Ecometrics: A Trait-Based Approach to Paleoclimate and Paleoenvironmental Reconstruction

Abstract

Ecometrics is a trait-based approach to study ecosystem variability through time. An ecometric value is derived from describing the distribution of functional traits at the community level , which may arise by environmental filtering, extinction, or convergence. An ecometric relationship describes the correspondence between spatially explicit ecometric values and corresponding environmental variation. Transfer functions and maximum likelihood approaches have been developed with modern trait-environment relationships to reconstruct paleotemperature , paleoprecipitation , and paleovegetation cover given the distribution of functional traits within a community. Because the focus for this approach is on the traits and not on species, it is transferable through space and time and can be used to compare novel communities. In this paper we review the concepts and history of ecometric analysis and then describe practical methods for implementing an ecometric study.

Appendix 17.1. Ecometrics Workflow and R Code

This section demonstrates an ecometric modeling workflow using the R Statistical Programing Language. To demonstrate these models in R, we will work with spatial data. There are special functions in two packages, raster and sp, that allow for relatively quick processing of spatial information (Bivand et al. 2013; Hijmans 2015; Pebesma and Bivand 2005). We will use climate data from the worldclim database (Hijmans et al. 2005) and we will use trait data body mass and hypsodonty from the PanTHERIA database (Jones et al. 2009) and from Eronen et al. (2010b). The code below can be typed directly into an R console or can be entered into an R script file. A bold word indicates that the word is a function. To start the analysis, load the two required libraries. If they are not installed yet on your computer, install them with the function install.packages().

library (raster) ## Loading required package: sp library (sp)

Load the sampling locations and look at the first six rows of data with the functions read.csv() and head(). The first function read.csv() is a wrapper for another function called read.table(), which can be used in place of read.csv(), if the data are in tab delimited format. Use the help() function to see the documentation associated with each function.

points <-  read.csv (“data/SamplingPoints.csv”) head (points) ##   GLOBALID Longitude Latitude ## 1   103148  -42.1727 83.26264 ## 2   103149  -38.3442 83.26264 ## 3   103150  -34.5156 83.26264 ## 4   103151  -30.6871 83.26264 ## 5   103152  -26.8586 83.26264 ## 6   103235  -79.4690 82.81348

Plot the sampling locations with the function plot() to visualize the geographic distribution of the sampling locations. In this example, we use 50 km equidistant points sampled across North America (Fig. 17.A1). These are the same points used in Polly (2010).

Fig. 17.A1

An example of output in the R Statistical Programing Language from calling the plot function for plotting the latitude and longitude of 50 km equidistant points sampled from across North America

plot (points[,2:3], col = ”gray”, pch = 16)

Download raster climate data from the worldclim database using the getData() function from the package raster that we loaded with the library() function (Hijmans et al. 2005; Hijmans 2015). In this example, we download the 10-minute resolution, but if you would like to try a higher resolution data set, then change the argument named res to 2.5 or 0.5. Extract the temperature and precipitation for each sampling location using the extract() function.

bioclim <-  getData (“worldclim”, download = T, path = ”data”, var = ”bio”, res = 10)

Extract the temperature for each sampling location.

temperature <-  extract (bioclim[[1]], points[,2:3])

Calculate the temperature range for all the sampling localities to make a plot of the temperature. We add one to the range to make the range equal to index values that we can use to subset the color function. The R language starts the subset of data at an index value of 1.

Calculate the color value associated with each temperature value and the temperature values associated with even breaks to assign legend values. Figure 17.A2 is a map of the mean annual temperatures.

Fig. 17.A2

A heat map of the mean annual temperature (°C), where the hotter colors represent warmer places and cooler colors represent colder places

temp_range <- 1 +  max (temperature, na.rm = T) -  min (temperature, na.rm = T) colfunc_temp <-  colorRampPalette ( c (“darkblue”, ”blue”, ”gray”, ”yellow”,  “red”))(temp_range)[1 + temperature -  min (temperature, na.rm = T)] h <-  hist (temperature, breaks = 5) plot (points[,2:3], col = colfunc_temp, pch = 16, main = ”Mean Annual Temperature (C)”) legend (“bottomright”, legend = h$breaks/10, pch = 16, col =  colorRampPalette ( c (“darkblue”, ”blue”, ”gray”, ”yellow”, ”red”))( length (h$breaks)))

Extract the precipitation for each sampling locality.

precipitation <-  extract (bioclim[[12]], points[,2:3])

Calculate the precipitation range for all the sampling localities to make a plot of the precipitation. Also, calculate color value associated with each precipitation value and the precipitation values associated with even breaks to assign legend values. Figure 17.A3 is a map of the precipitation values.

