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When I had lunch with two phoneticians the other day, the question came up whether there is a correlation between the size of the phoneme inventory of a language and its population size. Neither of us knew, and we started to speculate in which direction it should go. My guess was that larger languages should have smaller inventories and vice versa, while the two expert expected the opposite. One of the reasons for my conjecture was the observation by Lupyan and Dale (2010) in Plos ONE (Lupyan G, Dale R (2010) Language Structure Is Partly Determined by Social Structure. PLoS ONE 5(1): e8559. doi:10.1371/journal.pone.0008559) that larger languages tend to have less morphological complexity (and vice versa). Lupyan and Dale speculate that this may be due to the fact that large language communities comprise a larger proportion of L2 learners. As L2 learners - I am simplifying here, of course - have a hard time acquiring all morphological complexities, they cause an overall simplification of their adopted language in the long run.Well, as most of us know from own frustrating experience, mastering the sound inventory of a foreign language as an adult is even harder than mastering the morphology. By the same logic, one should assume that larger languages, having more L2 speakers, have a smaller sound inventory.The following day I learned that this issue has been resolved already back in 2007, in a Language article by Jennifer Hay and Laurie Bauer (Phoneme inventory size and population size, Language 83(2), 388-400). They found exactly the opposite of what I expected - so the phoneticians were right and I was wrong.As I had started to explore this issue on my own already, I want to share my findings nevertheless, even though its no news anymore.I went to the data base of the Automated Similarity Judgment Program (http://wwwstaff.eva.mpg.de/~wichmann/ASJPHomePage.htm), which consists of 40-item Swadesh lists from more then 5,000 languages and dialects. All words are given in a uniform, rather coarse grained phonetic transcription. Conveniently, the data base also reports population size according to Ethnologue. As a crude measure of the sound inventory of a language, I simply counted the number of different symbols occurring within its Swadesh list. The method is quick and dirty because (a) the transcriptions are phonetic rather than phonemic, so I count different sounds rather than different phonemes and (b) there is no guarantee that all sounds of a language occur within such a short word list, but it should give us a rough idea at least.Plotting population size against sound inventory size looks like this:The tendency is obviously the same that Hay and Bauer report: small languages tend to have small sound inventories and vice versa. Here is some statistics if you care for numbers rather than images:correlation between log population size and sound inventory size: 0.26, 95% confidence interval: (0.24,0.28), p&#60; 2e-16.a linear regression of sound inventory size against log population size gives R-squared = 0.067. When controlling for the size of the word list (because ASJP has many missing entries, and sometimes we have more than one word per concept), R-squared is still 0.064.So, to put it in a crude way: small languages tend to have few sounds and many morphemes, and large languages behave the opposite way. Now the question arises: are phonology and morphology independently affected by population size, or is there something to this popular myth after all that there is a tradeoff in complexity between different levels of linguistic structure?P.S. It turns out that this is not just old news, but very old news. Basically the very same analysis, along with a lot of other interesting stuff, can be found in a 2011 paper by Wichmann, Rama and Holman: http://www.degruyter.com/view/j/lity.2011.15.issue-2/lity.2011.013/lity.2011.013.xmlP.P.S. Wichman et al. did their study with version 13 of ASJP, while I used version 15. So my work was not entirely in vain. Also, they show that there is a negative correlation between population size and average word length. Since there is also a negative correlation between average word length and sound inventory size, the causal chain might be something likelarge population -&#62; shorter words -&#62; more phonemesHowever, when I control for average word length (in the ASJP word list), the correlation between log population size and sound inventory size is still signficant, r=0.18, R-squared=0.03. With the caveat that (unweighted) average word length in a 40-item Swadesh list is a very crude estimate of average word length in actual language use, it seems that the effect of population size on sound inventory size cannot fully be mediated by word length.