A: The green crab (Carcinus maenas) is a European species that was introduced to North America in the 1800s (Ropes 1968). It inhabits a variety of different habitat types, including rocky intertidal zones, rocky subtidal zones, and estuaries. A researcher samples green crabs in these three habitat types and asks you to analyze relative abundances to determine whether the green crab has a preference for one of the three habitats. There were 50 crabs observed: 22 in the rocky intertidal habitat, 18 in the rocky subtidal, and 10 in the estuary. The researcher has no a priori hypothesis about which habitat might be preferred. Therefore, use a chi-square goodness-of-fit test in SPSS (AnalyzeNonparametric TestsLegacy DialogsChi square) to test the null hypothesis that the green crab has no preference. To set up the data, you will need a column for habitat type and a column for the count of crabs. Before running the analysis, you will need to weight the analysis by the number of crabs (DataWeight Cases). 1. What is the value of the test statistic (χ 2 )? 2. What is the probability of obtaining a value of χ 2 as large as you did (or larger), by chance (sampling error) alone, if the null hypothesis were true (i.e., the P-value or significance level)? 3. Draw both a statistical conclusion (i.e., do you reject the null hypothesis) and a biological conclusion (i.e., does the green crab have a habitat preference, and if so, what is it) about habitat preferences of the green crab.

B: Background: In a variety of corn, grains may have one of four phenotypes, as pictured below: Purple & Smooth (A), Purple & Shrunken (B), Yellow & Smooth (C) and Yellow & Shrunken (D). These four grain phenotypes are produced by the following two pairs of heterozygous genes (P & p and S & s) located on two pairs of homologous chromosomes (each gene on a separate chromosome). P (purple) and S (smooth) are dominant to p (yellow) and s (shrunken), respectively.

Fig. 1: An ear of corn, displaying the four phenotypes of grain.

4. If an ear of corn is produced from a dihybrid cross between two heterozygous parents (PpSs × PpSs), what is the expected phenotypic ratio of grains? (Be complete; list all of the possible phenotypes and their expected ratios.) 5. If the ear of corn in question 1 has a total of 384 grains, how many grains of each phenotype should be expected? 6. Observed phenotypes are: purple and smooth (210 grains), purple and shrunken (80 grains), yellow and smooth (65 grains), and yellow and shrunken (29 grains). Conduct a chi-square goodness-of-fit test in SPSS to test the hypothesis that this ear of corn was produced by a dihybrid cross between two heterozygotes. Note: To do this analysis properly, you will need to input the expected values instead of assuming that all categories are equal. For some reason, SPSS sorts the observed values before running the analysis, so you will need to enter the observed values in order from smallest to largest and the expected values in the same order. Provide the value of the test statistic and the P-value (significance level). 7. Draw statistical and biological conclusions.

Part II: Chi-square Test of Independence (Contingency Table). Green crabs (C. maenas) and Asian shore crabs (Hemigrapsus sanguineus) are non-native species that compete for shelter and food on rocky shores of northeastern North America (Lohrer and Whitlatch 2002). Because complete competitors cannot coexist indefinitely (competitive exclusion principle, Gause 1934), we might expect one (or both) species to alter habitat use in the presence of the competing species. Field studies on both species suggest that their habitat preferences are nearly identical: in the absence of competitors, they both prefer complex, rocky substrates. To test effects of competition, researchers set up an experiment. 50 crabs of each species are simultaneously given a choice of three habitats: high rock cover (>80%), medium rock cover (40-60%), or low rock cover (<20%). After 24 hours, crabs of each species in each habitat are counted. The data are provided on Blackboard. 8. If interspecific competition does not significantly affect habitat selection, what outcome should you expect?

Fig. 2: Asian shore crab Fig. 3: Green crab

9. Conduct a chi-square test of independence (AnalyzeDescriptive StatisticsCrosstabs) to test the null hypothesis that habitat selection is not dependent on species (i.e., both species select habitats in the same way). When entering your variables into the analysis, put Species in rows and Rock_Cover in Columns. Be sure to check the proper options to obtain a χ 2 test statistic (under Statistics), observed and expected values (under Cells), and the standardized residuals (under Cells). Provide a table of the observed and expected counts, the test statistic and P-value, and a clustered bar graph of the observed counts. The bar graph will help you interpret the results of the analysis. 10. The standardized residuals are a measure of how much each observed count differs from the expected count, scaled to fit a normal distribution. In this way, you can think of a standardized residual as being the number of standard deviations an observed value is away from the expected value. Based on the range rule, we would consider an observation unusually high or low if it were greater than _________ standard deviations from the mean. [Fill in the blank.] This would indicate that this observation significantly contributed to an overall significant result. 11. Did any of the observations in this analysis meet the criterion you stated in #9? If so, which one(s)? 12. Draw statistical and biological conclusions about effects of competition on habitat selection by green crabs and Asian shore crabs.

Literature Cited

Gause, G. F. 1934. The struggle for existence. Hafner Press, New York, New York, USA. Lohrer, A. M., and R. B. Whitlatch. 2002. Interactions among aliens: apparent replacement of one exotic species by another. Ecology 83:719-732. Ropes, J. W. 1968. The feeding habits of the green crab, Carcinus maenas (L). Fishery Bulletin 67:183-203.