Fig. 17.A3

A heat map of the annual precipitation (mm), where greener colors represent wetter places and browner colors represent drier places

precip_range <- 1 +  max ( log (precipitation), na.rm = T) -  min ( log (precipitation), na.rm = T) colfunc_pr <-  colorRampPalette ( c (“brown”, ”green”))(precip_range)[1 +  log (precipitation) –  min ( log (precipitation), na.rm = T)] h <-  hist ( log (precipitation), breaks = 5) plot (points[,2:3], col = colfunc_pr, pch = 16, main = ”Precipitation (mm)”) legend (-36.25, 60.5, legend =  round ( exp (h$breaks)), pch = 16, col =  colorRampPalette ( c (“brown”, ”green”))( length (h$breaks)))

Compile the climate variables into a new data.frame called climate. Remove the variables that are taking up memory with the rm() function if your memory is getting sluggish.

climate <-  cbind (points, temperature, precipitation) #rm(bioclim, temperature, precipitation, points)

Visually check the climate variables for normality and if they are not mostly normally distributed, transform them for normality (Fig. 17.A4).

Fig. 17.A4

A histogram of the mean annual temperature (°C × 10) of all of the sampling locations

head (climate) ##   GLOBALID Longitude Latitude temperature precipitation ## 1   103148  -42.1727 83.26264        -169           139 ## 2   103149  -38.3442 83.26264        -170           141 ## 3   103150  -34.5156 83.26264        -175           149 ## 4   103151  -30.6871 83.26264        -185           166 ## 5   103152  -26.8586 83.26264        -180           139 ## 6   103235  -79.4690 82.81348        -207            90

hist (climate[,4], main = ”“, xlab = ”Mean Annual Temperature”, col = ”gray”)

Temperature appears to be reasonably normally distributed, so now we check precipitation (Fig. 17.A4).

Fig. 17.A5

A histogram of annual precipitation (mm) of all the sampling locations

hist (climate[,5], main = ”“, xlab = ”Annual Precipitation”, col = ”gray”)

Precipitation appears to be log distributed (Fig. 17.A5). We log transform this variable to get it closer to normality (Fig. 17.A6).

Fig. 17.A6

A histogram of log annual precipitation (mm) of all sampling locations

climate[,5] <-  log (climate[,5]) hist (climate[,5], main = ”“, xlab = ”Log Annual Precipitation”, col = ”gray”)

Next, we read in the trait data from a folder called data. We assign the row names of the new data frame to the names of the taxon within the dataset. We look at the first six rows of the trait data frame with the head() function. The two traits that we use in this example are body mass and hypsodonty index . Body mass is reported in grams and is the mass of any adult reported in the PanTHERIA database (Jones et al. 2009) from live or freshly-killed specimens. These include captive, wild, provisioned, or unspecified populations and include male, female, and sex unspecified individuals. The mean for each species is reported for each species. The second trait that we use is an index for hypsodonty from Eronen et al. (2010b).

traits <-  read.csv (“data/NAmammalTraits.csv”) rownames (traits) <- traits$TaxonName head (traits) ##                                     TaxonName BodyMass hypsodonty_index ## Didelphis virginiana     Didelphis virginiana 3.387760                1 ## Aplodontia rufa               Aplodontia rufa 2.906448                3 ## Sciurus carolinensis     Sciurus carolinensis 2.736715                1 ## Sciurus griseus               Sciurus griseus 2.847480                1 ## Sciurus niger                   Sciurus niger       NA                1 ## Tamiasciurus douglasii Tamiasciurus douglasii 2.352183                1

Now we read in shapefiles containing polygons that represent the geographic ranges for all of the species of interest. These specific shape files were obtained from IUCN Redlist using their spatial data download option (www.iucnredlist.org). If you are dealing with large shapefiles, then this step will take a reasonable amount of processing time.

geography <-  shapefile (“data/TERRESTRIAL_MAMMALS/TERRESTRIAL_MAMMALS.shp”)

Next we create a list of species at each sampling locality by first turning the sampling points into spatial points with the function SpatialPoints(). We assign the coordinate reference system of our spatial points to a proj4string to match the coordinate reference system of the spatial polygons representing the geographic ranges . We then create a list with the function over(). If you are dealing with large shapefiles, keep in mind that the over() function will take a reasonable amount of time to process.

