The analysis of association between traits when differences between trait States matter.

Area of Science:

• Ecology
• Population Genetics
• Genomics
• Biostatistics

Background:

• Measures of association are crucial across scientific disciplines.
• Existing methods often overlook associations between complex traits with variable state differences.
• Complex traits include genetic characters, species attributes, and environmental variables, which can be mutually and asymmetrically associated.

Purpose of the Study:

• To develop a concept of directed association for complex traits.
• To introduce new measures for quantifying trait relationships and differentiation.
• To explore applications in various scientific fields.

Main Methods:

• Developed a concept of directed association based on difference measures between trait states.
• Considered associations at three levels: individual states, individual state to variable totality, and between variables.
• Identified relations to existing association and differentiation concepts.

Main Results:

• Introduced a new framework for directed association between complex traits.
• Demonstrated that measures at two levels are interpretable as differentiation measures.
• Provided examples of applications in functional relationships, variation distribution, genomic associations, and spatiogenetic structure.

Conclusions:

• The developed concept offers a novel approach to understanding trait associations, especially for complex and asymmetric relationships.
• The proposed measures provide valuable tools for analyzing differentiation in population genetics, ecology, and genomics.
• This framework enhances the analysis of complex biological systems and their spatial structures.