Movement between patches, unequal competitors and the ideal free distribution

Researchers have often commented on the ability of the original ideal free distribution (IFD) model to approximate observed animal distributions even though the critical assumption that competitors are of equal ability is usually violated. We provide an explanation by recognizing that animals will occasionally move between patches for reasons other than to simply maximize their resource payoffs, given perfect (i.e. ideal) information about the current payoff in each patch, and that these movements will continue to occur even after an equilibrium is reached. When such movements are incorporated into an unequal competitors IFD model, a single, stable distribution of each competitor type is predicted. This equilibrium will usually be characterized by under-matching of total competitive units relative to the distribution of resources (i.e. too few competitive units in the good patch). More importantly, it will often resemble the original, equal competitors IFD, in that total competitor numbers will come close to matching the distribution of resources. We argue that researchers claiming to have observed an IFD of equal competitors have actually observed this equilibrium distribution of unequal competitors. Our model predicts that the deviation from input-matching will usually be an under-matching of total competitor numbers relative to resources (i.e. too few competitors in the good patch). Examination of published data reveals that post-equilibrium movement between patches occurs frequently and, although the reported distributions are similar to those predicted by input-matching, under-matching is usually observed.     

The ideal free distribution of clonal plant's ramets among patches in a heterogeneous environment

The plastic response of clonal plant to different patch quality is not always the same and the degree is different too. So the result of this kind of foraging behaviour is different. In order to make clear whether the ramtes stay in favourable patches and get the quantitative relationship between the ramets distribution among patches and the available resource amount in heterogeneous environment, we develop a theoretical work under ideal free distribution (IFD) theory framework by neglecting some morphological plasticity of the spacer in this article. The results of our general model show that the ramet distribution should obey input matching rule at equilibrium. That means the ratio of ramet number in different patches should be equal to the ratio of available resource amount in these patches. We also use the simulation to predict the distribution pattern under history mattering. The results show that the initial ramets number has significant influence on the final distribution: over matching and under matching both can occur. More initial ramets in favourable patch result in over matching and more initial ramets in unfavourable patch result in under matching. The degree of the deviation from input matching rule is great when the difference of patches is small. These results prove that ideal free distribution theory works the same with animals. The ramets can stay in favourable patches sometimes in spite of the plasticity of the spacer, and the distribution depends on both patch quality and the history factors. But these results are true only when the functional response is type II.     

A two-stage model for the SIR outbreak: accounting for the discrete and stochastic nature of the epidemic at the initial contamination stage

The evolution of an infectious disease outbreak in an isolated population is split into two stages: a stochastic Markov process describing the initial contamination and a linked deterministic dynamical system with random initial conditions for the continued development of the outbreak. The initial contamination stage is well approximated by the randomized SI (susceptible/infected) model. We obtain the probability density function for the early behavior of the epidemic. This provides an appropriate distribution for the initial conditions with which to describe the subsequent deterministic evolution of the system. We apply the method of matching asymptotic expansions to link the two stages. This allows us to estimate the standard deviation of the number of infectives in the developed outbreak, and the statistical characteristics of the outbreak time. The potential trajectories caused by the stochastic nature of the contamination stage show greatest divergence at the initial and fade-out stages and coincide most tightly just after the peak of the epidemic. The time to the peak of the outbreak is not strongly dependent on the initial trajectory.     

On the importance of body size in the colonisation of ephemeral resource patches by vagile consumers

A study on the colonisation of leaf detritus patches by vagile macroinvertebrates in a brackish lagoon is presented in the framework of a conceptual model where a body size-related constraint on patch use behaviour is explicitly considered. Abundance patterns of dominant macroinvertebrate taxa were characterised by short-term, non-random fluctuations, showing significant site-dependent variations. Yet, a site-independent covariation was observed between patterns’ fractal dimension and the average body mass of each taxon, indicating that, while the temporal scales characterising the colonisation patterns may be highly species-specific, cross-species generalisations are possible based on body size. The generality of these results was supported by literature data on temporal patterns of carcass colonisation by bathyal fish. The importance of size-related mechanisms in regulating the aggregation of vagile consumers on resource patches and, ultimately, their coexistence at both an inter- and intra-specific level, is discussed.     

Effect of aggregation on the reproductive rate of populations

The effect of spatial distribution on the reproductive rate of a population was examined by applying an approximate equation to several data based on the entomological literature. This study suggests that aggregation generally reduces the equilibrium level of the population density if the population density is not very high.     

