Dear morpho people,

I am writing to ask a rarely discussed question, which is to test 
associations between genomic data and shape variation.

To describe my system and bit first, I am working with four sympatric fish 
morphs in a lake. I have both genetic data (SNP generated by ddRADSeq, 
around 12000 SNPs) and shape data (landmarks and semilandmarks-based GM for 
the head shape) of the same fish samples. The genetics indicate that three 
morphs are genetically distinct, while one is of hybridization origin 
between two morphs with different degrees of introgression. I like to ask 
the question: for the three related morphs (two parental morphs and one 
hybrid morph) there any correlation between the degree of genetic 
introgression and the shape variation? 

I was suggested to apply a 2b-PLS to test it. Then I searched for some 
literature and find a few cases. However, the studies vary for the input 
data of both genetics and morphometrics. For genetics, people have used 
genetic distances (calculated as Fst/(1-Fst), Fst is a measurement of 
genetic differentiation), Prevosti distance, allele frequencies (a few 
microsatellites), and expression results (numeric and continuous). For the 
shape data, people used Eucidean distances, GPA coordinates, centroid 
sizes, etc.

So my questions are:
1. Do you all agree that sb-PLS should also make sense for such a 
comparison?
2. What you will suggest for the input files? (I do have some 
considerations to discuss)
3. Is there any other analysis you will recommend? 

I know normally people will use GWAS to search for associations, however, I 
am looking for something that can tolerate a smaller sample size (30 fish 
per morph). Also, the potential transgressive shape of hybrids may be a 
confounding factor, especially there is different allometry observed.

I appreciate all kinds of suggestions and comments.

Best regards,
Han Xiao

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