Modelling metapopulations with stochastic membrane systems

Metapopulations, or multi-patch systems, are models describing the interactions and the behavior of populations living in fragmented habitats. Dispersal, persistence and extinction are some of the characteristics of interest in ecological studies of metapopulations. In this paper, we propose a novel method to analyze metapopulations, which is based on a discrete and stochastic modelling framework in the area of Membrane Computing. New structural features of membrane systems, necessary to appropriately describe a multi-patch system, are introduced, such as the reduction of the maximal parallel consumption of objects, the spatial arrangement of membranes and the stochastic creation of objects. The role of the additional features, their meaning for a metapopulation model and the emergence of relevant behaviors are then investigated by means of stochastic simulations. Conclusive remarks and ideas for future research are finally presented.     

Genetic variation of salt-stressed durum wheat (Triticum turgidum subsp. durum Desf.) genotypes under field conditions and gynogenetic capacity

Agriculture has new challenges against the climate change: the preservation of genetic resources and the rapid creation of new varieties better adapted to abiotic stress, specially salinity. In this context, the agronomic performance of 25 durum wheat (Triticum turgidum subsp. durum Desf.) genotypes (nineteen landraces and six improved varieties), cultivated in two semi-arid regions in the center area of Tunisia, were assessed. These sites (Echbika, 2.2?g?l^?1; Barrouta, 4.2?g?l^?1) differ by their degree of salinity of the water irrigation. The results showed that most of the agronomic traits (e.g. spike per meter square, thousand kernels weight and grain yield) were reduced by salinity. Durum wheat landraces, Mahmoudi and Hmira, and improved varieties, Maali and Om Rabia showed the widest adaptability to different quality of irrigation water. Genotypes including Jneh Kotifa and Arbi were estimated as stable genotypes under adverse conditions. Thereafter, salt-tolerant (Hmira and Jneh Khotifa) and the most cultivated high-yielding (Karim, Razzak and Khiar) genotypes were tested for their gynogenetic ability to obtain haploids and doubled haploid lines. Genotypes with good induction capacity had not necessarily a good capacity of regeneration of haploid plantlets. In our conditions, Hmira and Khiar exhibited the best gynogenetic ability (3.1% and 2.9% of haploid plantlets, respectively).     

Phenological match drives pollen‐mediated gene flow in a temporally dimorphic tree

• Variation in flowering phenology is common in natural populations, and is expected to be, together with inter‐mate distance, an important driver of effective pollen dispersal. In populations composed of plants with temporally separated sexual phases (i.e. dichogamous or heterodichogamous populations), pollen‐mediated gene flow is assumed to reflect phenological overlap between complementary sexual phases. In this study, we conducted paternity analyses to test this hypothesis in the temporally dimorphic tree Acer opalus.
• We performed spatially explicit analyses based on categorical and fractional paternity assignment, and included tree size, pair‐wise genetic relatedness and morph type as additional predictors. Because differences between morphs in flowering phenology may also influence pollination distances, we modelled separate pollen dispersal kernels for the two morphs.
• Extended phenological overlap between male and female phases (mainly associated with inter‐morph crosses) resulted in higher siring success after accounting for the effects of genetic relatedness, morph type and tree size, while reduced phenological overlap (mainly associated with intra‐morph crosses) resulted in longer pollination distances achieved. Siring success also increased in larger trees.
• Mating patterns could not be predicted by phenology alone. However, as heterogeneity in flowering phenology was the single morph‐specific predictor of siring success, it is expected to be key in maintaining the temporal dimorphism in A. opalus, by promoting not only a prevalent pattern of inter‐morph mating, but also long‐distance pollination resulting from intra‐morph mating events.

     

Biodiversity and species interactions: extending Lotka–Volterra community theory

A new analysis of the nearly century‐old Lotka–Volterra theory allows us to link species interactions to biodiversity patterns, including: species abundance distributions, estimates of total community size, patterns of community invasibility, and predicted responses to disturbance. Based on a few restrictive assumptions about species interactions, our calculations require only that the community is sufficiently large to allow a mean‐field approximation. We develop this analysis to show how an initial assemblage of species with varying interaction strengths is predicted to sort out into the final community based on the species’ predicted target densities. The sorting process yields predictions of covarying patterns of species abundance, community size, and species interaction strengths. These predictions can be tested using enrichment experiments, examination of latitudinal and productivity gradients, and features of community assembly.     

