Experimental design on the simplex

Optimum experimental designs depend on the design criterion, the model andthe design region. The talk will consider the design of experiments for regressionmodels in which there is a single response with the explanatory variables lying ina simplex. One example is experiments on various compositions of glass such asthose considered by Martin, Bursnall, and Stillman (2001).Because of the highly symmetric nature of the simplex, the class of models thatare of interest, typically Scheff´e polynomials (Scheff´e 1958) are rather differentfrom those of standard regression analysis. The optimum designs are also ratherdifferent, inheriting a high degree of symmetry from the models.In the talk I will hope to discuss a variety of modes for such experiments. ThenI will discuss constrained mixture experiments, when not all the simplex is availablefor experimentation. Other important aspects include mixture experimentswith extra non-mixture factors and the blocking of mixture experiments.Much of the material is in Chapter 16 of Atkinson, Donev, and Tobias (2007).If time and my research allows, I would hope to finish with a few comments ondesign when the responses, rather than the explanatory variables, lie in a simplex.ReferencesAtkinson, A. C., A. N. Donev, and R. D. Tobias (2007). Optimum ExperimentalDesigns, with SAS. Oxford: Oxford University Press.Martin, R. J., M. C. Bursnall, and E. C. Stillman (2001). Further results onoptimal and efficient designs for constrained mixture experiments. In A. C.Atkinson, B. Bogacka, and A. Zhigljavsky (Eds.), Optimal Design 2000,pp. 225–239. Dordrecht: Kluwer.Scheff´e, H. (1958). Experiments with mixtures. Journal of the Royal StatisticalSociety, Ser. B 20, 344–360.1

Identification and conservation of remnant genetic resources of brown trout in relict populations from Western Mediterranean streams

Brown trout is a cold-adapted freshwater species with restricted distribution to headwater streams in rivers of the South European peninsulas, where populations are highly vulnerable because Mediterranean regions are highly sensitive to the global climatic warming. Moreover, these populations are endangered due to the introgressive hybridization with cultured stocks. Individuals from six remnant populations in Western Mediterranean rivers were sequenced for the complete mitochondrial DNA control region and genotyped for 11 nuclear markers. Three different brown trout lineages were present in the studied region. Significant genetic divergence was observed among locations and a strong effect of genetic drift was suggested. An important stocking impact (close to 25%) was detected in the zone. Significant correlations between mitochondrial-based rates of hatchery introgression and water flow variation suggested a higher impact of stocked females in unstable habitats. In spite of hatchery introgression, all populations remained highly differentiated, suggesting that native genetic resources are still abundant. However, climatic predictions indicated that suitable habitats for the species in these rivers will be reduced and hence trout populations are highly endangered and vulnerable. Thus, management policies should take into account these predictions to design upstream refuge areas to protect remnant native trout in the region