due 20 Feb 2020

The western predatory mite Metaseiulus occidentalis has been used as a biological control agent of spider mites in orchards and vineyards. Since resistance to some insecticides was found to develop naturally in M. occidentalis, and the species was documented to be an acarine predator of economic importance, it was selected as a candidate for genetic improvement.

The data for this assignment involve an insecticide-resistant strain of M. occidentalis developed by crossing colonies with field-developed resistances with a laborary-selected resistant colony. Our data come from an experiment aimed at determining the genetic basis for susceptibility to the insecticide permethrin.

The experiment was carried out in a lab at the Department of Entomology, University of California, Berkeley. Mites were expesed in 11-14 groups of ten to a given dose of permethrin for a fixed interval of time, and the number of mites dead in each group of ten at the end of the interval was recorded. This was done for each of seven doses, expressed in grams of active ingredient per 100 liters.

a. Consider the data in hw1_mitesA.txt. At each of seven doses we have the number of dead out of ten, for between 11 and 14 groups of ten. Use this data to examine the hypothesis that at any given dose the mites are dying independently with a constant probability. Consider using computer simulations.

b. Make the binomial assumption for mites at each dose and pool the data across groups. Then fit a dose-response curve of a standard type (e.g., probit, logit, complementary log-log, etc.), justifying your choice. That is, fit a generalized linear model (with glm in R, or with the python module statsmodels).

c. Estimate the LD50 (the dose at which the probability of death is 50%) and its standard error (SE).

d. How might you need to modify your analyses in (b) and (c) in light of your conclusions in (a)?

e. Repeat (a)-(d) for data on a second strain of mites, in hw1_mitesB.txt.

f. Assess whether the does-response curves for the two strains are parallel.

Resources

• Venables and Ripley (2002) Modern applied statistics with S, 4th edition, chapter 7
• GLM documentation for python module statmodels

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This assignment is a slightly modified version of one designed by Terry Speed for an applied statistics course at the University of California, Berkeley.