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It's possible that this question is better suited for stack overflow, but I think the ecologists on this site might be better equipped to answer it.

I'm trying to study two geographically-isolated populations of the same species. Inspecting the distributions, I see that both are bimodal (there's some seasonality to their occurrence), but the peaks in one population are much higher and much narrower (i.e., the variance of the local peaks is smaller).

What sort of statistical test would be appropriate to determine whether these differences are significant?

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There's now way that I could ever answer this, but it seems a little cryptic. What is the parameter that is being measured in these distributions? –  Alan Boyd Nov 18 '13 at 18:51
    
Number of individuals caught in a trap on the y-axis, julian day on the x. –  Atticus29 Nov 18 '13 at 18:53
    
While I am sure someone on this site could help you, this is really better suited to Cross Validated since the fact that you are looking at biological data is completely irrelevant to the actual question. I suggest you flag your post for moderator attention and ask them to migrate it. –  terdon Nov 18 '13 at 19:25
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I think that the question is useful here as well - this type of problems are common in ecology and there also exists a number of relatively ecology-specific software for studying this. @terdon –  fileunderwater Nov 18 '13 at 19:33
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@fileunderwater I agree which is why I did not vote to close. I just think the OP is likelier to get an answer on the stats site. There are more users and all of them are stats people. Here we have both fewer users and a smaller percentage of statsheads. –  terdon Nov 18 '13 at 19:42
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1 Answer

These are just some preliminary ideas...

I think you should look at the seasonal distributions separately, since the bimodal distribution is the outcome of two fairly separate processes. The two distributions might also be controlled by different mechanisms, so that e.g. winter distributions might be more sensitive to yearly climate. If you want to look at population differences and reasons for these I think it is therefore more useful to study seasonal distributions separately. An exploratory analysis could be to compare distribution percentiles (north/south and east/west coordinates) to look at range edges, or to use a fixed number of edge observations to establish borders. The weighted centre-point of population distributions can be used to look for differences in overall position. If you have grid occurences, percentage overlap between species/populations could maybe also be useful.

If you haven't already, you look also look at Maxent, which is a widely used software for modelling species distributions and habitats. Look at Elith et al. (2011) for an overview. If you want to look at changes over time (even if this doesn't seem to be your main point) you should also check out dynamic occupancy models that use occurrence records to model species distribution while taking detectability into account, e.g. MacKenzie et al. (2009).

As for a simple test for differences in variance (basically a test of homoscedasticity), there is Levine's test, which is used to compare variances of distributions between groups. Bartlett's test is an alternative, but Levene's test is supposed to be more robust to non-normality. In R the Levene's and Bartlett's tests are found in library(car). However, these are only suitable for unimodal distributions so, again, you should look at seasons independently.

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