  We study the effects of demographic stochasticity on the long-term dynamics
of biological coevolution models of community assembly. The noise is induced in
order to check the validity of deterministic population dynamics. While
mutualistic communities show little dependence on the stochastic population
fluctuations, predator-prey models show strong dependence on the stochasticity,
indicating the relevance of the finiteness of the populations. For a
predator-prey model, the noise causes drastic decreases in diversity and total
population size. The communities that emerge under influence of the noise
consist of species strongly coupled with each other and have stronger linear
stability around the fixed-point populations than the corresponding noiseless
model. The dynamics on evolutionary time scales for the predator-prey model are
also altered by the noise. Approximate $1/f$ fluctuations are observed with
noise, while $1/f^{2}$ fluctuations are found for the model without demographic
noise.
