Computerized evaluation of mean residence times in multicompartmental linear system and pharmacokinetics.

Deriving mean residence times (MRTs) is an important task both in pharmacokinetics and in multicompartmental linear systems. Taking as starting point the analysis of MRTs in open or closed (Garcia-Meseguer et al., Bull Math Biol 2003, 65, 279) multicompartmental linear systems, we implement a versatile software, using the Visual Basic 6.0 language for MS-Windows, that is easy to use and with a user-friendly format for the input of data and the output of results. For any multicompartmental linear system of up to 512 compartments, whether closed or open, with traps or without traps and with zero input in one or more of the compartments, this software allows the user to obtain the symbolic expressions, in the most simplified form, and/or the numerical values of the MRTs in any of its compartments, in the entire system or in a part of the system. As far as we known from the literature, such a software has not been implemented before. The advantage of the present software is that it reduces on the work time needed and minimizes the human errors that are frequent in compartmental systems even those that are relatively staightforward. The software bioCelTer, along with instructions, can be downloaded from http://oretano.iele-ab.uclm.es/~fgarcia/bioCelTer/.

Positive interactions, discontinuous transitions and species coexistence in plant communities.

The population and community level consequences of positive interactions between plants remain poorly explored. In this study we incorporate positive resource-mediated interactions in classic resource competition theory and investigate the main consequences for plant population dynamics and species coexistence. We focus on plant communities for which water infiltration rates exhibit positive dependency on plant biomass and where plant responses can be improved by shading, particularly under water limiting conditions. We show that the effects of these two resource-mediated positive interactions are similar and additive. We predict that positive interactions shift the transition points between different species compositions along environmental gradients and that realized niche widths will expand or shrink. Furthermore, continuous transitions between different community compositions can become discontinuous and bistability or tristability can occur. Moreover, increased infiltration rates may give rise to a new potential coexistence mechanism that we call controlled facilitation.

The role of reproductive plant traits and biotic interactions in the dynamics of semi-arid plant communities.

The dynamics of semi-arid plant communities are determined by the interplay between competition and facilitation among plants. The sign and strength of these biotic interactions depend on plant traits. However, the relationships between plant traits and biotic interactions, and the consequences for plant communities are still poorly understood. Our objective here was to investigate, with a modelling approach, the role of plant reproductive traits on biotic interactions, and the consequences for processes such as plant succession and invasion. The dynamics of two plant types were modelled with a spatially-explicit integrodifferential model: (1) a plant with seed dispersal (colonizer of bare soil) and (2) a plant with local vegetative propagation (local competitor). Both plant types were involved in facilitation due to a local positive feedback between vegetation biomass and soil water availability, which promoted establishment and growth. Plants in the system also competed for limited water. The efficiency in water acquisition (dependent on reproductive and growth plant traits) determined which plant type dominated the community at the steady state. Facilitative interactions between plant types also played an important role in the community dynamics, promoting establishment in the driest conditions and recovery from low biomass. Plants with vegetative propagation took advantage of the ability of seed dispersers to establish on bare soil from a low initial biomass. Seed dispersers were good invaders, maintained high biomass at intermediate and high rainfall and showed a high ability in taking profit from the positive feedback originated by plants with vegetative propagation under the driest conditions. However, seed dispersers lost competitiveness with an increasing investment in fecundity. All together, our results showed that reproductive plant traits can affect the balance between facilitative and competitive interactions. Understanding this effect of plant traits on biotic interactions provides insights in processes such as plant succession and shrub encroachment.

Simplified method for the computation of parameters of power-law rate equations from time-series.

Modeling biological processes from time-series data is a resourceful procedure which has received much attention in the literature. For models established in the context of non-linear differential equations, parameter-dependent phenomenological tentative response functions are tested by comparing would-be solutions of those models to the experimental time-series. Those values of the parameters for which a tested solution is a best fit are then retained. It is done with the help of some appropriate optimization algorithm which simplifies the searching procedure within the range of variability of the parameters that are to be estimated. The procedure works well in problems with a small number of adjustable parameters or/and with narrow searching ranges. However, it may start to be problematic for models with a large number of problem parameters inasmuch as convergence to the best fit is not necessarily ensured. In this case, a reduction in size of the parameter estimation problem must be undertaken. We presently address this issue by proposing a systematic procedure that does so in problems in which the system's response to a sufficiently small pulse perturbation of steady-state can be obtained. The response is then assumed to be a solution of the linearized equations, the Jacobian of which can be retrieved by a simple multilinear regression. The calculated n(2) Jacobian entries provide as many relationships among problem parameters, thus cutting substantially the size of the starting problem. After this preliminary treatment is applied, only (kappa-n(2)) of the initial kappa adjustable parameters are left for evaluation by means of a non-linear optimization procedure. The benefits of the present variant are both in economy of computation and in accuracy in determining the parameter values. The performance of the method is established under different circumstances. It is illustrated in the context of power-law rates, although this does not preclude its applicability to more general functional responses.

Graph-theoretic description of the interplay between non-linearity and connectivity in biological systems.

The purpose of this article is to stress the implications that the consideration of nonlinearity has upon the extension and strength of connectivity, if this is understood as a characterization of the degree of interrelation between parts of the system. This objective is reached within the QP formalism for non-linear ODEs. The formalism is developed in a graph-theoretic setting, with the help of which the connectionist aspect of non-linearity becomes apparent. Topology-preserving transformations involve an exchange between the degree of non-linearity and the strengths of interactions, thus assembling systems of apparently different nature into classes of equivalence. We argue that, if we have in mind a classification of systems according to behavior, these classes of equivalence should be given their proper singularity. We characterize globally the connectivity of a class with an index, although we point out during the discussion that the mathematical conception of the complex idea of connectivity is still incomplete.