Permanence and global attractivity for Lotka–Volterra difference systems

 The permanence and global attractivity for two-species difference systems of Lotka–Volterra type are considered. It is proved that a cooperative system cannot be permanent. For a permanent competitive system, the explicit expression of the permanent set E is obtained and sufficient conditions are given to guarantee the global attractivity of the positive equilibrium of the system. Received: 21 May 1997 / Revised version: 25 November 1998     

Kinetics of diffusion-influenced multisite phosphorylation with enzyme reactivation

The simplest way to account for the influence of diffusion on the kinetics of multisite phosphorylation is to modify the rate constants in the conventional rate equations of chemical kinetics. We have previously shown that this is not enough and new transitions between the reactants must also be introduced. Here we extend our results by considering enzymes that are inactive after modifying the substrate and need time to become active again. This generalization leads to a surprising result. The introduction of enzyme reactivation results in a diffusion-modified kinetic scheme with a new transition that has a negative rate constant. The reason for this is that mapping non-Markovian rate equations onto Markovian ones with time-independent rate constants is not a good approximation at short times. We then developed a non-Markovian theory that involves memory kernels instead of rate constants. This theory is now valid at short times, but is more challenging to use. As an example, the diffusion-modified kinetic scheme with new connections was used to calculate kinetics of double phosphorylation and steady-state response in a phosphorylation-dephosphorylation cycle. We have reproduced the loss of bistability in the phosphorylation-dephosphorylation cycle when the enzyme reactivation time decreases, which was obtained by particle-based computer simulations.     

Equality of average and steady-state levels in some nonlinear models of biological oscillations

Nonlinear oscillatory systems, playing a major role in biology, do not exhibit harmonic oscillations. Therefore, one might assume that the average value of any of their oscillating variables is unequal to the steady-state value. For a number of mathematical models of calcium oscillations (e.g. the Somogyi–Stucki model and several models developed by Goldbeter and co-workers), the average value of the cytosolic calcium concentration (not, however, of the concentration in the intracellular store) does equal its value at the corresponding unstable steady state at the same parameter values. The average value for parameter values in the unstable region is even equal to the level at the stable steady state for other parameter values, which allow stability. This holds for all parameters except those involved in the net flux across the cell membrane. We compare these properties with a similar property of the Higgins–Selkov model of glycolytic oscillations and two-dimensional Lotka–Volterra equations. Here, we show that this equality property is critically dependent on the following conditions: There must exist a net flux across the model boundaries that is linearly dependent on the concentration variable for which the equality property holds plus an additive constant, while being independent of all others. A number of models satisfy these conditions or can be transformed such that they do so. We discuss our results in view of the question which advantages oscillations may have in biology. For example, the implications of the findings for the decoding of calcium oscillations are outlined. Moreover, we elucidate interrelations with metabolic control analysis. This paper is dedicated to the memory of the late Reinhart Heinrich, who was the academic teacher of S.S. and, to a great extent, also of M.M.     

The shape of the competition and carrying capacity kernels affects the likelihood of disruptive selection

Many quantitative genetic and adaptive dynamic models suggest that disruptive selection can maintain genetic polymorphism and be the driving force causing evolutionary divergence. These models also suggest that disruptive selection arises from frequency-dependent intraspecific competition. For convenience or historical precedence, these models assume that carrying capacity and competition functions follow a Gaussian distribution. Here, we propose a new analytical framework that relaxes the assumption of Gaussian competition and carrying capacity functions, and investigate how alternative shapes affect the likelihood of disruptive selection. We found that the shape of both carrying capacity and competition kernels interact to determine the likelihood of disruptive selection. For certain regions of the parametric space disruptive selection is facilitated, whereas for others it becomes more difficult. Our results suggest that the relationship between the degree of frequency dependence and the likelihood of disruptive selection is more complex than previously thought, depending on how resources are distributed and competition interference takes place. It is now important to describe the empirical patterns of resource distribution and competition in nature as a way to determine the likelihood of disruptive selection in natural populations.     

Measuring tendon properties in mdx mice: Cell viability and viscoelastic characteristics

Muscular dystrophy is a genetic disorder of skeletal muscle characterized by progressive muscle weakness. Here we assessed whether muscle wasting affects cell viability and mechanical properties of extensor digitorum longus (EDL) and of tibialis anterior (TA) tendons from mdx dystrophic mice compared to wild type (WT) mice. mdx mice represent the classical animal model for human Duchenne muscular dystrophy, and show several signs of the pathology, including a decrease in specific force and an increase of fibrotic index. Cell viability of tendons was evaluated by histological analysis, and viscoelastic properties have been assessed by a rapid measurement protocol that allowed us to compute, at the same time, tissue complex compliance for all the frequencies of interest. Confocal microscopy and mechanical properties measurements revealed that mdx tendons, compared to WT ones, have an increase in the number of dead cells and a significant reduction in tissue elasticity for all the frequencies that were tested. These findings indicate a reduced quality of the tissue. Moreover, mdx tendons have an increase in the viscous response, indicating that during dynamic loading, they dissipate more energy compared to WT. Our results demonstrate that muscular dystrophy involves not only muscle wasting, but also alteration in the viscoelastic properties of tendons, suggesting a paracrine effect of altered skeletal muscle on tendinous tissue.