Computing observed T-statistics (T for Traits) and null expectations.

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Description

Computing observed T-statistics (T for Traits) as three ratios of variance, namely T_IP.IC, T_IC.IR and T_PC.PR. This function can also return the distribution of this three statistics under null models.

Usage

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	Tstats(traits, ind.plot, sp, SE = 0, reg.pool = NULL, 
	SE.reg.pool = NULL, nperm = 99, printprogress = TRUE)
	
	sum_Tstats(x, val.quant = c(0.025, 0.975), type = "all")
	
	ses.Tstats(x, val.quant = c(0.025, 0.975))
		
	## S3 method for class 'Tstats'
barplot(height, val.quant = c(0.025, 0.975), 
	col.index = c("red", "purple", "olivedrab3", "white"), ylim = NULL, ...)
                 
	## S3 method for class 'Tstats'
plot(x, type = "normal", col.index = c("red", "purple", "olivedrab3"),
	add.conf = TRUE, color.cond = TRUE, val.quant = c(0.025, 0.975), ...)
		
	## S3 method for class 'Tstats'
print(x, ...)
		
	## S3 method for class 'Tstats'
summary(object, ...)

Arguments

traits

Individual Matrix of traits with traits in columns. For one trait, use as.matrix().

ind.plot

Factor defining the name of the plot in which the individual is.

sp

Factor defining the species which the individual belong to.

SE

A single value or vector of standard errors associated with each traits. Especially allow to handle measurement errors. Not used with populational null model.

reg.pool

Regional pool data for traits. If not informed, 'traits' is considered as the regional pool. This matrix need to be larger (more rows) than the matrix "traits". Use only for null model 2 (regional.ind).

SE.reg.pool

A single value or vector of standard errors associated with each traits in each regional pool. Use only if reg.pool is used. Need to have the same dimension as reg.pool.

nperm

Number of permutations. If NULL, only observed values are returned;

printprogress

Logical value; print progress during the calculation or not.

x

An object of class Tstats.

height

An object of class Tstats.

object

An object of class Tstats.

val.quant

Numeric vectors of length 2, giving the quantile to calculation confidence interval. By default val.quant = c(0.025,0.975) for a bilateral test with alpha = 5%.

ylim

Numeric vectors of length 2, giving the y coordinates range

col.index

A vector of three color correspond to the three T-statistics.

color.cond

Logical value; If color.cond = TRUE, color points indicate T-statistics values significatively different from the null model and grey points are not different from null model.

type

For the plot function, type of plot. Possible type = "simple", "simple_range", "normal", "barplot" and "bytraits". For the summary function, type of summary statistics. Either "binary", "percent", "p.value", "site" or "all".

add.conf

Logical value; Add confidence intervals or not.

...

Any additional arguments are passed to the plot function creating the core of the plot and can be used to adjust the look of resulting graph. See plot.listofindex for more arguments.

Details

S3 method plot:

-Normal type plot means, standard deviations, ranges and confidence intervals of T-statistics.

-Simple_range type plot means, standard deviations and range of T-statistics

-Simple type plot T-statistics for each site and traits and the mean confidence intervals by traits

-Barplot type plot means, standard deviations and confidence intervals of T-statistics in a barplot fashion

-Bysites type plot each metrics for each sites

-Bytraits type plot each metrics for each traits

S3 method print: print the structure if the object of class Tstats

S3 method summary: print the summary statistics of the three T-statistics

Method summary sum_Tstats:

-Binary type only test if a T-statistics is significatively different from the null expectation for each trait.

-Percent type determine the percentage of sites were the T-statistics is significatively different from the null expectation for each trait. Asterix shows global significance of the test.

-P-value type determine the p-value (two unilateral tests) of the T-statistics for each trait and sites.

-Site type allows to know in which sites T-statistics deviate from the null expectation.

-All type do all the precedent type of summary.

Value

A list of statistics:

Tstats$T_IP.IC

Observed ratio between variance of individuals in populations and individuals in communities

Tstats$T_IC.IR

Observed ratio between variance of individuals in communities and individuals in the region

Tstats$T_PC.PR

Observed ratio between variance of populations in communities and populations in the region

