Question on theta values and optimization

[jdalapicolla]

Dear Dr. Pope,

My name is Jeronymo Dalapicolla, a postdoc at the Instituto Tecnólogico Vale in Belém, Brazil. We have a question about a specific warning that we're getting when we try to run the radish with our data. The warning is the following:

"warning ("Optimum for subproblem is on boundary (e.g. no spatial genetic structure): cannot optimize theta. \ nTry different starting values. ")"

We tried different starting values for theta (1, 10, 100) but the warning remains. When we run your ex ample script and data, everything runs perfectly.

Our data are geographically restricted (around 50 Km²) with some samples aggregated, located in the same pixel. In addition, We are using Relatedness as a genetic metric instead FST. We also tested with coordinates in decimal degrees and in UTM. Same warning in all tests.

With this warning, the object “ fit_nnls” is created but when we applied summary (fit_nnls) the results did not indicate the estimates, only values of Loglikelihood, AIC, alpha, beta, and thau.

Thus, we would like to ask if you have any tips to remove this warning:

1. Should we try larger values for theta?
2. Should we remove individuals from the same localities/pixels?
3. Are there another option that we haven't tried yet?

Thank you so much for your time,
Have a nice week,
Sincerely,

Jeronymo Dalapicolla

[nspope]

Hi Jeronymo, If you are using relatedness (e.g. similarity) instead of divergence (dissimilarity), then that is the issue. The way radish works is that it constrains the slope of the genetic-vs-geographic distance regression to be positive: in other words, it makes the a priori assumption that divergence always increases with distance. It then tries to find "weights" for the spatial covariates that result in resistance distances that are most concordant with the observed genetic distance. If the optimizer ends up on the boundary (where the genetic-vs-resistance distance slope is 0) then it takes that to mean that there's no genetic structure and exits. Without this sign constraint on the regression slope, the optimizer can easily end up in local optima that are biological nonsensisical. Of course, for relatedness, you'd expect the slope to be negative (b/c genetic similarity decreases with distance). So the optimizer is ending up on the boundary. So: either flip the sign of relatedness, or use a different metric like distance from genetic covariance. There is also an option to disable the sign constraint on the slope, but I wouldn't recommend doing this. hth, Nate

[jdalapicolla]

Hi Nate

Thank you so much for your reply and explanation. We flipped the sigh of relatedness multiplying by (-1) and it worked!
Thank you again,

Sincerely,

Jeronymo