Question

Plants can produce chemicals that, when released to the soil, inhibit the
growth of other plants. These chemicals can act by inhibiting respiration,
photosynthesis, cell division, protein synthesis, mineral uptake, or altering
the function of membranes. For instance, sandhill rosemary (Ceratiola ericoides),
an evergreen shrub found along the coastal plain of the southeastern
United States, produces ceratiolin. This chemical washes from the leaves
and degrades to hydrocinnamic acid, a compound that effectively inhibits
seed germination of many competing species (Hunter and Menges 2002). Assume that this chemical is increasingly effective at germination inhibition
with increasing concentrations. Assume the highest concentration released
to be 60 ppm (parts per million) and that concentration decreases linearly
from the tips of the outermost leaves (for periods without rain).
a. Model inhibition of a competing plant species, where the effective concentrations
of the toxin are between 20 and 60 ppm.

b. Model inhibition for this species with 2 cm rain per day. Set your own
decrease in concentration per cm of rain for your model.

Answer 1

a. Model inhibition of a competing plant species:

Pg = Cjtot + (Sm(NiXi/Nj)q / KqS + (NiXi/Nj)q - Im (NiXi/Nj)q / KqI + (NiXi/Nj)q

in which Pg is the germination probability

Cg is the probability of a non-toxic compound

Im is the concentration inhibitory

KI is the concentration when I = Im/2

Ks and Sm are parameters of stimulatory attribute.

q is the constant that controls curve shape

b. Model inhibition for this species with 2 cm rain per day

To determine the inhibition per unit area, Pg should be multiplied by the number of fertil seeds per unit area:

PN = PgNj