Mathematical models used to predict microbial growth are based on liquid cultures data. Models describing growth on solid surfaces, highlighting the differences with liquids cultures, are scarce. In this work, we have demonstrated that a single Gompertz equation describes accurately the increase of the yeast colonies, up to the point where they reach their maximum size. The model can be used to quantify the differences in growth kinetics between solid and liquid media. Moreover, as all its parameters have biological meaning, it could be used to build secondary models predicting yeast growth on solid surfaces under several environmental conditions.

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The colony shape of four yeast species growing on agar medium was measured for 116 days by image analysis. Initially, all the colonies are circular, with regular edges. The loss of circularity can be quantitatively estimated by the eccentricity index, E i , calculated as the ratio between their orthogonal vertical and horizontal diameters. E i can increase from 1 (complete circularity) to a maximum of 1.17-1.30, depending on the species. One colony inhibits its neighbour only when it has reached a threshold area. Then, E i of the inhibited colony increases proportionally to the area of the inhibitory colony. The initial distance between colonies affects those threshold values but not the proportionality, E i /area; this inhibition affects the shape but not the total surface of the colony. The appearance of irregularities in the edges is associated, in all the species, not with age but with nutrient exhaustion. The edge irregularity can be quantified by the Fourier index, F i , calculated by the minimum number of Fourier coefficients that are needed to describe the colony contour with 99% fitness. An ad hoc function has been developed in Matlab v. 7.0 to automate the computation of the Fourier coefficients. In young colonies, F i has a value between 2 (circumference) and 3 (ellipse). These values are maintained in mature colonies of Debaryomyces, but can reach values up to 14 in Saccharomyces. All the species studied showed the inhibition of growth in facing colony edges, but only three species showed edge irregularities associated with substrate exhaustion.