THE DEVELOPMENT OF ENDOMYCORRHIZAL ROOT SYSTEMS

III. THE MATHEMATICAL REPRESENTATION OF THE SPREAD OF VESICULAR-ARBUSCULAR MYCORRHIZAL INFECTION IN ROOT SYSTEMS

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Summary

We have modelled the spread of vesicular-arbuscular mycorrhizas (VAM) from localized inoculum in a developing root system by assuming that the rate of spread of infection at a particular time is proportional to the product of the length of root already infected and the fraction of the total root which is susceptible to infection at that time. An important parameter of the model is its asymptote n, the maximum fraction of the root system which becomes mycorrhizal. Our model is formally similar to the logistic equation for growth.

An earlier model by Tinker (1975), which predicts that rate of spread of infection would be enhanced by increased density of roots L, (cm cm −3), was compared with ours, using results of experiments on wheat and clover sown at three densities. The new model fitted the data for spread of infection much better, especially that of young infections. The relative rates were generally little altered by total length of roots, Lt, but the absolute values for the two hosts differed widely. This suggests that infection spreads primarily along roots, rather than by random contact between roots and hyphae. This type of model may be useful for exploring the mechanisms by which environmental changes affect spread of vesicular-arbuscular mycorrhizas.

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