Ecological reading of random numbers

Numerical simulation of species assemblages is presented. When the level of the external disturbance is below the species tolerance, the size of every population changes by addition of positive or negative random number to the previous number. In the opposite case, the number of individuals in a population converges to zero. External disturbances change randomly between time steps for each species independently. The tolerances are the species attributes, they are constant and differ among species. Twelve assemblages are considered. They differ by the sets of the species' tolerances and by the carrying capacity of the environment, that is the potential species richness. Sets of tolerances determine the predictability of the assemblage, which is the squared coefficient of correlation between all previous and subsequent states of the assemblage. The average relative species richness correlates to predictability. Distributions of species by abundance are studied in momentary states chosen from each assemblage. In most cases, they fit simultaneously the exponential, lognormal and negative-binomial models being tested by Chi-square test. Individual-species curves fit well both the models of Preston and Fisher. Core and satellite species may be observed during short time intervals. Non-numerous persistent core species are more abundant. These two groups may differ in their species-abundance distributions. Positive correlation is found between species richness and abundance of assemblage in time series of every assemblage. Negative correlation is found between the maxim species range and the relative rate of extinction. The results may serve as the null-model for certain community models. This approach may be used also in modeling of species assemblages composed of populations with stochastic dynamics.