  We present a novel communication-free algorithm for individual-based
probabilistic neutral biodiversity simulations. The algorithm transforms a
neutral Moran ecosystem model into an embarrassingly parallel problem by
trading off inter-process communication at the cost of some redundant
computation.
  Specifically, by careful design of the random number generator that drives
the simulation, we arrange for evolutionary parent-child interactions to be
modelled without requiring knowledge of the interaction, its participants, or
which processor is performing the computation. Critically, this means that
every individual can be simulated entirely independently. The simulation is
thus fully reproducible irrespective of the number of processors it is
distributed over. With our novel algorithm, a simulation can be (1) split up
into independent batch jobs and (2) simulated across any number of
heterogeneous machines - all without affecting the simulation result.
  We use the Rust programming language to build the extensible and statically
checked simulation package $\texttt{necsim-rust}$. We evaluate our
parallelisation approach by comparing three traditional simulation algorithms
against a CPU and GPU implementation of our Independent algorithm. These
experiments show that as long as some local state is maintained to cull
redundant individuals, our Independent algorithm is as efficient as existing
sequential solutions. The GPU implementation further outperforms all algorithms
on the CPU by a factor ranging from $\sim 2$ to $\sim 80$, depending on the
model parameterisation and the analysis that is performed. Amongst the parallel
algorithms we have investigated, our Independent algorithm provides the only
non-approximate parallelisation strategy that can scale to large simulation
domains.
