zigzag confidence interval in a plot

Dear All,

When I plot the values and linear regression line for one data set, it is fine. But for another one I see zigzags, when I plot the confidence interval

cd

Depth	CHAOsep12RNA
9,94	804
25,06	1476,833333
40,04	1540,561404
50,11	1575,166667
52,46	349,222222
54,92	1941,5
57,29	1053,507042
60,11	1535,1
70,04	2244,963303
79,97	1954,507042
100,31	2679,140625

plot(cd$CHAOsep12RNA,cd$Depth, ylim = rev(range(0:100)), xlab="CHAO", ylab="Depth", pch=15, las=2, main="Sep12-RNA", cex.main=1)
lmR <- lm(cd$Depth~cd$CHAOsep12RNA)
abline(lmR)

pconfR <- predict(lmR,interval="confidence")
matlines(cd$CHAOsep12RNA,pconfR[,c("lwr","upr")], col=1, lty=2)

I also tried

newx <- seq(min(cd$CHAOsep12RNA), max(cd$CHAOsep12RNA), length.out=11)
a <- predict(lmR, newdata=data.frame(CHAO=newx), interval=c("confidence"))
plot(cd$CHAOsep12RNA,cd$Depth, ylim = rev(range(0:100)), xlab="CHAO", ylab="Depth", pch=15, las=2, main="Sep12-RNA", cex.main=1)
abline(lmR)
lines(cd$CHAOsep12RNA, a[,2], lty=2)

But I see both cases kind of zigzags. What can it be the reason? thank you!