Stat/F&W/Hort 572 Ane February 12, 2009
Assignment #4 — Due Friday, Feb. 20, 2009, by 4pm
Turn in lecture, discussion, or to your TA’s mailbox. Please circle the discussion section you expect to pick up
this assignment:
311 312 313 314
Purpose: Get experience with logistic regression.
A biologist interested in crustaceans sought evidence of a geographic trend in allelic distribution in the gene
mannose-6-phosphate isomerase (Mpi) in populations of the amphipod crustacean Megalorchestia californiana
located along the Pacific coast. In eight populations ranging from Santa Barbara, California in the south to Port
Townsend, Washington in the north, the biologist genotyped individual crustaceans at the Mpi locus. Sample sizes
ranged from 30 to over 2000. Two alleles, Mpi90 and Mpi100 were prevalent. If latitude is helpful in predicting
allelic frequency of one of the alleles, say Mpi90, this would be evidence consistent with a story of differential
selection at this locus based on an environmental factor associated with latitude. Latitude is in degrees, north of
the equator.
The data is in the file crustacean.txt and is also shown below.
location latitude Mpi90 Mpi100
Port Townsend, WA 48.1 47 139
Neskowin, OR 45.2 177 241
Siuslaw R., OR 44.0 1087 1183
Umpqua R., OR 43.7 187 175
Coos Bay, OR 43.5 397 671
San Francisco, CA 37.8 40 14
Carmel, CA 36.6 39 17
Santa Barbara, CA 34.3 30 0
(a) Read the data into R, create a data frame from this data, then add a column with the total sample size, and
another column with the proportion of Mpi90. Plot these proportions versus latitude. Explain why logistic
regression is an appropriate model to address this question. (Include the plot with your solution.)
(b) Fit a logistic regression model to this data and report the coefficients. Is the latitude effect significant?
(c) On a single plot, include
•the observed proportion of Mpi90 allele versus latitude, as in question (a),
•the total number of samples from each location, next to each point. Hint: the text function can add
text to a plot. It can work like this:
text(x=latitudeValues, y=Mpi90proportions, labels=as.character(totalNumbers), pos=4)
The option pos can be ommitted. If provided, the ‘labels’ will be shifted either down (1), left (2), up
(3) or right (4).
•a curve of the estimated probability of Mpi90 allele versus latitude. Hint: the predict function can
take the logistic regression fit and use it to predict the proportion on Mpi90 allele at new latitude. To
use this function, you may create new latitude values, and a new data set with these values like this:
newlatitude = seq(20, 60, by=.5)
newlatitude
newdat = data.frame( latitude=newlatitude )
