2/21/2018. Geographic Distance. Returns the Z-statistic No partial Mantel option No strata option

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1 Mantel function in ape package Returns the Z-statistic No partial Mantel option No strata option Z-statistic is unbound Allows for testing of directional hypothesis (1-tailed test) Must convert distance matrices to square (as.matrix), function works with lower triangle. Density 0.0e e e e e-07 density.default(x = nullstats) 3.65e e e+08 N = 1000 Bandwidth = 4.719e+05 $z.stat [1] $p [1] $alternative [1] "two.sided" Geographic Distance With longitude and latitude variables, your geographic distance (Euclidean) can be calculated using the dist function. That assume the Earth is flat, and returns values in decimal degrees units. Function earth.dist corrects for this and returns values in km. For this dataset, the two are correlated (0.989) earth.dist (km) Euclidean dist, decimal degrees Geographic Distance Another function is distgeo (geosphere package) that is supposed to be more accurate, allows you to specify ellipsoid parameters. Basic Mapping library(maps) library(mapdata) # North American fish example nafish<-read.table("na_fish_diversity.csv",header=t,sep=",",row.names="huc_8") map("state", fill=f) points(nafish$lat,nafish$long,cex=0.5,col="red",pch=19) Correlation= Maximum discrepancy for the dataset was 5.7 km Earth.dist (km) distgeo (m) 1

2 Basic Mapping div_bubble<-scale(nafish$diversity) div_bubble<-(div_bubble+-1*(min(div_bubble)))/2 map("state", fill=f) points(nafish$lat,nafish$long,cex=div_bubble,col="red",pch=19) Adding shapefiles to maps Package maptools contains functions to import and work with GIS data. Function readshapespatial (and other readshape functions) will import standard file formats. Downloaded HUC shapefiles for MS. HUCs<-readShapePoly("wbdhu8_a_ms.shp") plot(hucs, col=huc_colors) text(ms_fish_huc$lat,ms_fish_huc$long,label=ms_fish_huc$diversity,col="gray",cex=0.75) map("state","mississippi", add=t, fill=f, col="white") Missing data Missing data should be coded as blank cells Reported as NA Function is.na() can be used to look for missing data, returns TRUE/FALSE [,1] [,2] [,3] [,4] [,5] [1,] [2,] [3,] NA NA [4,] NA [5,] NA [6,] [7,] [8,] NA [9,] [10,] [,1] [,2] [,3] [,4] [,5] [1,] FALSE FALSE FALSE FALSE FALSE [2,] FALSE FALSE FALSE FALSE FALSE [3,] TRUE FALSE FALSE FALSE TRUE [4,] FALSE FALSE FALSE TRUE FALSE [5,] FALSE FALSE FALSE TRUE FALSE [6,] FALSE FALSE FALSE FALSE FALSE [7,] FALSE FALSE FALSE FALSE FALSE [8,] FALSE FALSE FALSE FALSE TRUE [9,] FALSE FALSE FALSE FALSE FALSE [10,] FALSE FALSE FALSE FALSE FALSE Missing Data Some functions do not expect missing data > mean(temp[1,]) [1] > mean(temp[3,]) [1] NA > mean(temp[3,],na.rm=t) [1] How much missing data? sum(is.na(temp)) 5 Total missing data by row apply(is.na(temp),1,sum) [1] As we did before, you could exclude rows or columns based on the amount of missing data. 2

3 Saving Graphs two methods 1. Right-click on graph and copy. Paste into powerpoint as enhanced metafile. Default 480x480 res= x2000 res=72 2. Alternatively, use jpeg() function to write the graph directly to a file. jpeg("filename.jpg",width = 2000, height=2000,res = 72) plot( ) dev.off() Height and width determine the size of the image (default =480) Res determines the resolution (default 72) If you want things to scale properly, you need to increase resolution. It is normally 72 points per inch, at 480 points, this is a 6.6 inch image Increasing to 2000 points for the same size image (6.6 inch), we would want a resolution of 300 (2000/6.6) 2000x2000 res=300 Default 240x240 res=36 Hist function hist(rnorm(10000)) Histogram of rnorm(10000) hist(rnorm(10000), breaks=50, axes=false) Histogram of rnorm(10000) rnorm(10000) rnorm(10000) hist(rnorm(10000), plot=false) $breaks [1] $counts [1] Publication quality (what most journals will accept as a minimum) is 300 dpi $density [1] $mids [1] $xname [1] "rnorm(10000)" 3

4 Hist function var1<-rnorm(1000, mean=1) var2<-rnorm(1000, mean=2) Loops Simple loop y<-0 for (x in 1:10) { y<-y+x } Loops 10 times, adding x each time: y=55 hist(var1,col="blue") hist(var2,col="red",add=t) hist(var1,col=rgb(0,0,1,0.5),main="var1 and var2") hist(var2,col=rgb(1,0,0,0.5),add=t) Basis for any kind of permutation test Observed statistic (e.g. R statistic in ANOSIM) Loop: Permute the dataset, calculate statistic Compare observed statistic to distribution of observed values Loops Two samples, traditional t-test var1<-rnorm(100,mean=4) var2<-rnorm(100,mean=4.25) t.test(var1,var2) Welch Two Sample t-test data: var1 and var2 t = , df = , p-value = alternative hypothesis: true difference in means is not equal to 0 95 percent confidence interval: sample estimates: mean of x mean of y Permutation test: observed_diff<-mean(var1)-mean(var2) combined_vars<-c(var1,var2) Histogram of permuted_differences permuted_differences<-0 for(x in 1:10000) { permuted_differences permuted_var<-sample(combined_vars,300,replace=f) permuted_differences[x]<-mean(permuted_var[1:150])- mean(permuted_var[151:300]) } Observed difference 0.29 # permuted differences more extreme: 201 Additional Mantel Example Goal of study was to characterize plant assemblages at a fine scale along a 500 m transect. Divided assemblage into four types (palms, trees melastomes, pteridophytes) Soils changed over gradient Used clustering to put look at groups of 4 plant types Do the plant types respond the same along the gradient? Permuted P =

5 Mantel tests comparing pairs of plant types Partial mantel tests control for spatial component (position along the gradient) 5