Optimising the number of isolates to be used to estimate growth parameters of mycotoxigenic species

The aim of the present work was to mathematically assess the minimum number of isolates that would lead to equivalent growth parameters estimates to those obtained with a high number of strains. The datasets from two previous works on 30 Aspergillus carbonarius isolates and 62 Penicillium expansum isolates were used for this purpose. First, the datasets were used to produce a global estimation of growth parameters μ (growth rate, mm/d) and λ (time to visible growth, d) under the different experimental conditions, providing also a 95% confidence interval. Second, a computational algorithm was developed in order to obtain an estimation of the growth parameters that one would obtain using a lower number of isolates and/or replicates, using a bootstrap procedure with 5000 simulations. The result of this algorithm was the probability that the obtained estimation falls in the 95% confidence interval previously produced using all sample isolates. Third, the algorithm was intensively applied to obtain these probabilities for all possible combinations of isolates and replicates. Finally, these results were used to determine the minimum number of isolates and replicates needed to obtain a reasonable estimation, i.e. inside the confidence interval, with a probability of 0.8, 0.9 and 0.95. The results revealed that increasing the number of isolates may be more effective than increasing the number of replicates, in terms of increasing the probability. In particular, 12–17 isolates of A. carbonarius led to the same growth parameters as the total 30 (p = 0.05) or 9 isolates with p = 0.20; by contrast, 25–30 isolates of P. expansum led to the same growth parameters as the total 62 (p = 0.05) or 18–21 isolates with p = 0.20. As far as we know, this is the first study that provides a systematic evaluation of the number of isolates and replicates needed when designing an experiment involving mycotoxigenic moulds responses to environmental factors, and may serve to support decision making in this kind of studies or other similar ones.

The authors are grateful to the European (MYCORED KBBE-2007-2-5-05 project), Spanish (AGL2010-22182-C04-04 project), Comissionat per a Universitats i Recerca d'Innovació, Universitats i Empresa de la Generalitat de Catalunya (AGAUR) and European Social Fund for the financial support.