|Created: 22 Sep 2014||Modified: 23 Jul 2020||BibTeX Entry||RIS Citation|
I’m throwing out the data from
equifinality-1 because I believe the innovation rates were off in the simulation code. The observed number of variants in the population were much higher than I’d expect given the Wright-Fisher estimates from the frequency spectrum, so I checked deeper with both population and sampled data. It wasn’t simply a factor of two, either, which is the usual difference between WF and Moran dynamics for some quantities.
I looked at Ewens (2004) again, and added a method to the
pytransmission library to calculate the expected number of alleles in a sample, and its variance, given Equations 3.83 - 3.86.
These changes are split across the
pytransmission codebases, involving at most single lines of code in several places.
One potential issue is that I have two possible implementations of a neutral copying model, and one for frequency-dependent bias.
There is, in a sense, no “right” way to write a copying algorithm. Most cultural evolutionary models of bias in the anthropological literature employ a single locus, and thus there is no difference. In the genetic case, “all-locus” copying is overwhelmingly more common than single locus copying, due to the nature of genetic replication.
In the cultural case with many traits, it is distinctly a modeling choice. We might postulate, for example, that “all-trait” copying is likely prevalent only in early childhood development and social learning, when children are exposed to their parent’s cultural repertoire at high frequency and intensity. In contrast, we might expect that single trait copying would be the typical mode for adult individuals, as they engage in social learning within a specific task or context, with consequently smaller changes in their overall repertoire. This kind of developmental change, incidentally, may help account for why some aspects of cultural repertoires exhibit slow change empirically, despite the rapidity with which traits turn over in our simple models. By narrowing the “volume” of a repertoire that is changed at any given time as an adult, cultural evolution becomes “conservative” without necessarily employing frequency-dependent bias or homophilic preferences.
So, in a sense, we could consider equifinality issues between both “all-locus” and “single-locus” neutral models, and bias models with both types of copying. Currently, the design of the FD bias algorithm makes it difficult to perform an “all-locus copy”, and it’s not entirely clear what it means to perform a biased copy of “most common” or “least common” traits. Do we:
One way to resolve this issue is to restrict the current study to copying models which are most realistic for adult learners: single trait copying models. Employing the
NeutralRandomLocusCopyingRule in direct comparison to the
ctmixtures creates an apples-to-apples contrast.
The downside is that the neutral single-locus copying rule does not directly calibrate with the analytic expectations of the Moran infinite-alleles process, as described by Ewens, but today’s multiple calibration runs sheds light on why this is the case.
I feel comfortable configuring simulation runs for
equifinality-2, using the revised code, which will be released as Version 2.4.
Ewens, Warren J. 2004. Mathematical Population Genetics, Volume 1: Theoretical Introduction. 2nd ed. New York, Springer.