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FourHnullplaneD <- function(boots) {
#Collect each of the dimensions of the 4H index, and sigma
union<-boots[,2]
intersection<-boots[,1]
gain<-boots[,3]
loss<-boots[,4]
sigma<-boots[,5]
#For each bootstrap, calculate theta
theta<-gain+loss
#Use theta to calculate the expected union fraction for each bootstrap
union_expectation<-(1-sigma)*(1-theta)
#Use theta to calculate the expected intersection fraction for each bootstrap
intersection_expectation<-sigma*(1-theta)
diffI<-intersection-intersection_expectation
diffU<-union - union_expectation
#Make a histogram of the difference between the true intersection dimension and the expected intersection dimension
#This will be positive when the true intersection is more than the expected intersection (hybrids are more likely to retain microbes shared by both progenitors)
graphics::hist(intersection-intersection_expectation)
#Mean intersection preference:
mean_intersection_preference<-mean(intersection-intersection_expectation)
#Standard deviation in intersection preference:
sd_intersection_preference<-stats::sd(intersection-intersection_expectation)
#p-value (fraction of bootstraps where the true intersection was LESS than the expected intersection):
p_value_intersection_preference<-length(which(intersection-intersection_expectation<0))/length(union)
expectationdf<-data.frame(sigma,theta,union,union_expectation,intersection,intersection_expectation,diffI,diffU)
return(list("trials"=expectationdf,"mean_intersection_preference"=mean_intersection_preference,"standard_deviation_intersection_preference"=sd_intersection_preference,"p_value_intersection_preference"=p_value_intersection_preference))
}
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