How spatial resource distribution and memory impact foraging success: A hybrid model and mechanistic index

Understanding how animals forage has always been a fundamental issue in Ethology and has become critical more recently in Environmental Conservation. Since the formalization of optimal foraging theory, theoretical models intended to depict the behavior of a generic forager have served as the main tools to analyze and ultimately comprehend the mechanisms of foraging. Due to complexity and technical constraints, these models have traditionally focused on single aspects of foraging, leaving out other concurrent processes that may also interplay. The recent inclusion of several facets inside united models has given rise to interesting results on the importance of interacting factors such as memory and resource heterogeneity.In this paper, we present a hybrid model integrating metabolism, foraging decisions, memory, as well as spatially explicit movement and resource distribution. We use it to examine the effects of spatial resource distribution – an aspect often neglected in favor of probabilistic resource heterogeneity – on the viability of a generic random-walking forager, and rely on the model to devise an ecological metric that can explain and render the relative profitability of given spatial distributions. Furthermore, we assess the significance of memory properties relatively to the profitability of resource distributions. Most notably, we reveal contrasted effects of memory depending on the aspect of resource varied in space (i.e. prey abundance, or prey body mass).On the whole, a general comparison of our findings with results obtained with spatially implicit models leads us to stress the complex interaction between memory and spatial resource distribution as well as the criticality of spatial representation in the modeling of foraging. Accordingly, we conclude with a discussion on the ecological implications of these results, as well as the advantages of hybrid modeling for the accurate simulation of foraging.     

Wright-Fisher model of social insects with haploid males and diploid females

An inhomogeneous discrete Markov model is formulated for sexual random mating in finite populations of haploid male and diploid female individuals. This is a Wright-Fisher type of model for social insects. The generations are non-overlapping and of given finite sizes. Bottlenecks are included, allowing different sizes to change from generation to generation. Mutations and selection are included in this exact model for the stochastic process. Computations of the exact Markov model are presented, focussing on the sexually asymmetric genetic drift caused by haplodiploidy.     

The relative importance of herbivory and carnivory on the distribution of energy in a stochastic tri-trophic food web

A three-state, discrete-time Markov chain is used to model the dynamics of energy flow in a tri-trophic food web. The distribution of energy in the three trophic levels is related to the rates of flow between the trophic levels and calculated for the entire range of possible flow values. These distributions are then analysed for stability and used to test the idea that plants are resource-limited and herbivores are predation-limited. Low rates of death and decomposition, when coupled with low rates of herbivory and carnivory, tend to destabilize this food web. Food webs with higher rates of death and decomposition are relatively more stable regardless of rates of herbivory and carnivory. Plants are more prone to resource-limitation and herbivores are, in general, limited by their predators, which supports Hairston et al. (Am. Nat. 94 (1960) 421). The rate of decomposition often mediates the roles of top-down and bottom-up control of energy flow in the food web.     

A stochastic model for a single click of Muller's ratchet

This work presents a new approach to Muller's ratchet, where Haigh's model is approximately mapped into a simpler model that describes the behaviour of a population after a click of the ratchet, i.e., after loss of what was the fittest class. This new model predicts the distribution of times to the next click of the ratchet and is equivalent to a Wright-Fisher model for a population of haploid asexual individuals with one locus and two alleles. Within this model, the fittest members of a population correspond to carriers of one allele, while all other individuals have suboptimal fitness and are represented as carriers of the other allele. In this way, all suboptimal fitness individuals are amalgamated into a single “mutant” class.The approach presented here has some limitations and the potential for improvement. However, it does lead to results for the rate of the ratchet that, over a wide range of parameters, are accurate within one order of magnitude of simulation results. This contrasts with existing approaches, which are designed for only one or other of the two different parameter regimes known for the ratchet and are more accurate only in the parameter regime they were designed for.Numerical results are presented for the mean time between clicks of the ratchet for (i) the Wright-Fisher model, (ii) a diffusion approximation of this model and (iii) individually based simulations of a full model. The diffusion approximation is validated over a wide range of parameters by its close agreement with the Wright-Fisher model.The present work predicts that: (a) the time between clicks of the ratchet is insensitive to the value of the selection coefficient when the genomic mutation rate is large compared with the selection coefficient against a deleterious mutation, (b) the time interval between clicks of the ratchet has, approximately, an exponential distribution (or its discrete analogue). It is thus possible to determine the variance in times between clicks, given the expected time between clicks. Evidence for both (a) and (b) is seen in simulations.     

