  Dispersal of propagules (seeds, spores) from a geographically isolated
population into an uninhabitable matrix can threaten population persistence if
it prevents new growth from keeping pace with mortality. Quantifying propagule
loss can thus inform restoration and conservation of vulnerable populations in
fragmented landscapes. To model propagule loss in detail, one can integrate
dispersal kernels (probabilistic descriptions of dispersal) and plant
densities. However, one might lack the detailed spatial information and
computational tools needed by such integral models. Here we derive two upper
bounds on the probability of propagule loss--one assuming rotational symmetry
of dispersal and the other not--that require only habitat area, habitat
perimeter, and the mean dispersal distance of a propagule. We compare the
bounds to simulations of integral models for the population of Asclepias
syriaca (common milkweed) at McKnight Prairie--a 13.7 hectare reserve
surrounded by agricultural fields in Goodhue County, Minnesota--and identify
conditions under which the bounds closely estimate propagule loss.
