A simple stochastic model for resource-limited populations is proposed
and its properties examined by simulations. Features of the model are
an explicit resource-limit. which cannot be exceeded, and a realised
population growth-rate which is influenced by resource availability. I
n a range of simulations, the size and variability of resource levels
and growth-rates were varied, but the pattern of variability of each p
arameter was kept the same. At most resource-levels and growth-rates c
onsidered, the model populations showed the general synchrony typical
of many monitored butterfly populations and also showed strong synchro
ny between fluctuations in resource level and population size. As reso
urce-levels and/or population growth-rates declined, both types of syn
chrony were eventually lost as the model populations became highly uns
table and liable to extinction. Other properties of the model are disc
ussed and contrasted with classical population models based on differe
nce equations.