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I am referring to Winn et al. 2011

Last sentence of the first paragraph is

Although sampling bias against both selfing and highly outcrossing species may inflate the frequency of mixed-mating populations, the number of species reported to show mixed mating is not trivial, and calls into question the status of mixed-mating populations as transitional, and therefore the sufficiency of the theory to explain the observed distribution of mating systems in hermaphroditic species.

I do not really understand what is the logic behind the highlighted part and what is its purpose.

  1. Is the number of mixed mating species supposed to be trivial in a case where the number is inflated (So there is a need to clarify it is non trivial)?

  2. How does the fact that it is not trivial bring up the question below the highlighted part?

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    $\begingroup$ I edited your post. Feel free to roll back if you don't like the edit $\endgroup$ – Remi.b Oct 18 '16 at 6:02
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I think the main message of the quote is

"Many would have expected that mixed mating can only exist as a transitional state and thought that stable equilibriums are either pure selfing or pure mixing (or both). The observation of a non-trivial number of mixed mating populations suggest that our expectations were wrong."

The first sentence of the quote is a statistical detail of their paper and not a premise for the conclusion that there is a non-trivial number of populations that show mixed mating.

The evolution of selfing is a large topic in evolutionary biology and cannot really be summarized in a single post (even more so that many question are still open to debate). Goodwillie et al. 2005 is a review on the subject that will help you understand the work that has been done on the evolution of selfing. Very related is the evolution of hermaphrodism, dioecy and other mating systems in plants. Pannell 2002 is a very good paper on the evolution of androdioecy and the maintenance of these unexpected mating systems.

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  • $\begingroup$ If the first sentence is only a detail, then why does it use "although" to begin the sentence? I would assume the first sentence is somehow supportive of the opinion that the number of mixed mating species should be trivial. That is exactly where I do not understand why (the relationship that "inflation" implies "trivial"). $\endgroup$ – cr001 Oct 18 '16 at 6:10
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As I understand the section, it could be rephrased as:

Even though the frequency of mixed-mating populations might be artificially inflated due to sampling bias against both selfing and highly outcrossing species, this is only a partial explanation. Also when taking the sampling induced bias into account (i.e. controlling for sampling bias), the number of mixed-mating species is still not insignificantly small. This observation challenges the notion that mixed-mating populations are supposed to be transitional, and therefore also the current theory used to explain the observed distribution of mating systems in hermaphroditic species.

So, for you questions, I would say:

  1. The number of mixed mating species is non-trivial (i.e. not small and insignificant), even after removing the inflated numbers caused by sampling bias.

  2. The fact that the number is non-trivial, and not only caused by a sampling artifact, fits poorly (according to the authors) with the idea that mixed-mating populations are supposed to be transitional. Therefore, by extension, the observation of a non-trivial frequency of mixed-mating populations also challenges the theory used to explain mating systems in hermaphroditic species.

As a final sidenote, this question could just as well be posed at English-SE (or SE-English language learners), since it is mostly a question about the english language.

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