A method to implement continuous characters in digital identification keys that estimates the probability of an annotation

Abstract

Premise: Species identification is vital to many disciplines. Digital technology has improved identification tools, but the direct use of characters with continuous states has yet to be fully realized. To achieve full use of continuous characters for identification, I propose a classifier that calculates a posterior probability (degree of belief) in possible name assignments and an estimate of the relative evidence for the candidate annotations.

Methods: A model for a species is defined using continuous morphological characters, and an algorithm for identification with a naive Bayesian classifier, using the model, is presented. A method of estimating the strength of evidence for candidate species is also described.

Results: The proposed method is applied in two example identifications: native vs. invasive Myriophyllum in North America and vegetative Rhipidocladum bamboos in Mexico. In each instance, the new method provides a probability and estimate of the strength of the probability to enhance the name assignment in situations where taxa are difficult to differentiate using discrete character states.

Discussion: Naive Bayesian classifiers take advantage of the predictive information inherent in continuous morphological characters. Application of this methodology to plant taxonomy advances our ability to leverage digital technology for improved interactive taxonomic identifications.

Keywords: continuous; identification; key; morphology; naive Bayesian classifier.

Figure 1

Probability densities for the number of leaf segments in Myriophyllum spicatum (solid green), M. sibiricum (solid orange), and the M. sibiricum × M. spicatum hybrid (dashed blue). Mean and variance parameters were estimated from data extracted from Moody and Les (2007).

Figure 2

Evidence, 10 times the log ratio of the probability for a species over the probability against a species (Jaynes, 2003), expressed in decibels (dB) along a continuum of leaf segment number for three taxa of watermilfoil: Myriophyllum spicatum (solid green), M. sibiricum (solid orange), and the M. sibiricum × M. spicatum hybrid (dashed blue). The dotted black line depicts the point of equal odds; when a curve is above this line, there is positive evidence for species identification. Underlying probabilities were generated from data in Moody and Les (2007).

Figure 3

Probability densities for each of four species of Mexican bamboo, Rhipidocladum bartlettii (solid green), R. martinezii (dash‐dot purple), R. pittieri (dashed blue), and R. racemiflorum (solid orange), for two characters: (A) foliage leaf width (mm) and (B) number of branches per mid‐culm node.

Figure 4

Evidence surfaces, 10 times the log ratio of the probability for a species over the probability against a species (Jaynes, 2003), in decibels (dB) for each of four species of Mexican bamboo across two characters: foliage leaf width (mm) and number of branches per mid‐culm node. (A) Rhipidocladum bartlettii, (B) R. martinezii, (C) R. pittieri, and (D) R. racemiflorum. Dashed lines depict the level of equal odds. Areas of the surfaces that lie above the equal odds plane are colored and represent combinations of character states with evidence favoring a taxon's identification.

Figure 5

Contours of the odds in favor of a specimen belonging to one of four species of Mexican bamboo (Rhipidocladum bartlettii [solid black on green], R. martinezii [dash‐dot black on purple], R. pittieri [dashed black on blue], and R. racemiflorum [solid gray on orange]) plotted across the continuum of states for foliage leaf widths in millimeters (x‐axis) and the number of branches per mid‐culm node (y‐axis). Marginal plots show the evidence, 10 times the log ratio of the probability for a species over the probability against a species (Jaynes, 2003), in decibels (dB), for each character independently. Line colors in marginal plots conform to their respective species.