## sábado, 9 de diciembre de 2017

### Brownian Motion GIF with R and ImageMagick

Hi there!

Last Monday we celebrated a “Scientific Marathon” at Royal Botanic Garden in Madrid, a kind of mini-conference to talk about our research. I was talking about the relation between fungal spore size and environmental variables such as temperature and precipitation. To make my presentation more friendly, I created a GIF to explain the Brownian Motion model. In evolutionary biology, we can use this model to simulate the random variation of a continuous trait through time. Under this model, we can notice how closer species tend to maintain closer trait values due to shared evolutionary history. You have a lot of information about Brownian Motion models in evolutionary biology everywhere!
Here I will show you how I built a GIF to explain Brownian Motion in my talk using R and ImageMagick.

`````` # First, we simulate continuous trait evolution by adding in each iteration
# a random number from a normal distribution with mean equal to 0 and standard
# deviation equal to 1. We simulate a total of 4 processes, to obtain at first
# two species and a specieation event at the middle of the simulation, obtaining
# a total of 3 species at the end.
df1<- data.frame(0,0)
names(df1)<- c("Y","X")
y<-0
for (g in 1:750){
df1[g,2] <- g
df1[g,1] <- y
y <- y + rnorm(1,0,1)
}
#plot(df1\$X,df1\$Y, ylim=c(-100,100), xlim=c(0,1500), cex=0)
#lines(df1\$X,df1\$Y, col="red")
df2<- data.frame(0,0)
names(df2)<- c("Y","X")
y<-0
for (g in 1:1500){
df2[g,2] <- g
df2[g,1] <- y
y <- y + rnorm(1,0,1)
}
#lines(df2\$X,df2\$Y, col="blue")
df3<- data.frame(750,df1[750,1])
names(df3)<- c("Y","X")
y<-df1[750,1]
for (g in 750:1500){
df3[g-749,2] <- g
df3[g-749,1] <- y
y <- y + rnorm(1,0,1)
}
#lines(df3\$X,df3\$Y, col="green")
df4<- data.frame(750,df1[750,1])
names(df4)<- c("Y","X")
y<-df1[750,1]
for (g in 750:1500){
df4[g-749,2] <- g
df4[g-749,1] <- y
y <- y + rnorm(1,0,1)
}
#lines(df4\$X,df4\$Y, col="orange")
``````

`````` # Now, we have to plot each simmulation lapse and store them in our computer.
# I added some code to make lighter the gif (plotting just odd generations) and
# to add a label at the speciation time. Note that, since Brownan Model is a
# stocasthic process, my simulation will be different from yours.
# You should adjust labels or repeat the simulation process if you don't
# like the shape of your plot.
parp<-rep(0:1, times=7, each= 15)
parp<- c(parp, rep(0, 600))
for (q in 1:750){
if ( q %% 2 == 1) {
id <- sprintf("%04d", q+749)
png(paste("bm",id,".png", sep=""), width=900, height=570, units="px",
pointsize=18)
par(omd = c(.05, 1, .05, 1))
plot(df1\$X,df1\$Y, ylim=c(-70,70), xlim=c(0,1500), cex=0,
main=paste("Brownian motion model \n generation=", 749 + q) ,
xlab="generations", ylab="trait value", font.lab=2, cex.lab=1.5 )
lines(df1\$X,df1\$Y, col="red", lwd=4)
lines(df2\$X[1:(q+749)],df2\$Y[1:(q+749)], col="blue", lwd=4)
lines(df3\$X[1:q],df3\$Y[1:q], col="green", lwd=4)
lines(df4\$X[1:q],df4\$Y[1:q], col="orange", lwd=4)
if (parp[q]==0)
text(750, 65,labels="speciation event", cex= 1.5, col="black", font=2)
if (parp[q]==0)
arrows(750, 60, 750, 35, length = 0.20, angle = 30, lwd = 3)
dev.off()
}
}
``````

Now, you just have to use ImageMagick to put all the PNG files together in a GIF using a command like this in a terminal:

`````` convert -delay 10 *.png bm.gif
``````

Et voilà!

## martes, 5 de diciembre de 2017

### Computing wind average in an area using rWind

Hi all!

A researcher asked me last week about how to compute wind average for an area using rWind. I wrote a simple function to do this using dplyr library (following the advice of my friend Javier Fajardo). The function will be added to rWind package as soon as possible. Meanwhile, you can test the results... enjoy!

`````` # First, charge the new function
library(dplyr)
wind.region <- function (X){
X[,3] <- X[,3] %% 360
X[X[,3]>=180,3] <- X[X[,3]>=180,3] - 360
avg<-summarise_all(X[,-1], .funs = mean)
wind_region <- cbind(X[1,1],avg)
return(wind_region)
}
``````

Once you have charged the function, let’s do an example...

`````` # Get some wind data and convert it into a raster to be plotted later
library(rWind)
library(raster)
wind_data<-wind.dl(2015,2,12,0,-10,5,35,45)
wind_fitted_data <- wind.fit(wind_data)
r_speed <- wind2raster(wind_fitted_data, type="speed")
``````

Now, you can use the new function to obtain wind average in the study area:

`````` myMean <- wind.region(wind_data)
myMean
``````

`````` # Now, you can use wind.fit to get wind speed and direction.
myMean_fitted <- wind.fit(myMean)
myMean_fitted
``````

`````` # Finally, let's plot the results!
library(rworldmap)
library(shape)
plot(r_speed)
lines(getMap(resolution = "low"), lwd=4)
alpha <- arrowDir(myMean_fitted)
arr.length = 2, arr.type="curved")
text(myMean_fitted\$lon+1, myMean_fitted\$lat+1,
paste(round(myMean_fitted\$speed,2), "m/s"), cex = 2)
``````

## martes, 9 de mayo de 2017

### niceOverPlot, or when the number of dimensions does matter

Hi there!