A stochastic model for the economic management of a renewable animal resource

An optimal economic harvesting policy, which maximizes the present value of an animal population, capable of renewing itself, is discussed. It is assumed that, unhindered, the successive population levels, X_n, form a Markov chain, with transitions

$\text{X}{}_{\mathrm{n+1}}\text{=?(X}{}_{\mathrm{n}}\text{) + ?}{}_{\mathrm{n}}\text{?(X}{}_{\mathrm{n}}\text{)}$

, where f is the recruitment function, and {?_n} is an iid sequence of random shocks. When a positive set-up cost is present an optimal policy is of the (S,s) type. The optimal population level is compared with that of an equivalent deterministic model. Bioeconomic conditions, which imply the optimality of conservation, or extinction are investigated.     

Particle size,resource concentration,and the distribution of net-spinning caddisflies

Summary The dimensions of net meshes constructed by hydropsychid Trichoptera vary both within and between species. Despite these catchnet differences, the diets of most Hydropsychidae studied in Utah streams were statistically indistinguishable. There was no relationship between the size of available resources and catchnet construction among species assemblages inhabiting 10 different localities. A particle-size model of caddis communities, suggesting that taxa feed selectively on particle sizes corresponding to the dimension of catchnet meshes, is not supported by these data.Diatom concentration increased regularly with downstream passage in two different drainages. The identity and number of coexisting hydropsychid species and the size of their catchnets were strongly correlated with diatom concentration. Taxa with large catchnet mesh were the only residents at sites where diatom concentration was very low; as resource concentration increased downstream, species with successively smaller mesh joined the coexisting guild. Together, the broad dietary similarities and distributional pattern from Utah streams suggest that resource concentration, rather than particle size, is the basis of community organization among the hydropsychid Trichoptera.     

Measuring the functionality of the mitochondrial pumping complexes with multi-wavelength spectroscopy

The proton pumps of the mitochondrial electron transport chain (ETC) convert redox energy into the proton motive force (ΔP), which is subsequently used by the ATP synthase to regenerate ATP. The limited available redox free energy requires the proton pumps to operate close to equilibrium in order to maintain a high ΔP, which in turn is needed to maintain a high phosphorylation potential. Current biochemical assays measure complex activities far from equilibrium and so shed little light on their function under physiological conditions. Here we combine absorption spectroscopy of the ETC hemes, NADH fluorescence spectroscopy and oxygen consumption to simultaneously measure the redox potential of the intermediate redox pools, the components of ΔP and the electron flux in RAW 264.7 mouse macrophages. We confirm that complex I and III operate near equilibrium and quantify the linear relationship between flux and disequilibrium as a metric of their function under physiological conditions. In addition, we quantify the dependence of complex IV turnover on ΔP and the redox potential of cytochrome c to determine the complex IV driving force and find that the turnover is proportional to this driving force. This form of quantification is a more relevant metric of ETC function than standard biochemical assays and can be used to study the effect of mutations in either mitochondrial or nuclear genome affecting mitochondrial function, post-translation changes, different subunit isoforms, as well as the effect of pharmaceuticals on ETC function.     

A comparison of three different stochastic population models with regard to persistence time

Results are summarized from the literature on three commonly used stochastic population models with regard to persistence time. In addition, several new results are introduced to clearly illustrate similarities between the models. Specifically, the relations between the mean persistence time and higher-order moments for discrete-time Markov chain models, continuous-time Markov chain models, and stochastic differential equation models are compared for populations experiencing demographic variability. Similarities between the models are demonstrated analytically, and computational results are provided to show that estimated persistence times for the three stochastic models are generally in good agreement when the models are consistently formulated. As an example, the three stochastic models are applied to a population satisfying logistic growth. Logistic growth is interesting as different birth and death rates can yield the same logistic differential equation. However, the persistence behavior of the population is strongly dependent on the explicit forms for the birth and death rates. Computational results demonstrate how dramatically the mean persistence time can vary for different populations that experience the same logistic growth.     

