Applications of Search in Biology: Some Open Problems - Search Theory: A Game Theoretic Perspective - page 287

These models can be improved. When there is a large number of predator and
prey, then intraspecific competition and population dynamics may play a role, with
consequences for the elusive stock-recruitment relationship. Swimming may be
more saltatory or Levy-like than a simple constant swim [ 4 ]. The environment is
also more complex than simple independent spheres; the interaction between in-
dividual swimming and larger-scale fluid flow can induce structures and patterns
requiring modified theory [ 11 ]. Also, swimming faster makes the larva more visible
to its predators, a further (but quantifiable) blurring of princesses and monsters.
Evolution adds a further, and potentially large, twist. Typically only <1 % of
hatched larvae survive the early juvenile stage; the average fish is thoroughly dead.
“Optimality” therefore must be firmly rooted in the luckiest tails of the probability
distributions [ 24 ]. The mathematical frameworks exist to allow this to be quanti-
fied [ 9 ]; all that is needed is a careful definition of the ecological and evolutionary
problem, and intelligence and ambition in framing the research within the context
of sustainable fisheries management.
Problem 2: What Is the Difference Between a Plant
and a Fish? (Complications 2, 4, and 5)
Plants are important; we eat them, and through photosynthesis they are fundamen-
tal to terrestrial life as we know it. The diversity of plant species, and the vari-
ety of elaborate chemicals they produce, is staggering [ 13 ]; if plants need simply
to absorb nutrients and eat sunshine, then why is there not some dominant super-
species? Thinking more practically, agricultural use of artificial fertilisers is thought
to be necessary for sustained food production, but if applied inefficiently this is fi-
nancially expensive and incurs severe detrimental downstream ecological costs. A
better knowledge of how plants search for, and exploit, nutrient patches is there-
fore of both practical and intellectual value. There are obvious similarities with fish:
a “predator” (root tip) with only local knowledge moves through a complex and
possibly dynamic environment seeking “prey” (patches of nutrient). However, the
differences cannot be ignored; a plant has many roots and can preferentially prolif-
erate root growth towards regions of higher nutrient concentration, but unlike most
animals it cannot completely relocate itself in response to threat from competitors,
consumers, or the environment.
A simple model by Croft et al. [ 10 ] imagines a plant growing in one-dimensional
soil, whose growth is enhanced by finding discrete patches of nutrient, and which
can “choose” to proliferate roots preferentially to the left or right depending on the
location of the most recently acquired patch. For an isolated plant in a uniformly
random environment all proliferation strategies are equal. In a patchy environment
it becomes strongly favourable to proliferate in the direction of the most recently
acquired patch. None of this is surprising. However, when a population of identical
plants competes for resources, things change. Even in a uniformly random environ-
ment there is an evolutionary pressure to proliferate towards the most recent patch.