Motivation: Growth rate is a major component of the evolutionary fitness of microbial organisms and an excellent surrogate for cell health. In the high-throughput procedures QFA and SGA, microbial cultures are inoculated in an array on solid agar, and growth is measured to obtain quantitative fitness estimates. Neighbouring cultures, which are often different genetic strains, consume nutrients at different rates, creating gradients in nutrient density. We believe that diffusion of nutrients between cultures is affecting growth in these experiments. Current analysis does not account for this; instead, it is assumed that cultures grow independently. I use a network model of nutrient diffusion and nutrient-dependent growth, to correct for competition, to try to improve the accuracy and precision of fitness estimates. I test the model against QFA data from studies on telomere function in Saccharomyces cerevisiae. Ultimately, the model might be used to improve the reliability of screens for genetic interaction and drug sensitivity. Results: I fit the competition model to a QFA plate from Addinall et al. (2011). Using far fewer parameters (387 vs 1152), the new model fits timecourses with similar closeness to the previous model. Fitness estimates are less precise for the fastest growing strains, but more precise for the majority of strains (36 out of 50). Fitness rankings agree in the positions of the fastest and slowest growing strains, but disagree in the middle positions. In a cross-plate validation experiment, the competition model overestimates timecourses to a similar degree that the previous model underestimates. A different method of fitting is required to find globally optimal solutions which might improve reliability. Availability and Implementation: CANS, a Python package developed for the analysis in this paper, is freely available at https://github.com/lwlss/CANS.