumber plants in a greenhouse. The interaction of the predatory mite and the spider mite is highly unstable, and ends either by herbivores overexploiting the plant or predators exterminating the herbivores. We studied the effect of IGP on the transient dynamics of this system, and compared the dynamics with that predicted by a simple population-dynamical model with IGP added. Behavioural studies showed that the predatory bug and the predatory mite were both attracted to plants infested by spider mites and that the two predators did not avoid plants occupied by the other predator. Observations on foraging behaviour of the predatory bug showed that it attacks and kills large numbers of predatory mites and spider mites. The model predicts strong effects of predation and prey preference by the predatory bugs on the dynamics of predatory mites and spider mites. However, experiments in which the predatory bug was added to populations of predatory mites and spider mites had little or no effect on numbers of both mite species, and cucumber plant and fruit weight.     

Consequences of symbiosis for food web dynamics

Basic Lotka-Volterra type models in which mutualism (a type of symbiosis where the two populations benefit both) is taken into account, may give unbounded solutions. We exclude such behaviour using explicit mass balances and study the consequences of symbiosis for the long-term dynamic behaviour of a three species system, two prey and one predator species in the chemostat. We compose a theoretical food web where a predator feeds on two prey species that have a symbiotic relationships. In addition to a species-specific resource, the two prey populations consume the products of the partner population as well. In turn, a common predator forages on these prey populations. The temporal change in the biomass and the nutrient densities in the reactor is described by ordinary differential equations (ODE). Since products are recycled, the dynamics of these abiotic materials must be taken into account as well, and they are described by odes in a similar way as the abiotic nutrients. We use numerical bifurcation analysis to assess the long-term dynamic behaviour for varying degrees of symbiosis. Attractors can be equilibria, limit cycles and chaotic attractors depending on the control parameters of the chemostat reactor. These control parameters that can be experimentally manipulated are the nutrient density of the inflow medium and the dilution rate. Bifurcation diagrams for the three species web with a facultative symbiotic association between the two prey populations, are similar to that of a bi-trophic food chain; nutrient enrichment leads to oscillatory behaviour. Predation combined with obligatory symbiotic prey-interactions has a stabilizing effect, that is, there is stable coexistence in a larger part of the parameter space than for a bi-trophic food chain. However, combined with a large growth rate of the predator, the food web can persist only in a relatively small region of the parameter space. Then, two zero-pair bifurcation points are the organizing centers. In each of these points, in addition to a tangent, transcritical and Hopf bifurcation a global heteroclinic bifurcation is emanating. This heteroclinic cycle connects two saddle equilibria where the predator is absent. Under parameter variation the period of the stable limit cycle goes to infinity and the cycle tends to the heteroclinic cycle. At this global bifurcation point this cycle breaks and the boundary of the basin of attraction disappears abruptly because the separatrix disappears together with the cycle. As a result, it becomes possible that a stable two-nutrient–two-prey population system becomes unstable by invasion of a predator and eventually the predator goes extinct together with the two prey populations, that is, the complete food web is destroyed. This is a form of over-exploitation by the predator population of the two symbiotic prey populations. When obligatory symbiotic prey-interactions are modelled with Liebigs minimum law, where growth is limited by the most limiting resource, more complicated types of bifurcations are found. This results from the fact that the Jacobian matrix changes discontinuously with respect to a varying parameter when another resource becomes most limiting.Revised version: 21 July 2003     

The phylogenetic component of food web structure and intervality

Despite the exceptional complexity formed by species and their interactions in ecological networks, such as food webs, regularities in the network structures are repeatedly demonstrated. The interactions are determined by the characteristics of a species. The characteristics are in turn determined by the species’ phylogenetic relationships, but also by factors not related to evolutionary history. Here, we test whether species’ phylogenetic relationships provides a significant proxy for food web intervality. We thereafter quantify the degree to which different species traits remain valuable predictors of food web structure after the baseline effect of species’ relatedness has been removed. We find that the phylogenetic relationships provide a significant background from which to estimate food web intervality and thereby structure. However, we also find that there is an important, non-negligible part of some traits, e.g., body size, in food webs that is not accounted for by the phylogenetic relationships. Additionally, both these relationships differ depending if a predator or a prey perspective is adopted. Clearly, species’ evolutionary history as well as traits not determined by phylogenetic relationships shapes predator-prey interactions in food webs, and the underlying evolutionary processes take place on slightly different time scales depending on the direction of predator-prey adaptations.     

Simultaneous effects of food limitation and inducible resistance on herbivore population dynamics

Many herbivore populations fluctuate temporally, but the causes of those fluctuations remain unclear. Plant inducible resistance can theoretically cause herbivore population fluctuations, because herbivory may induce plant changes that reduce the survival or reproduction of later-feeding herbivores. Herbivory can also simply reduce the quantity of food available for later feeders and this, too, can cause population fluctuations. Inducible resistance and food limitation often occur simultaneously, yet whether they jointly facilitate or suppress herbivore fluctuations remains largely unexplored. We present models that suggest that food limitation and inducible resistance may have synergistic effects on herbivore population dynamics. The population-level response of the food plant to herbivory and the details of how inducible resistance affects herbivore performance both influence the resulting herbivore dynamics. Our results identify some biological properties of plant-herbivore systems that might determine whether or not cycles occur, and suggest that future empirical and theoretical population dynamics studies should account for the effects of both food limitation and inducible resistance.     

