  This article is concerned with a version of the contact process with sexual
reproduction on a graph with two levels of interactions modeling
metapopulations. The population is spatially distributed into patches and
offspring are produced in each patch at a rate proportional to the number of
pairs of individuals in the patch (sexual reproduction) rather than simply the
number of individuals as in the basic contact process. Offspring produced at a
given patch either stay in their parents' patch or are sent to a nearby patch
with some fixed probabilities. Specifically, we prove lower and upper bounds
for the probability of long-term survival for the process starting with a
single fully occupied patch. Our main finding is that, with probability close
to one and for a certain set of parameters, the metapopulation survives in the
presence of nearest neighbor interactions while it dies out in the presence of
long range interactions, suggesting that the best strategy for the population
to expand in space is to use intermediate dispersal ranges. This result is due
to the presence of a so-called strong Allee effect induced by the birth
mechanism and does not hold for the basic contact process.
