Help us interpretate this graph (EIGEN)!

[RaRo Team]

Hey people, we are new to this forum! We are two students from environmental sciences and we created a graph that we can't interpretate. We put this in "analysis" because we think that is a very complicated graph from a strange equation, so, we think this is the better place. If we are not right, please tell us!

Well the fact is that we were using "R" to study ecology population of some fish specie.

We created a vector to study the population increase in a empty river starting from 100 individuals. Then we used the eigen analysis (eigen matrix) to know the transition matrix of that population in 50 years. Then, we plotted the eigen analysis, and we came out with our unknown graph.

Obviously we commited some error during our reasoning, or during the programation of the plot / matrix. So we want to know what have we done wrong, or if the graph its OK and we just don't know how to interpretate it.

 

We researched the internet the eigen matrix and we found its about changing some vectors and giving that changes a value from 0 to 1 (or something like this).

We have some hughe lack of knowledge on this area so we want to know exactly what we found and if we are wrong or we just did things wrong.

 

I attach the R code so if someone knows to program in R or S language, could find the error.

taxvit <- list(

sou = 0.8, #egg surv

s0 = 0.045, #1yo surv

sa = 0.57, #1yo surv and 2+yo surv

pf3 = 0.62, #rep. prov 3yo

pf4 = 0.94, #rep. prov 4yo

pf5 = 0.20, #rep. prov. 5yo

f3 = 106, #average size 3yo(rep)

f4 = 188, #average size 4yo(rep)

f5 = 280) #average size 5yo(rep)

# postreproduction symbolic transition matrix:

matsim <- expression(0, 0, 0, pf3*f3*sou*0.5, pf4*f4*sou*0.5, pf5*f5*sou*0.5, 0,

s0, 0, 0, 0, 0, 0, 0,

0, sa, 0, 0, 0, 0, 0,

0, 0, sa, 0, 0, 0, 0,

0, 0, 0, sa, 0, 0, 0,

0, 0, 0, 0, sa, 0, 0,

0, 0, 0, 0, 0, sa, 0)

# evaluate the symbolic matrix, matsim,

Apre <- matrix(sapply(matsim, eval, taxvit), ncol=7, byrow=TRUE)

rownames(Apre) <- colnames(Apre) <- c("Alevi", "Juvenil", "Adult +2", "Adult +3", "Adult +4", "Adult +5", "Adult +6")

Apre

# population vector, 100 individuals 3 and 4 yo matrix

n100 <- matrix(

c(0, 0, 0, 50, 50, 0, 0),

ncol=1)

# multiply matrix per vector

new <- Apre %*% n100

# popbio package

install.packages("popbio")

library(popbio)

n<- pop.projection (Apre, n100, 51)

n

lambda(Apre)

#graph projection from now to 50 years

plot(n$stage.vectors)

plot(n$pop.sizes, type="l", xlab="years", ylab="pop size")

n0pre <- matrix( c(0, 0, 0, 0, 100, 0, 0), ncol=1)

n<-pop.projection (Apre, n100, 50)

n

lambda(Apre)

plot(n$stage.vectors)

plot(n$pop.sizes, type="l", xlab="yrs", ylab="populationsize")

#eiugen function

vp<-eigen(Apre)

vp

plot(vp$vectors)

plot(vp$vectors, type="l", xlab="years", ylab="population size")

I also attach the graph (obviously)


Thank you for your attention and sorry for our lack of knwoledge. Tell us if we have done something wrong posting this here.


PS: Anys == Years

Mida de població == Population size

Edited November 13, 2014 by RaRo Team