Rapid contemporary evolution and clonal food web dynamics

Character evolution that affects ecological community interactions often occurs contemporaneously with temporal changes in population size, potentially altering the very nature of those dynamics. Such eco-evolutionary processes may be most readily explored in systems with short generations and simple genetics. Asexual and cyclically parthenogenetic organisms such as microalgae, cladocerans and rotifers, which frequently dominate freshwater plankton communities, meet these requirements. Multiple clonal lines can coexist within each species over extended periods, until either fixation occurs or a sexual phase reshuffles the genetic material. When clones differ in traits affecting interspecific interactions, within-species clonal dynamics can have major effects on the population dynamics. We first consider a simple predator–prey system with two prey genotypes, parametrized with data from a well-studied experimental system, and explore how the extent of differences in defence against predation within the prey population determine dynamic stability versus instability of the system. We then explore how increased potential for evolution affects the community dynamics in a more general community model with multiple predator and multiple prey genotypes. These examples illustrate how microevolutionary ‘details’ that enhance or limit the potential for heritable phenotypic change can have significant effects on contemporaneous community-level dynamics and the persistence and coexistence of species.     

The role of mixotrophic protists in the population dynamics of the microbial food web in a small artificial pond

• 1 The seasonal variations of protist and rotifer populations were monitored over 1 year in a small artificial pond. Grazing rates on fluorescently labelled bacteria were also determined.
• 2 The data showed population dynamics similar to other small freshwater bodies; diatoms were numerous during the spring, chlorophytes dominated during the summer months, and mixotrophs, in particular Gymnodinium, dominated during the autumn and winter.
• 3 The mixotrophic dinoflagellates were responsible for a high chlorophyll concentration during the autumn and winter. Mixotrophs were important consumers of bacteria, particularly during the autumn when population densities of pure heterotrophs were low. Mixotrophs were an important component of the microbial food web in this pond.

     

The effects of energy input,immigration and habitat size on food web structure: a microcosm experiment

It has been hypothesised that larger habitats should support more complex food webs. We consider three mechanisms which could lead to this pattern. These are increased immigration rates, increased total productivity and spatial effects on the persistence of unstable interactions. Experiments designed to discriminate between these mechanisms were carried out in laboratory aquatic microcosm communities of protista and bacteria, by independently manipulating habitat size, total productivity and immigration rate. Larger habitats supported more complex food webs, with more species, more links per species and longer maximum and mean food chains, even in the absence of differences in total energy input. Increased immigration rate resulted in more complex food webs, but habitats with higher energy input per unit area supported less complex food webs. We conclude that spatial effects on the persistence of unstable interactions, and variation in immigration rates, are plausible mechanisms by which habitat size could affect food web structure. Variation in total productivity with habitat area seems a less likely explanation for variation in food web structure.     

Cascading extinctions and ecosystem functioning: contrasting effects of diversity depending on food web structure

The consequences of species loss on cascading extinctions in food webs have been the focus of several recent theoretical studies, with differing results. Changes in ecosystem properties consecutive to cascading extinctions have received far less attention even though such dramatic events might strongly alter ecosystem functioning. Here we use various food web models to investigate the effects of species loss and diversity on both secondary extinctions and their associated changes in ecosystem properties. Our analysis shows that diversity has contrasting effects depending on the presence of self-limiting terms at consumer levels and, to a lower extent, on connectance and interspecific competition. Ecosystems that lose a high proportion of species through cascading extinctions exhibit the most important changes in ecosystem properties. Linking studies on cascading extinctions in food webs with studies that investigate the effects of biodiversity on ecosystem functioning appears crucial for a better understanding of the consequences of species extinctions.     

Predicting the effects of temperature on food web connectance

Few models concern how environmental variables such as temperature affect community structure. Here, we develop a model of how temperature affects food web connectance, a powerful driver of population dynamics and community structure. We use the Arrhenius equation to add temperature dependence of foraging traits to an existing model of food web structure. The model predicts potentially large temperature effects on connectance. Temperature-sensitive food webs exhibit slopes of up to 0.01 units of connectance per 1°C change in temperature. This corresponds to changes in diet breadth of one resource item per 2°C (assuming a food web containing 50 species). Less sensitive food webs exhibit slopes down to 0.0005, which corresponds to about one resource item per 40°C. Relative sizes of the activation energies of attack rate and handling time determine whether warming increases or decreases connectance. Differences in temperature sensitivity are explained by differences between empirical food webs in the body size distributions of organisms. We conclude that models of temperature effects on community structure and dynamics urgently require considerable development, and also more and better empirical data to parameterize and test them.