sp <-  SpatialPoints (climate[,2:3], proj4string =  CRS ( proj4string (geography))) o <-  over (sp, geography, returnList = T)

The sample size at each site is calculated by determining the length of the vector returned for each site. The ecometric for body mass and hypsodonty index are summarized for the community level distribution. Here, we summarize with the mean.

richness <-  unlist ( lapply (o, function(x)  length (traits[x$binomial,”hypsodonty_index”]))) ecometric_bodymass <-  unlist ( lapply (o, function(x)  mean (traits[x$binomial,”BodyMass”],  na.rm = T))) ecometric_hypsodonty <-  unlist ( lapply (o, function(x)  mean (traits[x$binomial,”hypsodonty_index”], na.rm = T)))

First Approximation with Transfer Function

Now we create a model describing the relationship between traits and climate. First, we consider the relationship between hypsodonty and precipitation. We build a simple linear model to describe the variation in precipitation due to the variation in hypsodonty using the function lm(). We only use sites that we have data for more than five species. We look at a summary of the model using the function summary(). Both the intercept and the coefficient (here the coefficient represents the slope of the linear relationship) are not zero (p < 0.001). The amount of explained variation (R²) is 30%. We then make a scatterplot of those variables to look at the general spread of data and add the linear model with the function abline() (Fig. 17.A7).

Fig. 17.A7

A scatterplot of hypsodonty and log annual precipitation with a trend line

model_mass <-  lm (climate[richness > 5,4] ~ ecometric_bodymass[richness > 5]) summary (model_mass) ## Call: ## lm(formula = climate[richness > 5, 4] ~ ecometric_bodymass[richness >  5]) ## Residuals: ##     Min      1Q  Median      3Q     Max  ## -170.72  -65.22  -24.73   43.71  375.19  ## Coefficients: ##                                  Estimate Std. Error t value Pr(>|t|)     ## (Intercept)                       471.512      6.571   71.76   <2e-16 *** ## ecometric_bodymass[richness > 5] -153.559      2.304  -66.64   <2e-16 *** ## --- ## Signif. codes:  0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 ## Residual standard error: 92.6 on 8651 degrees of freedom ##   (15 observations deleted due to missing data) ## Multiple R-squared:  0.3392, Adjusted R-squared:  0.3391  ## F-statistic:  4440 on 1 and 8651 DF,  p-value: < 2.2e-16 plot (ecometric_bodymass[richness > 5], climate[richness > 5,4], ylab = ”MAT”, xlab = ”Body  Mass”, pch = 16, col = ”gray”) curve (model_mass$coefficients[1] + model_mass$coefficients[2] * x, col = ”red”, lwd = 4,  add = T)

From this model, we can see there is some predictive power in this transfer function , but the linear model does not capture the relationship well. In the next section we will show how to estimate annual precipitation from hypsodonty with a maximum likelihood approach that better captures the relationship between annual precipitation and hypsodonty.

Now we create a model describing the relationship between the body mass and temperature. We build a linear model to describe the variation in body mass due to the variation in temperature using the function lm(). We look at a summary of the model using the function summary(). Both the intercept and all the coefficients are significantly different from zero (p < 0.001). The amount of explained variation (R²) is approximately 34%. We then make a scatterplot of those variables to look at the general spread of data and add the model with the function curve() (Fig. 17.A8).

Fig. 17.A8

A scatterplot of body mass and mean annual temperature with a trend line

model_mass <-  lm (climate[richness > 5,4] ~ ecometric_bodymass[richness > 5]) summary (model_mass) ## Call: ## lm(formula = climate[richness > 5, 4] ~ ecometric_bodymass[richness >  5]) ## Residuals: ##     Min      1Q  Median      3Q     Max  ## -170.72  -65.22  -24.73   43.71  375.19  ## Coefficients: ##                                  Estimate Std. Error t value Pr(>|t|)     ## (Intercept)                       471.512      6.571   71.76   <2e-16 *** ## ecometric_bodymass[richness > 5] -153.559      2.304  -66.64   <2e-16 *** ## --- ## Signif. codes:  0 ’***’ 0.001 ’**’ 0.01 ’*’ 0.05 ’.’ 0.1 ’ ’ 1 ## Residual standard error: 92.6 on 8651 degrees of freedom ##   (15 observations deleted due to missing data) ## Multiple R-squared:  0.3392, Adjusted R-squared:  0.3391  ## F-statistic:  4440 on 1 and 8651 DF,  p-value: < 2.2e-16 plot (ecometric_bodymass[richness > 5], climate[richness > 5,4], ylab = ”MAT”, xlab  = ”Body Mass”, pch = 16, col = ”gray”) curve (model_mass$coefficients[1] + model_mass$coefficients[2] * x, col = ”red”, lwd  = 4, add = T)

