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Exploring Jordan's rule in Pacific three-spined stickleback Gasterosteus aculeatus
M R J Morris1, E Petrovitch1, E Bowles1
1Department of Biological Sciences, University of Calgary, 2500 University Dr NW, Calgary, Alberta, T2N 1N4, Canada.
Abstract:
Coastal marine Gasterosteus aculeatus were captured from seven locations along the Pacific coast of North America, ranging across 21·8° latitude to test Jordan's rule, i.e. that vertebral number should increase with increasing latitude for related populations of fish. Vertebral number significantly increased with increasing latitude for both total and caudal vertebral number. Increasing length with latitude (sensu Bergmann's rule) was also supported, but the predictions for Jordan's rule held when controlling for standard length. Pleomerism was weakly evidenced. Gasterosteus aculeatus exhibited sexual dimorphism for Jordan's rule, with both sexes having more vertebrae at higher latitudes, but only males showing a positive association between latitude and the ratio of caudal to abdominal vertebrae. The number of dorsal- and anal-fin rays and basals increased with increasing latitude, while pectoral-fin ray number decreased. This study reinforces the association between phenotypic variation and environmental variation in marine populations of G. aculeatus.
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Testing a Claim about Population Proportion
There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...

