Stochastic models of plant growth and competition

Plants have been observed to show a range of plastic responses to environmental
conditions. For example, the abundance and distribution of nutrients, as well as the
presence and proximity of local competition, have been seen to result in changes in
root proliferation and architecture. However, whilst some species have been witnessed
displaying certain responses under given circumstances, experimental evidence suggests
that responses to environmental factors can be far from simple, and sometimes
counter-intuitive. Plant responses to components of the environment, and the benefit
of such responses, are highly context sensitive.
This thesis explores some of the real world complexities that result in the observed
responses to hierarchical sets of environmental factors, and presents a theoretical
model that seeks to elucidate the interplay between different factors and their effects
on “optimal” behaviour by both individuals and populations.
Starting with a simple one-dimensional model comprising a linearised approximation
of a Gompertz growth function with nutrient patch dependent growth, the
individual and combined effects of stochasticity in resource and competitor distribution
are investigated. Complexity and functionality are progressively built up, with
a resource dependent proliferation response, a scaling up into two-dimensions, and
finally different intrinsic plant growth strategies trading growth rate against root
system efficiency all introduced and investigated.
Throughout the work presented in this thesis, complex and subtle behavioural
responses and patterns emerge from seemingly simple models. The importance of
stochasticity on individual and population level performance is also highlighted, and
the results demonstrate the inability for mean-field approximations and expected
results to capture the emergent behaviour.