lambda {formula}										R Documentation


Function to calculate population growth rates



Description:

	~~ The function returns the value for the assymptotic growth rate (lambda) and intrinsec population growth rate (r) from given values following a partial life-cicle model (Oli and Zinner 2001, Stahl and Oli 2006), which in this particular case has the assumption that every individual reachs maturity with one year after the individual had born.


Usage:

	lambda=function(x, nomes=x[,1], Pa=x[,2], Pj=x[,3], m=x[,4], save=FALSE|TRUE)
	

Arguments:

 	x 	- an object with the name of the species, if you will set the values for all the arguments, or a dataframe which columns must follow the order: nomes=x[,1], Pa=x[,2], Pj=x[,3], m=x[,4];
	Pa	- the survival probability for adults;
	Pj	- the survival probability for juveniles;
	m	- the fecundity, as rate of female produced per female monitored in one season;
	save	- the function automatically save the result as a dataframe object in a file .RData (save=TRUE); to show the dataframe in the console set save=FALSE.


Value:

     lambda calculates the value of assymptotic growth rate (lambda, λ) and the intrinsec population growth rate (r). If values of lambda are close to 1 and r close to 0, the population seems as stable (λ ≈ 1, r ≈ 0), 



Details:

	##### original equation:  λ^(alfa+1)-((λ^alfa)*(Pa))-(Pj^(alfa-1)*F*λ)+(Pj^(alfa-1)*F*Pa)-Pj^(alfa)*F=0   (Stahl and Oli 2006)

	where alfa is the age of maturity (here, alfa=1).


Warning:

	I do not take any responsability on the results if you set crazy numbers for modelling.


Author(s):

     André M. X. Lima (versão:1.2012)

References:

    - Oli, Madan K., and Bertram Zinner. 2001. Partial life-cycle analysis: a model for birth-pulse populations. Ecology 82:1180–1190
    - Stahl, Justyn T. and Oli, Madan K. 2006. Relative importance of avian life-history variables to population growth rate. Ecological Modelling 198:23-39.


Example:

##checking lambda for a single population

x="name of the species"
lambda(x, Pa=0.78, Pj=0.6, m=1.2, save=FALSE)


##checking for several populations or species

nomes=c("C.melanops","M.gularis","T.caerulescens","D.mentalis","P.nudicollis")
Pa=c(0.44, 0.5, 0.6, 0.8, 0.92)
Pj=Pa/1.5
m=c(0.4, 0.6, 0.8, 0.5, 0.3)
(x=data.frame(nomes, Pa, Pj, m))

lambda(x, save=FALSE)
lambda(x, Pj=0.5, save=TRUE)
lambda(x, Pj=0.5, save=FALSE)