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.