What can the F2 hybrid P-matrix tell us about craniofacial traits on SSI?
In this study we include calculations of the regression coefficient and the squared correlation coefficient between traits. The regression coefficients calculated in this study describe how much change is observed in Trait B when Trait A increases by one unit. Values close 0 suggest that Trait A has little effect on Trait B, values close to positive or negative one suggests that the magnitude of change A and B are similar, and values outside of negative to positive one range suggest that change in Trait B exceeds that of Trait A (although the sign dictates if the change is in the same direction as Trait A; Kelly 2009). The formula for squared correlation coefficients is often used between genetic loci to calculate the strength of association between alleles (i.e. r2 as a measure of linkage disequilibrium; VanLiere and Rosenberg 2008). In the context of this study, high values suggests that individuals with large trait values for Trait A also have large values for Trait B and vice versa. Interpreting the patterns of both estimates together may give us insight into the traits which are integral to producing the unique craniofacial pupfish traits found on SSI. For instances, head depth in both Little Lake and Crescent Pond produced the largest amount of change in other traits which could mean that the underlying mechanisms responsible for variation in this trait are reused across most other craniofacial traits in pupfishes. Maxilla length and palatine height in Crescent Pond, and lower jaw length and dentigerous arm width in Little Lake also produced large changes in other traits further supporting this idea. The average squared correlation coefficients were also significantly higher for these traits compared to most of the remaining traits in the dataset. From a mechanistic view point this pattern may reflect high levels of linkage disequilibrium or it may suggest that these traits utilize a shared underlying mechanism either through pleiotropy or shared genetic or developmental pathways. Previous work in pupfishes has found differential gene expression and fixed single nucleotide polymorphism differences between species for regions of the genome associated with the wnt signaling pathway which has ties to craniofacial diversity across a wide array of organisms (Lencer et al. 2017; Lencer and Mccune 2020; Richards and Martin 2022). While much more work is needed to determine if this specific pathway produces the observed craniofacial diversity on SSI, these previous results support at least the possibility of the reuse of a conserved evolutionary pathway as a mechanism for producing pupfish diversity.