$Tstats$T_IP.IC_nm

If nperm is numeric; Result of simulation for T_IP.IC

$Tstats$T_IC.IR_nm

If nperm is numeric; Result of simulation for T_IC.IR

$Tstats$T_PC.PR_nm

If nperm is numeric; Result of simulation for T_PC.PR

$variances$var_IP

variance of individuals within populations

$variances$var_PC

variance of populations within communities

$variances$var_CR

variance of communities within the region

$variances$var_IC

variance of individuals within communities

$variances$var_PR

variance of populations within the region

$variances$var_IR

variance of individuals within the region

$variances$var_IP_nm1

variance of individuals within populations in null model 1

$variances$var_PC_nm2sp

variance of populations within communities in null model 2sp

$variances$var_IC_nm1

variance of communities within the region in null model 1

$variances$var_IC_nm2

variance of individuals within communities in null model 2

$variances$var_PR_nm2sp

variance of populations within the region in null model 2sp

$variances$var_IR_nm2

variance of individuals within the region in null model 2

$traits

traits data

$ind.plot

name of the plot in which the individual is

$sp

groups (e.g. species) which the individual belong to

$call

call of the function Tstats

Author(s)

Adrien Taudiere and Cyrille Violle

References

Violle, Cyrille, Brian J. Enquist, Brian J. McGill, Lin Jiang, Cecile H. Albert, Catherine Hulshof, Vincent Jung, et Julie Messier. 2012. The return of the variance: intraspecific variability in community ecology. Trends in Ecology & Evolution 27 (4): 244-252. doi:10.1016/j.tree.2011.11.014.

See Also

ComIndex; ComIndexMulti; plotCorTstats; plotSESvar; plot.listofindex

Examples

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	data(finch.ind)

	res.finch <- Tstats(traits.finch, ind.plot = ind.plot.finch, 
	sp = sp.finch, nperm = 9, print = FALSE)
	
	res.finch

	#Tstats class is associated to S3 methods plot, barplot and summary
	
	plot(res.finch)
	
	## Not run: 
	plot(res.finch, type = "simple")
	plot(res.finch, type = "simple_range")
	plot(res.finch, type = "barplot")
	plot(res.finch, type = "bysites")
	plot(res.finch, type = "bytraits")
	
## End(Not run)
	
	attributes(sum_Tstats(res.finch))
	head(sum_Tstats(res.finch)$p.value, 10)
	
	sum_Tstats(res.finch, type = "binary")
	sum_Tstats(res.finch, type = "percent")
	sum_Tstats(res.finch, type = "site")
	sum_Tstats(res.finch, type = "p.value")
	sum_Tstats(res.finch, type = "all")
	
	barplot(res.finch)
	
	attributes(sum_Tstats(res.finch))
	head(sum_Tstats(res.finch)$p.value, 10)
	
	#### An other way to see "ses values" of T-statistics
	
	# Custom theme (from rasterVis package)
	require(rasterVis)
	
	my.theme <- BuRdTheme()
	# Customize the colorkey
	my.ckey <- list(col = my.theme$regions$col)
	
	levelplot(t(ses(res.finch$Tstats$T_IP.IC,res.finch$Tstats$T_IP.IC_nm)$ses), 
	colorkey = my.ckey, par.settings = my.theme,border = "black")
	
	
	## Not run: 
		#### Use a different regional pool than the binding of studied communities
		#create a random regional pool for the example
	
		reg.p <- rbind(traits.finch, traits.finch[sample(1:2000,300), ])
	
		res.finch2 <- Tstats(traits.finch, ind.plot = ind.plot.finch, 
	    sp = sp.finch, reg.pool=reg.p, nperm = 9, print = FALSE)	
	    
	    plot(as.listofindex(list(res.finch,res.finch2)))
    
    
	    #### Use a different regional pool for each communities
		#create a random regional pool for each communities for the example
		list.reg.p <- list(
		traits.finch[sample(1:290,200), ], traits.finch[sample(100:1200,300), ], 
		traits.finch[sample(100:1500, 1000), ], traits.finch[sample(300:800,300), ],
		traits.finch[sample(1000:2000, 500), ], traits.finch[sample(100:900, 700), ] )

		# Warning: the regional pool need to be larger than the observed communities
		table(ind.plot.finch)
		# For exemple, the third community need a regional pool of more than 981 individuals
		
		res.finch3 <- Tstats(traits.finch, ind.plot = ind.plot.finch, 
	    sp = sp.finch, reg.pool=list.reg.p, nperm = 9, print = FALSE)	
	    
	    plot(as.listofindex(list(res.finch, res.finch2, res.finch3)))	
	
## End(Not run)

	#### Use the standard errors of measure in the analysis (argument SE)
	## Not run: 
		res.finch.SE0 <- Tstats(traits.finch, ind.plot = ind.plot.finch, 
		sp = sp.finch, SE = 0, print = FALSE)
		
		res.finch.SE5 <- Tstats(traits.finch, ind.plot = ind.plot.finch, 
		sp = sp.finch, SE = 5, print = FALSE)
	
		plot(as.listofindex(list(res.finch.SE0, res.finch.SE5)))
	
## End(Not run)

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