Over the last few months, my lab-mate Irene Villa (see more of her work here!)
and I have been discussing ecological niche overlap. The niche concept dates back to ideas first proposed by ornithologist J. Grinnell (1917). Later on, G.E. Hutchinson
(1957) defined the ecological niche of a species as the n-dimensional hyper-volume of ecological factors that define a space where the species can exist indefinitely. These ecological factors can be either abiotic (fundamental niche) or biotic variables, and the intersection of both defines the realized niche, or potential ecological range where the species can survive. The last necessary element for the existence of a species in a particular place (actual presence or distribution) is related to the “movement” ability or dispersal capacity of the species to arrive to those places where ecological factors are suitable. This theory is nicely summarized in the BAM diagram (Biotic-Abiotic-Movement; Soberón, 2007).

In the last decades, with the development of cartographic information about climatic variables (mainly temperature and precipitation) and mathematical algorithms, many research efforts have been directed towards modeling the ecological niche of species from presence records and bioclimatic information (Elith & Leathwick, 2009). As these techniques were developed, many researchers focused on the comparison of ecological niches of two species, and the degree of overlap between them. A wide range of literature has been published about this topic (Peterson, 2011) but, in the last years, a general consensus has been reached about the methods to measure this overlap. Briefly, the method consists of two steps: 1) building an environmental space using bioclimatic values in the presence records and background points with any multivariate technique (usually Principal Component Analysis), and 2) representing both species niches in this space via kernel density, comparing them using D or I indexes and applying similarity or identity tests to assess significance (Warren et al., 2008).

Following this general approach, the R package ecospat (Di Cola et al., 2016) provides an easy way to perform a Principal Component Analysis and to compare two species niches using D overlapping index, identity tests, etc. However, Irene and I realized that, when using this approach, in many cases for which niche overlap was not obtained, this was due to the lack of overlap for just one of the two PC axes, while a complete overlap was retrieved for the other axis. Taking into account that both axes do not usually contribute equally to explain environmental space (the first axis usually explains much more variability than the following ones), we worked on a function using the ggplot2 R package to create a nice plot for visual exploration of the Principal Component scores in both axes. This plot allows us to examine the factors that are or are not producing niche overlap, since it shows three plots in one: each axis separately and the joint distribution.

Here is the function code (too large to print here). You can download and run it in an R console. The following is an example with two wall lizards from a Mediterranean area. You can download ecological values for the 19 bioclimatic variables at presence points of these two species here.

``````
##########################
#######   EXAMPLE   ######
##########################
library(ecospat)
library(ggplot2)
library(grid)
library(gridExtra)
library(gtable)
library(RColorBrewer)

# Read wall lizards ecological data

# Note: This data represent the values for the 19 bioclimatic variables at occurrence
# points for two Mediterranean wall lizards, Iberian wall lizard (Podarcis hispanicus,
# mainly in Iberian Peninsula) and Lilford's wall lizard (Podarcis lilfordi, from the
# The first 1125 rows are the bioclimatic values for P.hispanicus presences, while the
# next 44 rows represent bioclimatic values for P.lilifordi. The following rows represent
# available bioclimatic conditions (background) obtained from 10000 random points
# generated in a buffer of 400 km approximatively around presence points. Some inaccuracies
# (such as 2 Lilford's wall lizard presences in Iberian Peninsula) were not removed (this is
# just an example!!).
# *Data searches:

# From this data, we perform a Principal Component Analysis using "dudi.pca" function from "ecospat" package.
# We will choose 2 axes for the environmental space representation.

pca_Ph_Pl <-dudi.pca(na.omit(data_Ph_Pl, center = T, scale = T, scannf = F, nf = 2))
2

# Now, we can use directly this result with the niceOverPlot function to represent a
# 2D environmental space in a central plot, and each environmental gradient represented
# by each axis at top and right. We must provide to the function with the number of presences
# of each species in the same order as in the input data (nº of presences
# for Sp1 and nº of presences for Sp2)

niceOverPlot(pca_Ph_Pl, n1=1125 , n2= 44)
``````

Results from niceOverPlot (Blue area: P. lilifordi; Pink area: P. hispanicus)

This plot could help us to interpret the results obtained from niche overlap analysis for these two species. In this example, we can see that, in 2D environmental space, the bioclimatic preferences of the two wall lizard species do not overlap. But you can notice that this lack of overlap is due to Axis2 of the PCA, which represents around 18% of contribution in environmental space. Now, we can focus on the bioclimatic variables that are involved in this axis to understand which factors are preventing the overlap.
In upcoming posts, we will discuss some alternative ways to address the D overlap index to take into account cases like our example.

Have fun!

Podarcis lilifordi, from the Balearic Islands

References

-Soberón, J. (2007). Grinnellian and Eltonian niches and geographic distributions of species. Ecology letters, 10(12), 1115-1123.

-Elith, J., & Leathwick, J. R. (2009). Species distribution models: ecological explanation and prediction across space and time. Annual review of ecology, evolution, and systematics, 40, 677-697.

-Peterson, A. T. (2011). Ecological niche conservatism: A time‐structured review of evidence. Journal of Biogeography, 38(5), 817-827.

-Di Cola, V., Broennimann, O., Petitpierre, B., Breiner, F. T., D'Amen, M., Randin, C., ... & Pellissier, L. (2016). ecospat: an R package to support spatial analyses and modeling of species niches and distributions. Ecography.