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Extreme male reproductive skew limits effective population size in American Standardbred horses
Robin S Waples1, Anas M Khanshour2, E G Cothran2
1School of Aquatic and Fishery Sciences, University of Washington, Seattle.
Abstract:
Standardbred horses are widely used for harness racing in North America, Europe, Australia, and New Zealand. In the U.S., two gaits (Pacers and Trotters) are genetically differentiated at a level typical for different horse breeds. We used the complete pedigree for all registered American Standardbred foals born 1970-2014 (>200 K Trotters and > 500 K Pacers) to calculate annual and lifetime reproductive skew and its consequences for the effective number of breeders per year (Nb) and effective size per generation (Ne). With rare exceptions, females can only produce 0 or 1 foal per year, which limits annual and lifetime variance in offspring number. These constraints do not apply to males: with humans (rather than horses) deciding who breeds with whom, and how often, the most prolific stud regularly sires well over 100 foals each year and often over 1000 across its lifetime. Male reproductive skew increased over time in both gaits, with the most prolific studs producing 20% or more of all foals sired by members of their birth cohort. Although each gait in the U.S. is represented by tens of thousands of adult horses at any given time, male Ne is typically in the low hundreds, which drives the overall Ne/N ratio to or below 0.01-a value often considered to be "tiny." Ne/N ratios this low have rarely been reported for large mammals and generally are thought to apply primarily to some marine species with very high fecundity. When Ne/N is this low, even large populations can experience substantial erosion of genetic diversity.
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There are two methods of testing a claim about a population proportion: (1) Using the sample proportion from the data where a binomial distribution is approximated to the normal distribution and (2) Using the binomial probabilities calculated from the data.
The first method uses normal distribution as an approximation to the binomial distribution. The requirements are as follows: sample size is large...