From this model, we can see that, again, there is some predictive power in this transfer function , but the linear model does not capture the relationship well. In the next section we will show how to estimate mean annual temperature from body mass with a maximum likelihood approach that better captures the relationship between the two.

The coefficients that were estimated in both of these models can be used to estimate paleotemperature and precipitation. Confidence limits can also be calculated given the input dataset. It is important to note that the size of the confidence limits will vary with climate. For example, between 5 C and 28 C, there is a stronger relationship with body size than below or above those temperatures. Hypsodonty has high variability throughout the precipitation range present in North America; however, there is a central tendency about the average relationship between precipitation and hypsodonty index that is useful in reconstructing paleoprecipitation with confidence limits.

Maximum Likelihood Estimation

Although transfer functions , while easy to apply and adequate for first approximations, assume a fairly simple one-to-one relationship between environment and trait means. Combining different traits that have functional relationships with the same environmental factor is also awkward with conventional regression-based transfer functions, especially if the traits are fundamentally different in kind or scale (e.g., body mass measured in kg and humerus shape measured in Procrustes units).

An alternative strategy is to estimate the likelihood of environmental parameters given the distribution of traits in a community (Lawing et al. 2012; Polly and Head 2015). This approach, like many likelihood or Bayesian methods, requires far fewer assumptions about the statistical distributions of variables and it allows otherwise incommensurable data to be combined into the same estimate.

To begin, we need to create another variable at the community level , namely the standard deviation, to use in the maximum likelihood estimate of temperature.

sd_ecometric_bodymass <-  unlist ( lapply (o, function(x)  sd (traits[x$binomial,”BodyMass”], na.rm = T)))

We create bins using the body mass variable and extract the break points for each bin.

#bin the community level trait distribution into 25X25 #first take the range of each mtemp <-  range (ecometric_bodymass, na.rm = T) sdtemp <-  range (sd_ecometric_bodymass, na.rm = T) #get the break points for the mean and sd mbrks <-  seq (mtemp[1], mtemp[2],  diff (mtemp)/25) sdbrks <-  seq (sdtemp[1], sdtemp[2],  diff (sdtemp)/25) #assign bin codes for each mbc <-  .bincode (ecometric_bodymass, breaks = mbrks) sdbc <-  .bincode (sd_ecometric_bodymass, breaks = sdbrks)

We calculate the temperature for each bin.

#calculate the data for the raster obj <-  array (NA,dim =  c (25,25)) for(i in 1:25){   for(j in 1:25){     dat <-  round (temperature[ which (mbc==i & sdbc==j)]/10)     obj[26 - j,i] <-  mean (dat, na.rm = T)    } }

Next, we create a raster to store the body mass and temperature data for bins.

#make a raster r <-  raster ( extent (0,25,0,25), resolution = 1) #set the values to the obj r <-  setValues (r,obj)

Plot the raster and highlight the bin that we will use to extract data to show an example of that maximum likelihood estimate (Fig. 17.A9).

Fig. 17.A9

Ecometric space for the trait body mass with mean body mass on the x-axis and standard deviation of body mass on the y-axis. The colors represent the estimate of mean annual temperature for each mean and standard deviation combination. The hotter colors represent higher mean annual temperature and the cooler colors represent lower mean annual temperatures

#make an empty plot plot (1:25, 1:25, type = ”n”, xlim =  c (1,25), ylim =  c (1,25),      xaxs = ”i”, yaxs = ”i”, asp = 1, axes = F, xlab =““, ylab=““) #add the rectangle/box rect (0, 1, 25, 25, lwd = 3) #add the raster data plot (r, col =  colorRampPalette ( c (“darkblue”, ”blue”,      ”grey”,”yellow”, ”red”))( round ( maxValue (r) –      minValue (r))), add = T) #this is mean = 3.1, 12, and sd = 1.08, 10 rect (11, 9, 12, 10, lwd = 4)

The colors in this raster plot show the Mean Annual Temperature (MAT) maximum likelihood estimate given the associated mean and standard deviation of each bin.

