  Social insect colonies can be seen as a distinct form of biological
organization because they function as superorganisms. Understanding how natural
selection acts on the emergence and maintenance of these colonies remains a
major question in evolutionary biology and ecology. Here, we explore this by
using multi-type branching processes to calculate the basic reproductive ratios
and the extinction probabilities for solitary versus eusocial reproductive
strategies. In order to derive precise mathematical results, we use a simple
haploid, asexual model. In general, we show that eusocial reproductive
strategies are unlikely to materialize unless large fitness advantages are
gained by the production of only a few workers. These fitness advantages are
maximized through obligate rather than facultative eusocial strategies.
Furthermore, we find that solitary reproduction is `unbeatable' as long as the
solitary reproductive ratio exceeds a critical value. In these cases, no
eusocial parameters exist that would reduce their probability of extinction.
Our results help to explain why the number of solitary species exceeds that of
eusocial ones: eusociality is a high risk, high reward strategy, while solitary
reproduction is better at risk management.
