Digital Leaf Physiognomy (DiLP)

Digital leaf physiognomy (DiLP)

Digital leaf physiognomy (DiLP) harnesses the power of digital imaging, imaging manipulation, and software to measure irregular shapes. DiLP was developed in work by Huff et al. (2003), Royer et al. (2005), and Peppe et al. (2011, 2018). It is said to yield more accurate results than univariate methods, and to be an improvement over CLAMP analysis in the multivariate realm in that it is more repeatable and objective. It has been applied to a few fossil floras.

DiLP begins with digital imaging of leaves and manipulation of those images to allow for simple and consistent measurements. Note that only the leaf blade (lamina) is used in DiLP calculations. The first step in DiLP is to take digital photographs of the leaves of interest. Ideally, this will be done against a contrasting background to make later manipulation easier.

After images have been made, they can be processed to make the calculations necessary for DiLP simpler:

1. Missing or damaged margins must be reconstructed.
2. For fossil leaves, the rock matrix must be removed from around the actual leaf specimen.
3. The leaf petiole must be removed.
4. The leaf image should be processed so that the leaf blade is a solid color. This can be accomplished via different methods (see original papers).
5. Any holes in the leaf (due, e.g., to insect damage) should be mended (filled).

Fossil leaves are often fragmentary, so addition methods may be necessary to reconstruct a sufficient number of leaves to create a large enough dataset for DiLF.

ADD INFORMATION

Obviously, best practice dictates that all original and processed images be retained as the raw data for DiLP.

Measurements & variables

Leaf measurements for DiLP MAT and MAP equations¹

¹ After Royer et al. (2005), Peppe et al. (2011, 2018), Glade-Vargas et al. (2018), and Baumgartner et al. (2020). Since the abbreviations for measurements vary among sources, I have chosen a simple set of abbreviations for this discussion.

Leaf blade area (BA)

Leaf blade area is just the surface area of the leaf blade.

Feret's diameter & Feret's diameter ratio (FDR)

Feret's diameter ratio is a ratio of two measurements, Feret's diameter and length of the major leaf axis. Feret's diameter is defined as:

Feret's diameter: measure of an object in a single dimension or direction (length, width, height).

In the case of DiLP, Feret diameter has a specific, distinct meaning:

Feret's diameter (for leaf digital leaf physiognomy): Diameter of a circle with the same area as the leaf blade. This is calculated as 2 × the square root of (leaf area ÷ π).

FD (for DiLF) = 2√(BA ÷ π)

Major axis can be defined as follows:

Major axis (Maj): the longest straight line that connects any two points on the perimeter (edge) of a leaf blade. The major axis is often the length of the leaf blade.

The Feret's diameter ratio is the ratio of the Feret's diameter to the length of the major axis. It is calculated as:

Feret's diameter ratio (FDR) = Feret's diameter of a leaf blade ÷ length of the major axis of a leaf blade.

An example of how to calculate FDR is shown in the figure below. For a leaf with a blade 3.6 cm long and 2.4 cm wide, FDR is calculated as follows:

Major axis = 3.6 cm

BA = 6.8 cm²

Feret's diameter = 2√(6.8 ÷ 3.14) = 2.9 cm

FDR = 2.9 ÷ 3.6 = 0.81

Perimeter ratio (PR)

Perimeter ratio is the ratio of the leaf perimeter with teeth and without teeth. It is calculated as follows:

Perimeter ratio (PR) = perimeter of leaf ÷ perimeter of leaf with teeth removed.

If a leaf is entire, its perimeter ratio will be one because there are no teeth to be removed. Lobes are not removed in this procedure. For specific instructions for differentiating teeth and lobes, etc., see Royer et al. (2005).

Standardized tooth count (T:IP)

Standardized tooth count is the ratio of the number of leaf teeth to the perimeter of the leaf with the teeth removed.

Standardized tooth count (T:IP) = total number of leaf teeth ÷ perimeter of the leaf with teeth removed.

If the leaf is entire, the T:IP ratio will be zero, because zero divided by any value is zero. If teeth are compound, both primary and secondary teeth are included in the tooth count (see Royer et al., 2005).

Determining values for a flora

The above descriptions of measurements and variables describes how to determine values for individual leaves. When using these variables in an equation, however, we need a single number representing each variable to represent a whole flora, so we can plug into an equation. How do we determine these whole-flora values?

Morphotype-type mean values

First, we we need to assign a single value to each variable for each leaf morphotype in a flora. The first step in doing this is, of course, to sort leaf specimens into morphotype categories. After that, individual leaves can be digitized, measured, and scored. Scoring is just making a table of measurements and calculations that describe each leaf. An exemplar of at least one leaf representing each morphotype in a flora should be scored, if possible; ideally, more than one leaf will be scored per morphotype. Note that leaves can be scored for some values even if not all values can be measured. Once leaves are scored for features that can be directly measured or observed, variables (like Feret's diameter and Feret's diameter ratio) can be calculated for each leaf.

