Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a "canalization limit" is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V ). The rate of decrease of mutational variance V is found to be less than 10% of the initial V . From this result it is concluded that characters with typical mutational variances of about 10 V are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of mac...

Canalization is the suppression of phenotypic variation. Depending on the causes of phenotypic variation, one speaks either of genetic or environmental canalization. Genetic canalization describes insensitivity of a character to mutations, and the insensitivity to environmental factors is called environmental canalization. Genetic canalization is of interest because it influences the availability of heritable phenotypic variation to natural selection, and is thus potentially important in determining the pattern of phenotypic evolution. In this paper a number of population genetic models are considered of a quantitative character under stabilizing selection. The main purpose of this study is to define the population genetic conditions and constraints for the evolution of canalization. Environmental canalization is modeled as genotype specific environmental variance. It is shown that stabilizing selection favors genes that decrease environmental variance of quantitative characters. However, the theoretical limit of zero environmental variance has never been observed. Of the many ways to explain this fact, two are addressed by our model. It is shown that a "canalization limit" is reached if canalizing effects of mutations are correlated with direct effects on the same character. This canalization limit is predicted to be independent of the strength of stabilizing selection, which is inconsistent with recent experimental data (Sterns et al. 1995). The second model assumes that the canalizing genes have deleterious pleiotropic effects. If these deleterious effects are of the same magnitude as all the other mutations affecting fitness very strong stabilizing selection is required to allow the evolution of environmental canalization. Genetic canalization is modeled as an influence on the average effect of mutations at a locus of other genes. It is found that the selection for genetic canalization critically depends on the amount of genetic variation present in the population. The more genetic variation, the stronger the selection for canalizing effects. All factors that increase genetic variation favor the evolution of genetic canalization (large population size, high mutation rate, large number of genes). If genetic variation is maintained by mutation-selection balance, strong stabilizing selection can inhibit the evolution of genetic canalization. Strong stabilizing selection eliminates genetic variation to a level where selection for canalization does not work anymore. It is predicted that the most important characters (in terms of fitness) are not necessarily the most canalized ones, if they are under very strong stabilizing selection (k > 0.2V ). The rate of decrease of mutational variance V is found to be less than 10% of the initial V . From this result it is concluded that characters with typical mutational variances of about 10 V are in a metastable state where further evolution of genetic canalization is too slow to be of importance at a microevolutionary time scale. The implications for the explanation of mac...

The generic, quantitative, spatially explicit, individual-based model BacSim was developed to simulate growth and behaviour of bacteria. The potential of this approach is in relating the properties of microscopic entities -cells -to the properties of macroscopic, complex systems such as biofilms. Here, the growth of a single Escherichia coli cell into a colony was studied. The object-oriented program BacSim is an extension of Gecko, an ecosystem dynamics model which uses the Swarm toolkit for multi-agent simulations. The model describes bacterial properties including substrate uptake, metabolism, maintenance, cell division and death a t the individual cell level. With the aim of making the model easily applicable to various bacteria under different conditions, the model uses as f e w as eight readily obtainable parameters which can be randomly varied. For substrate diffusion, a two-dimensional diffusion lattice is used. For growth-rate-dependent cell size variation, a conceptual model of cell division proposed by Donachie was examined. A mechanistic version of the Donachie model led to unbalanced growth at higher growth rates, whereas including a minimum period between subsequent replication initiations ensured balanced growth only if this period was unphysiologically long. Only a descriptive version of the Donachie model predicted cell sizes correctly. For maintenance, the Herbert model (constant specific rate of biomass consumption) and for substrate uptake, the Michaelis-Menten or the Best equations were implemented. The simulator output faithfully reproduced all input parameters. Growth characteristics when maintenance and uptake rates were proportional to either cell mass or surface area are compared. The authors propose a new generic measure of growth synchrony to quantify the loss of synchrony due to random variation of cell parameters or spatial heterogeneity. Variation of the maximal uptake rate completely desynchronizes the simulated culture but variation of the volume-at-division does not. A new measure for spatial heterogeneity is introduced: the standard deviation of substrate concentrations as experienced b y the cells. Spatial heterogeneity desynchronizes population growth by subdividing the population into parts synchronously growing a t different rates. A t a high enough spatial heterogeneity, the population appears to grow completely asynchronously.

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