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 LD50 (Finney, 1971). On the contrary, the most variable ones are the extremes of the sigmoid graph. Consequently, when the estimation of the LD90 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. LD5, LD10, LD25, 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 LD50 should be as reproducible as possible (i.e. with a minimum variability.) Conversely, when the experimental conditions are modified, the LD50 correspondingly changes. Zbinden and Flury-Roversi (1981) noted that “every LD50 value must thus be regarded as a unique result of one particular biological experiment”.