In the honey bee, the possible long-term
exposure to a toxic agent by contamination
of stored food has been established by studying
the transfer of pesticides sprayed on crops
into the hive (137). Thus, the lethal dose estimated
during acute toxicity tests appears to be
a partial measure of the lethal effect because
of the short duration of these tests (1 to 3 days
in most cases). Studies concerning long-term
survival of honey bees raise the problem of
statistical analysis of survival data. In chronic
toxicity tests, most often only the end result of
long-term poisoning (i.e., an increase of cumulative
mortality) is analyzed (113). Some
approaches consider how the mortality rate
varied during the time of pesticide exposure
by a graphic interpretation (124, 126), but not
with statistical analysis. Conversely, when statistical
methods are employed in survival analysis
a parametric model is often used (63, 138).
However, these analyses depend strongly on
the validity of the assumption that the survival
time has a particular probability distribution.
Moreover, these statistical methods are generally
based on the hypothesis of independence
between bees belonging to the same group,
which is not realistic. Indeed, food exchanges,
contacts, and pheromonal communication occurring
among workers make survival of a bee
dependent on the survival of its nestmates.
Dechaume-Moncharmont et al. (26) demonstrated
this density dependence in pesticide
effects with the use of a Cox proportional
hazard model.