Effects of stochastic channel gating and distribution on the cardiac action potential

Ion channels exhibit stochastic conformational changes determining their gating behavior. In addition, the process of protein turnover leads to a natural variability of the number of membrane and gap junctional channels. Nevertheless, in computational models, these two aspects are scarcely considered and their impacts are largely unknown. We investigated the effects of stochastic current fluctuations and channel distributions on action potential duration (APD), intercellular conduction delays (ICDs) and conduction blocks using a modified ventricular cell model (Rudy et al.) with Markovian formulations of the principal ion currents (to simulate their stochastic open-close gating behavior) and with channel counts drawn from Poisson distributions (to simulate their natural variability). In single cells, APD variability (coefficient of variation: 1.6% at BCL=1000 ms) was essentially caused by stochastic channel gating of I_Ks, persistent I_Na and I_Ca,L. In cell strands, ICD variability induced by stochastic channel gating and Poissonian channel distributions was low under normal conditions. Nonetheless, at low intercellular coupling levels, Poissonian gap junctional channel distribution resulted in a large ICD variability (coefficient of variation >20%), highly heterogeneous conduction patterns and conduction blocks. Therefore, the stochastic behavior of current fluctuations and channel distributions can contribute to the heterogeneity of conduction patterns and to conduction block, as observed previously in experiments in cardiac tissue with altered intercellular coupling.     

Coevolution between crossbills and black pine: the importance of competitors,forest area and resource stability

Studies of predator‐prey interactions have found that geographically structured coevolution has played an important role in the adaptive diversification of crossbills (Loxia spp.). We extend those studies by considering common crossbills (L. curvirostra) in the Mediterranean where they rely on seeds in the cones of black pine (Pinus nigra). On the continent, where tree squirrels (Sciurus vulgaris) are present, enhanced defenses against crossbills were most evident in larger areas of pine forest. On islands in the absence of tree squirrels, crossbills and black pine have coevolved in a predator‐prey arms race on Cyprus but not Corsica. In contrast to other conifers that island endemic crossbills rely upon, black pine does not hold seeds in its cones year round. Consequently, key to the strong crossbill–pine interaction on Cyprus is likely the presence of an alternative conifer that provides seeds during early summer when black pine seeds are scarce.     

Species assembly in model ecosystems, II: Results of the assembly process

In the companion paper of this set (Capitán and Cuesta, 2010) we have developed a full analytical treatment of the model of species assembly introduced in Capitán et al. (2009). This model is based on the construction of an assembly graph containing all viable configurations of the community, and the definition of a Markov chain whose transitions are the transformations of communities by new species invasions. In the present paper we provide an exhaustive numerical analysis of the model, describing the average time to the recurrent state, the statistics of avalanches, and the dependence of the results on the amount of available resource. Our results are based on the fact that the Markov chain provides an asymptotic probability distribution for the recurrent states, which can be used to obtain averages of observables as well as the time variation of these magnitudes during succession, in an exact manner. Since the absorption times into the recurrent set are found to be comparable to the size of the system, the end state is quickly reached (in units of the invasion time). Thus, the final ecosystem can be regarded as a fluctuating complex system where species are continually replaced by newcomers without ever leaving the set of recurrent patterns. The assembly graph is dominated by pathways in which most invasions are accepted, triggering small extinction avalanches. Through the assembly process, communities become less resilient (e.g., have a higher return time to equilibrium) but become more robust in terms of resistance against new invasions.     

A probabilistic model of cell size reduction in Pseudo-nitzschia delicatissima (Bacillariophyta)

The pennate planktonic diatom Pseudo-nitzschia delicatissima is very common in temperate marine waters and often responsible for blooms. Due to its surrounding rigid silicate frustrule the diatom undergoes successive size reduction as its vegetative reproduction cycle proceeds. Since a long time the life cycle of diatoms has raised scientific interest and some years ago extensive samples of Pseudo-nitzschia have been taken from coastal waters. Mating and cell size reduction experiments were carried out and served us as a data basis for a probabilistic model of cell size reduction.We applied a homogenous non-stationary continuous-time Markov chain to model the development of individual diatoms from an initial size of about until cell death which occurred when the size reached its low at about . In contrast to conventional curve fitting models we are capable of calculating confidence intervals for estimates of the population ages as well as integrate the process of auxospore formation into the model. We thus propose a unique way to describe the stationary size distribution in a diatom population in terms of cell division and auxospore formation probabilities of its individuals.