Hi all,
I trying develop a code to implement a recommendation of Wilson et al (1991). In they text formula:
"...
LnA' = fitted mean ln abundance; sigma = fitted standar deviation of ln abundance.
In ranked-abundance terms:
lnAi = lnA' + sigma * fi^-1 * (S-i+0.5)/S
Where
S = number of species; Ai = abundance of ith out of S species; fi^-1 =
inverse cumulative distribution function of a norma distribution, i.e.
the ln abundance at which the area under the normal curve is the value
indicated.
..."
I developed this code:
rank.lognormal<-function(x){
? S <- length(x);
? xlog <- log(x);
? p <- ppoints(xlog);
? mulog <- mean(xlog);
? sdlog <- sd(xlog);
? fi <- function(y){ qnorm(y, mulog, sdlog)? };
? sapply(1:S, FUN=function(i){ exp(1) ^ (mulog + sdlog * fi(p[i]) * (S-i+0.5)/S) });
}
bci<-c(25, 24, 22, 21, 18, 17, 15, 14, 14, 13, 13, 12, 12, 11, 11,
?????? 10, 9, 8, 7, 6, 6, 6, 6, 5, 5, 5, 5, 5, 5, 4, 4, 4, 4, 4, 4,
?????? 3, 3, 3, 3, 3, 3, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2,
?????? 2, 2, 2, 2, 2, 2, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
?????? 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1);
sum(rank.lognormal(bci))
plot(log(rank.lognormal(bci)))
But the sum of fitted rank don't match with the sum of rank abundance. The curve don't like lognormal too.
I know rad.lognormal of vegan package, but I'd like follow Wilson recommendation and understand how this procedure works.
Thank you.
Best,
Mario
Wilson et al 1991 Methods for fitting dominance/diversity curves - Journal of Vegetation Science.
http://onlinelibrary.wiley.com/doi/10.2307/3235896/abstract
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Master student in Ecology
Institute of Biology, Dept. Plant Biology, Ecology Lab.
State University of Campinas - UNICAMP
Campinas, S?o Paulo, Brazil