EFFECTIVE POPULATION SIZE IN A CONTINUOUSLY DISTRIBUTED POPULATION

An individual-based simulation model was created to examine genetic variability, time until fixation and spatial genetic structure in a continuously distributed population. Previous mathematical models for continuously distributed populations have the difficulty that the assumption of independent reproduction and independent dispersal of offspring cause clumped spatial distribution and thus violate an assumption of random spatial distribution. In this study, this problem is avoided by considering the dispersal behavior of offspring. The simulation results showed that the inbreeding effective population size estimated by the rate of decrease of heterozygosity during the first 15 generations corresponds to the neighborhood size calculated by the standard deviation of the dispersal distance (σ_T). This inbreeding effective population size does not greatly change with the area of simulation when the densities and σ_T are the same. However, the inbreeding effective population size estimated by heterozygosity using the first 500 generations is larger than the neighborhood size calculated by the dispersal distance and increases with the area of simulation with the same densities. The variance effective population size, estimated by time until fixation of alleles, increases with dispersal distance (σ_T) and with the area of simulation given the same densities. The inbreeding effective population size and variance effective population size were smaller than the actual population size unless σ_T is sufficiently large (2 σ_T > approximate L/2, where L is a side of the simulation square).     

Modelling individual plant growth at a variable mean density or at a specific spatial setting

Neighbouring plants generally compete for the limiting resources in order to grow and reproduce. Some resources, e.g., sun light, may be monopolised by the larger plants and this may lead to asymmetric competition where a plant, which is twice as large, grows more than twice as fast. A previously published individual-based Richards growth model that describes the asymmetric growth of individual plants is here generalised with respect to a variable mean plant density and an explicit spatial setting.     

Relationship between the virtual dynamic thinning line and the self-thinning boundary line in simulated plant populations

The self-thinning rule defines a straight upper boundary line on log-log scales for all possible combinations of mean individual biomass and density in plant populations. Recently, the traditional slope of the upper boundary line, -3/2, has been challenged by -4/3 which is deduced from some new mechanical theories, like the metabolic theory. More experimental or field studies should be carried out to identify the more accurate self-thinning exponent. But it＇s hard to obtain the accurate self-thinning exponent by fitting to data points directly because of the intrinsic problem of subjectivity in data selection. The virtual dynamic thinning line is derived from the competition-density （C-D） effect as the initial density tends to be positive infinity, avoiding the data selection process. The purpose of this study was to study the relationship between the virtual dynamic thinning line and the upper boundary line in simulated plant stands. Our research showed that the upper boundary line and the virtual dynamic thinning line were both straight lines on log-log scales. The slopes were almost the same value with only a very little difference of 0.059, and the intercept of the upper boundary line was a little larger than that of the virtual dynamic thinning line. As initial size and spatial distribution patterns became more uniform, the virtual dynamic thinning line was more similar to the upper boundary line. This implies that, given appropriate parameters, the virtual dynamic thinning line may be used as the upper boundary line in simulated plant stands.     

Implementing behaviour in individual-based models using neural networks and genetic algorithms

Even though individual-based models (IBMs) have become very popular in ecology during the last decade, there have been few attempts to implement behavioural aspects in IBMs. This is partly due to lack of appropriate techniques. Behavioural and life history aspects can be implemented in IBMs through adaptive models based on genetic algorithms and neural networks (individual-based-neural network-genetic algorithm, ING). To investigate the precision of the adaptation process, we present three cases where solutions can be found by optimisation. These cases include a state-dependent patch selection problem, a simple game between predators and prey, and a more complex vertical migration scenario for a planktivorous fish. In all cases, the optimal solution is calculated and compared with the solution achieved using ING. The results show that the ING method finds optimal or close to optimal solutions for the problems presented. In addition it has a wider range of potential application areas than conventional techniques in behavioural modelling. Especially the method is well suited for complex problems where other methods fail to provide answers. This revised version was published online in July 2006 with corrections to the Cover Date.     

Fitness consequences of centrality in mutualistic individual-based networks

The relationships among the members of a population can be visualized using individual networks, where each individual is a node connected to each other by means of links describing the interactions. The centrality of a given node captures its importance within the network. We hypothesize that in mutualistic networks, the centrality of a node should benefit its fitness. We test this idea studying eight individual-based networks originated from the interaction between Erysimum mediohispanicum and its flower visitors. In these networks, each plant was considered a node and was connected to conspecifics sharing flower visitors. Centrality indicates how well connected is a given E. mediohispanicum individual with the rest of the co-occurring conspecifics because of sharing flower visitors. The centrality was estimated by three network metrics: betweenness, closeness and degree. The complex relationship between centrality, phenotype and fitness was explored by structural equation modelling. We found that the centrality of a plant was related to its fitness, with plants occupying central positions having higher fitness than those occupying peripheral positions. The structural equation models (SEMs) indicated that the centrality effect on fitness was not merely an effect of the abundance of visits and the species richness of visitors. Centrality has an effect even when simultaneously accounting for these predictors. The SEMs also indicated that the centrality effect on fitness was because of the specific phenotype of each plant, with attractive plants occupying central positions in networks, in relation to the distribution of conspecific phenotypes. This finding suggests that centrality, owing to its dependence on social interactions, may be an appropriate surrogate for the interacting phenotype of individuals.     

Intraspecific interactions affect the spatial pattern of a dominant shrub in a semiarid shrubland: A prospective approach

Dispersal, physical conditions and biotic interactions contribute to determine the spatial distribution of individuals in plant populations. Much of what we know has been learned from studies that retrospectively posit mechanisms presumed to have generated the observed spatial patterns. Here we present a prospective approach. We start by measuring spatial demographic effects and evaluate if they can generate observed spatial patterns. We evaluated the influence of interactions among conspecifics on vital rates, demography and spatial distribution of Croton aff. wagneri, a dominant shrub in dry Andean ecosystems. Recruitment, survival and growth varied in relation with distance to conspecifics neighbours and with their summed cover. We built a spatial individual-based model and simulated its population dynamics in 30 × 30 m plots for a 30-year period. We compared the predicted spatial pattern from these demographic models with that observed among plants in 16 independent plots with the same area. Simulated populations mimicked observed spatial patterns, although in plots at high elevations the simulated populations did not reproduce the observed inhibition at small scales. Observed and simulated patterns indicated differences between elevations in maximum aggregation and location of the distances with higher aggregation. We discuss how consideration of critical seed and juvenile stages and interspecific interactions could further improve our understanding of spatial pattern and recommend that these factors be considered in future models.