# 3.1.2. Exploration of acute poisoning using the lethality criterion

Lethality is the most common experimental criterion in bee toxicology. In toxicological tests, an insect usually is considered dead when it exhibits “no movements after prodding” (see section 2). Using this criterion, investigators often use correlation metrics to link the lethality and dose of a toxic substance to a test subject. This assumes that the group of subjects to be tested are randomly selected from a population with a normal distribution (Gaussian) susceptibility to the toxic substance.

The cumulative distribution of the normal probability density is an increasing sigmoidal function (Wesstein, http://mathworld.wolfram.com). In matter of toxicology, the consequence is that the theoretical dose-cumulated lethality (% lethality) relation is a sigmoid ranging from 0% to 100% lethality. To transform the sigmoid into a straight line, Bliss (1934) proposed to use the logarithm of the doses in X axis and the probability units or probits in Y axis, the probit being the percentage of killed individuals converted following a special table. At the present time, a nonlinear regression analysis (Seber and Wild, 1989) can be more relevant and efficient, particularly when using statistical analysis software.

Laboratory
experiments to establish the dose-lethality relation involve the administration
of increasing doses to groups of selected subjects and the count of the two
categories of subjects (dead or alive) after a specified time interval
(Robertson *et al*., 1984). Replications are needed to estimate the
variability of each point representing the lethality associated to a particular
dose.

From a
theoretical point of view, by considering the cumulative distribution function
(sigmoid) and its fluctuations due to the experimental replications, the less
variable point is the inflection point, in other words the 50 % lethality point
and its associated dose, the 50 % lethal dose or LD_{50} (Finney,
1971). On the contrary, the most variable ones are the extremes of the sigmoid
graph. Consequently, when the estimation of the LD_{90} is required,
e.g. efficiency of an insecticide against pests, special designs must be used
to guarantee its precision (Robertson *et al*., 1984). From an
experimental point of view, the graph of the cumulative distribution function
is not necessarily sigmoidal. For instance, after one imidacloprid contact
exposure, Suchail *et al*. (2000) evidenced that mortality rates were
positively correlated with doses lower than 7 ng/bee and negatively with doses
ranging from 7 to 15 ng/bee. In this situation, the calculation of any lethal
dose with the log-probit model is incorrect.

When
considering beneficial insect such as bees, the doses which cause slight
mortalities (e.g. LD_{5}, LD_{10}, LD_{25}, etc.) are
more pertinent, even if the variability of these LDs due to the toxin is
difficult to distinguish from that of the natural mortality deduced from the
control groups (Abbott, 1925). This variability is not to be rejected, because
its very existence in experimental conditions suggests that the same
variability also exists in field conditions.

The variability created by the replications refers mainly to the assumption concerning dealing with the random selection of the subjects and the normal distribution of population from which the subjects are chosen. The variability induced by the replications, meaning that the experiment is identically repeated several times, provides additional information on the reproducibility of the experiment.

For a set
of given experimental conditions often recommended by precise guidelines, the
LD_{50} should be as reproducible as possible (i.e. with a minimum
variability.) Conversely, when the experimental conditions are modified, the LD_{50}
correspondingly changes. Zbinden and Flury-Roversi (1981) noted that “every LD_{50}
value must thus be regarded as a unique result of one particular biological
experiment”.