반추위 in situ 실험을 수행한 이후 소실율 데이터를 이용하여 degradation parameters 및 effective degradability calculator을 계산하는 함수입니다.

1. Degradation parameter was made using the formula of Ørskov and McDonald (1979): $$P = a + b × ( 1 - e^-ct)$$
• where P: the actual degradation after time ‘t’; a: the intercept of the degradation curve at time zero; b: the potential degradability of the component of the protein which will, in time, be degraded; c: the rate constant for the degradation of ‘b’; t: time.
1. The effective degradability (ED) of DM and CP was calculated using the following equation: $$ED = a + (b × c)/(c + k)$$
• where k was the estimated rate of outflow from the rumen and a, b, and c are the same parameters as described above.
• The ED was estimated as ED2, ED5, and ED8 assuming rumen solid outflow rates of 0.02, 0.05, and 0.08/h, which was representative for low, medium, and high feeding intake respectively (ARC, 1984).

### R codes for calculation

#### for single data

hour<-c(0,2,4,8,16,24,48)
DMD<-c(90,88,80,75,58,43,10)

insitu<-function(hour,DMD){

require(dplyr)

df<-data.frame(hour,DMD)
n<-nrow(df)

df1<-mutate(df, DMD_1=(DMD-DMD[n])/100)
df2<-df1[-n,]
df2<-mutate(df2, DMD_exp=(log(DMD_1,exp(1))))

reg<-lm(df2$DMD_exp~df2$hour)
reg<-reg$coefficients intercept<-reg x<-reg b<-exp(intercept)*100 a<-100-b-df1$DMD[n]
c<-(-x)
ED2<-a+((b*c)/(c+0.02))
ED5<-a+((b*c)/(c+0.05))
ED8<-a+((b*c)/(c+0.08))

result<-data.frame(Item=c("a","b","c","ED2","ED5","ED8"), Value=c(a,b,c,ED2,ED5,ED8))

print(result)

}

insitu(hour,DMD)

#### for multiple data

library(dplyr)

result<-data.frame(Item=c("a","b","c","ED2","ED5","ED8"),"1"=NA,"2"=NA,"3"=NA,"4"=NA,"5"=NA,"6"=NA)

for(i in 1:14){

hour <- c(0,8,16,24,48)
DMD <- insitu[,i]

df<-data.frame(hour,DMD)
colnames(df) <- c("hour","DMD")

n<-nrow(df)
DMD_end <- as.numeric(DMD[n,])

df1<-mutate(df, DMD_1=(DMD-DMD_end)/100)
df2<-df1[-n,]
df2<-mutate(df2, DMD_exp=(log(DMD_1,exp(1))))

reg<-lm(df2$DMD_exp~df2$hour)
reg<-reg$coefficients intercept<-reg x<-reg b<-exp(intercept)*100 a<-100-b-df1$DMD[n]
c<-(-x)
ED2<-a+((b*c)/(c+0.02))
ED5<-a+((b*c)/(c+0.05))
ED8<-a+((b*c)/(c+0.08))

result[1,i+1] <- a
result[2,i+1] <- b
result[3,i+1] <- c
result[4,i+1] <- ED2
result[5,i+1] <- ED5
result[6,i+1] <- ED8

}

### Literature cited

1. ARC, 1984. The Nutrient Requirements of Ruminant Livestock, Suppl. No. 1. Agricultural Research Council, Commonwealth Agric. Bureau, Farnham Royal.
2. Ørskov, E. R., and I. McDonald. 1979. The estimation of protein degradability in the rumen from incubation measurements weighted according to rate of passage. J. Agric. Sci. 92:499.