We extract the data for the highlighted bin and plot the kernel density with a Gaussian kernel (Fig. 17.A10). This shows the distribution of the likelihood surface.

Fig. 17.A10

Kernel density estimation from one combination of mean and standard deviation of body mass

#grab all the data for that box dat <-  round (temperature[ which (mbc==12 & sdbc==10)]/10) #plot the kernel density with gaussian kernel, bandwidth = 1 mod <-  density (dat, bw = 1) plot (mod, ylim =  c (0,1), col = ”darkblue”, lwd = 2) polygon (mod$x, mod$y, col = ”skyblue”)

This likelihood surface shows a bimodal distribution of the most likely temperature. Although it is bimodal, it is much more likely that the temperature falls on the warm end of the spectrum, as opposed to the cold end.

Next, we calculate the maximum likelihood for all bins.

modmax <-  array (NA, dim =  length (points[,1])) mod <-  list () for(i in 1: length (points[,1])){   if(!( is.na (mbc[i]) |  is.na (sdbc[i]))){     dat <-  round (temperature[ which (mbc==mbc[i] & sdbc==sdbc[i])]/10)     mod[[i]] <-  density (dat, bw = 1)     modmax[i] <- mod[[i]]$x[ which.max (mod[[i]]$y)] }} modmax <-  round (modmax*10)

We only use bins with more than the number of species specified as the cutoff. Here we use seven. This means that there needs to be at least seven species recorded at each location to be included in the estimate.

cutoff <- 7 

To plot the maximum likelihood temperature estimate from the ecometric values, we create a color palette for the temperature estimates. In addition, we save the histogram with five break points to a variable to use in plotting (refer back to Fig. 17.A4).

colfunc_eco <-  colorRampPalette ( c (“darkblue”, ”blue”, ”gray”, ”yellow”,  “red”))(temp_range)[1 + modmax -  min (modmax, na.rm = T)] h <-  hist (temperature, main = ”“, xlab = ”Mean Annual Temperature”, col = ”gray”, breaks =  5)

We map the maximum likelihood temperature estimate from body mass (Fig. 17.A11).

Fig. 17.A11

A heat map of the estimate of mean annual temperature (°C) from the mean and standard deviation of body mass. The hotter colors represent higher temperature estimates and the cooler colors represent lower temperature estimates

plot (points[,2:3], col = ”gray”, pch = 16) points (points[richness > cutoff, 2:3], col = colfunc_eco[richness > cutoff], pch = 16) legend (-31.5, 61, legend = h$breaks/10, pch = 16, col =  colorRampPalette ( c (“darkblue”,  “blue”, ”gray”, ”yellow”, ”red”))( length (h$breaks)))

Next we plot the actual temperature to compare with the estimated temperature (refer back to Fig. 17.A2).

plot (points[,2:3], col = ”gray”, pch = 16, main = ”Mean Annual Temperature (C)”) points (points[richness > cutoff,2:3], col = colfunc_temp[richness > cutoff], pch = 16) legend (-31.5, 61, legend = h$breaks/10, pch = 16, col =  colorRampPalette ( c (“darkblue”,  “blue”, ”gray”, ”yellow”, ”red”))( length (h$breaks)))

We plot the anomaly to visualize the difference between the estimated and actual Mean Annual Temperature (Fig. 17.A12).

Fig. 17.A12

Anomaly between the observed mean annual temperature and the estimated mean annual temperature. The purple colors represent negative anomalies, up to −30°C. The green colors represent positive anomalies, up to 30°C

plot (points[,2:3], col = ”gray”, pch = 16) anom <- temperature – modmax colfunc_anom <-  colorRampPalette ( c (“purple”, ”grey”, ”green”))( max (anom, na.rm = T) –  min (anom, na.rm = T))[1 + anom -  min (anom, na.rm = T)] points (points[richness > cutoff, 2:3], col = colfunc_anom[richness > cutoff], pch = 16) legend (-31.5, 61, legend = h$breaks/10, pch = 16, col =  colorRampPalette ( c (“purple”,  “grey”, ”green”))( length (h$breaks)))

The anomaly between the estimated Mean Annual Temperature and the actual Mean Annual Temperature shows that most of the temperature estimates are less that 1°C divergent from the actual Mean Annual Temperature.