Their behaviour could be grouped in ways not derived primarily by sex?

The article links to another one[1], which might be boiled down to

> [...] peacocks still do not have genders. And the reason is that peacocks do not have culture.

[1] https://nautil.us/no-animals-do-not-have-genders-237938/

If you define socially constructed to mean a _human_ sort of society (which is probably how most people will read this, and the most reasonable way to read it), then they don't by definition.

I suspect to some extent you could argue this either way for social insects, however; is their 'society' so biologically programmed in that the pseudo-gender identities it _appears_ to create don't count?

There are also some primates which have, if not societies, things which look suspiciously like societies, of course. Still, the statement is probably basically true, with a little fuzziness around the edges.

Probably just simple observation - if culture was an element then we would expect to see diverging behaviors in different groups. Wouldnt require communicating.