Once you have made a table with the measurements and calculations for each leaf, you can determine morphotype-mean values for each morphotype. In order to do this, simply find the mean (average) of each measurement and variable for the set of leaves in each morphotype. If a scored leaf lacks a particular measurement or variable, leave it out of the average for the affected measurement or variable. If only one leaf was scored a morphotype, then its scores are the values for the morphotype.

Site-mean values

Finally, morphotype-mean values must be used to compute site-mean values. A site-mean value for a given variable is just the mean (average) of the morphotype-mean values for that variable. The site-mean values are the values actually used in the equations for mean annual temperature (MAT) and mean annual precipitation (MAP) given below.

Example table of leaf morphotype scores, calculated morphotype means, and calculated site means for leaf variables²

² The above table shows a hypothetical example of scoring of leaf morphotypes for DiLP analysis of MAT; only selected characters are shown in order to simplify the example. Individual leaves in each morphotype category are scored separately. The scores for each morphotype are averaged to produced a morphotype-mean value for each variable. Finally, the morphotype-mean values are averaged to produce a site-mean value for each variable.

Mean annual temperature

The mean annual temperature (MAT) equation for DiLF was proposed be Peppe et al. (2011). The equation is as follows:

MAT = 0.21E + 42.296(FDR) - 2.609(T:IP) - 16.004

Where:

MAT = mean annual temperature, the variable being calculated.

E = percent of species with entire (in this analysis, meaning untoothed) margins.

This value is calculated as follows: number of woody dicot species with entire-margined (untoothed) leaves ÷ total number of woody dicot species × 100

FDR = Feret's diameter ratio.

This value is the site-mean FDR. See above for calculation.

T:IP = number of teeth to internal leaf perimeter.

This value is the site-mean T:IP. The entire-margined species may be omitted from the site-mean T:IP. See above for calculation.

Origin of the equation

The equation above is based on an equation from multiple regression analysis. The general multiple regression equation looks like this:

y = b₁x₁ + b₂x₂ + b₃x₃ + a

The purpose of multiple regression analysis is to estimate a dependent variable (y) from a set of independent variables (x₁, x₂, x₃, etc.). In the equation above, the dependent variable (y) that we are estimating is mean annual temperature (MAT). The independent variables (x₁, x₂, x₃) that we are using to estimate MAT are:

x₁ = E, the percent entire-margined woody dicot species in a given flora.

x₂ = FDR, the site-mean Fermet's diameter ratio.

x₃ = T:IP, the site-mean standardized tooth count (number of teeth ÷ internal leaf perimeter in cm).

The numbers preceding each independent variable (b₁, b₂, b₃) are regression coefficients (regression weights) for each of the independent variables. Regression coefficients quantify the correlation in change between each independent variable and the dependent variable; they are equivalent to slopes for each of the independent variables. Remember:

Slope of a line = (change in y) ÷ (change in x)

For example, in the equation above, the regression coefficient for percent entire-margined woody dicot species (x₁ or E) is 0.21. Thus, there is a 0.21ºC change in mean annual temperature (MAT or y) for every 1% change in entire-margined woody dicot species (E) provided that the other independent variables (FDR and T:IP) do not change. Remember, the DiLP equation is balancing information from three independent variables (E, FDR, and T:IP) to predict one dependent variable (MAT). Thus, the regression coefficients help to determine the weights given to each of the independent variables.

Finally, a is a constant equivalent to the y-intercept (y=0). In the above equation, it is -16.004. Thus, when y = 0:

0.21E + 42.296(FDR) - 2.609(T:IP) = 16.004

Mean annual precipitation

Mean annual precipitation can be calculated using the following formula:

ln(MAP) = 0.298ln(BA*100) - 2.71ln(PR) + 0.279ln(T:IP) + 3.033

Where:

ln = natural logarithm.

ln(MAP) = natural logarithm of mean annual precipitation (MAP).

ln(BA in mm²) = site mean for the natural logarithm of leaf blade area in mm.

Note: BA in mm² = 100 × (BA in cm²)

ln(PR) = site mean for the natural logarithm of perimeter ratio (perimeter ÷ internal perimeter).

ln(T:IP) = site mean for the natural logarithm of standardized tooth count (teeth per cm of internal perimeter).

Make note of the fact that blade area is in millimeters squared (mm²), whereas standardized tooth count is expressed as teeth/cm (cm^-1).

The DiLP MAP equation has the same structure as the equation above, except that we are solving for the natural log (ln) of mean annual precipitation (MAP), rather than MAP directly. In order to calculate MAP, the equation must be solved for ln(MAP). Then, the following must be calculated.

MAP = e^ln(MAP)

Where:

e = 2.718281828459 . . .

The number represented by e is a mathematical constant, like pi (π, approximately 3.14).