A hybrid mathematical model of fungal mycelia : tropisms, polarised growth and application to colony competition

Abstract

Fungi are a crucial component of most ecosystems and are responsible for decomposing organic matter, distributing nutrients through the environment and supporting plants and animal life through symbiotic relationships. Certain species of fungi are common pathogens causing disease and infection in plants and animals. The highly integrated nature of fungi in relation to the environment and all life emphasises the importance of developing a greater understanding of the growth and morphology of such organisms. Mathematical modelling has provided a means through which key processes can be isolated to analyse and simulate a target system to allow observations and form predictions regarding unknown phenomena. Numerous models of fungal colonies have been produced and are generally categorised into two main groups; continuous and discrete. The following study combines the approaches so that the constructed hybrid model comprises a discrete network that represents the fungal mycelia and a continuous component to account for the continuous substrates and other compounds crucial to fungal growth and development. Key processes such as uptake, translocation and anastomosis are included in addition to the implementation of a flexible hyphal orientation scheme that facilitates a variety of tropisms to different influential factors. The hybrid model is used to investigate several scenarios such as the polarisation of growth in response to isolated nutrient resources, competition between multiple colonies and fungal development and persistence in polluted environments. These investigations demonstrate the versatility of the hybrid model and highlight the potential for further applications.