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I am doing a study to compare plant species richness (total number of species per site) to a bunch of environmental factors of sites at which these plants were surveyed. Because these sites are different in size, I have converted species richness to a species density measurement by dividing by the log of site area (species density = species richness/log[area]).

I log-transformed area, because the relationship between species richness and area at my sites is linear on a semi-log scale. Now that I have calculated species density in this way, I am having a hard time convincing myself that calculating density with log(area) was the correct approach. Does anyone have some insight on this? My community ecology background is not strong and I am getting bogged down in the literature.

Thanks!

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Let me offer my answer even though I have not worked in ecology.

You are asking two questions if I understand you correctly:

  1. Should you normalize to the area sampled?

The answer to that depends on whether the area sampled is a nuisance variable or not. Is it the case that you just happened to sample from areas with (largely) different sizes? Or do you rather expect or are interested in whether it may display some interaction with the environmental factors that you study? In the first case, normalize with clear conscience. On the latter, you should probably include the area sampled in your model. The reason for this is that by normalizing, you are assuming that the relationship between the response variable (number of species) and the predictor (area sampled) is fixed and has a slope of 1 irrespective of the variation of the rest of the variables included in your model. If that is not the case, you want to explicitly add the area sampled as a fixed factor in your model.

  1. Should you log-transform the area sampled?

If the answer to the first question is that the area sampled is a nuisance variable then it does not matter whether you log-transform or not as now you are interested in a new measurement, species density. Hence, you may work with the untransformed variable which would simplify the interpretation of the results by a tiny bit. If the answer to the first question is that you want to investigate the interaction of the variable 'area sampled' with your other predictor variables, then you do not need to log-transform your variable as this is rarely needed, even if you use parametric inference. To summarize, you do not need to transform the variable 'area sampled'.

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  • $\begingroup$ If the relation between species richness and area is linear on a semi-log scale (as the question states), wouldn't it be best to include log[area] in your model ? $\endgroup$ – RHA Sep 14 '17 at 12:16
  • $\begingroup$ Assuming that you will use a model with a linearity assumption, you don't need to transform the predictor variable. It's only a matter of taste for the interpretation of the results. The most common variable to transform is the response variable, if needed. But I am assuming that this follows a discrete distribution like poisson. So you wouldn't perform a linear regression but a poisson regression. We would need more details about the analysis to say more. $\endgroup$ – vkehayas Sep 14 '17 at 12:34
  • $\begingroup$ If you choose to study species density, which will follow a log-normal distribution as I understand, then you will probably need to transform the species density response variable, or use a GLM with a log-link. $\endgroup$ – vkehayas Sep 14 '17 at 12:36
  • $\begingroup$ I think that the latter will be the case. However, I am beginning to wonder if this question shouldn't be migrated to stats.exchange... $\endgroup$ – RHA Sep 14 '17 at 12:38
  • $\begingroup$ The important factor of the question on whether to normalize or not is a biological question (see my point 1). Regarding log-transformation of a predictor variable you will find many (potentially duplicate) posts in stats.exchage, including the one I linked. $\endgroup$ – vkehayas Sep 14 '17 at 12:43

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