The model describes the distribution of a numeric trait in a population
of size population. The trait can only assume the values
\((i-1)/(nspecies-1)\) for \(i=1,...,nspecies\). The local
competitive ability of a species with trait u is proportional to
$$F(u)=1-\omega+\omega\phi(u; \mu, \sigma)$$ where \(\omega\),
\(\mu\) and \(\sigma\) are parameters, and \(\phi(u;\mu,
\sigma)\) denotes the probability density function of a normal random variable with mean
\(\mu\) and variance \(\sigma^2\).
The traits of the initial
population are randomly drawn with probability proportional to
\(F(u)\). Then, for ngen steps, one individual randomly chosen
dies. It is replaced either by an immigrant (with probability
\(\gamma\)) or by a descendant of another randomly choosen existing
individual (with probability \(1-\gamma\)).
In the first case (immigration), the trait of the new individual is drawn with
probability proportional to \(F(u)\). In the second case
(reproduction), the the probability that the trait of
the new individual is u is proportional to the abundance of u in the
population times \(F(u)\).
The vector of model parameters is \(\theta=(\gamma, \mu, \sigma, \omega)'\).
Note that the parametrization used in this package differs from the one
originally suggested by Jabot (2010). Specifically, Jabot assumes that
\(\gamma=J/(J+population-1)\) and
\(F(u)=1+2A\pi\sigma\phi(u;\mu, \sigma)\)
where \(J\) and \(A\) are alternative parameters used in place of
\(\gamma\) and \(\omega\), respectively.