The use of binary and octal notation for designating races of plant pathogens

Abstract

2) and 1) proposed methods for assigning race names with the ability to convey analytical information for plant pathogens. Both proposals were based on the principle of defining a set of differential cultivars and, in a test with a pathogen isolate, classifying each cultivar in the set into either of two reaction classes, resistant or susceptible, for which the pathogen is classified correspondingly as avirulent or virulent, and assigning a 0 for resistance/avirulence and a 1 for susceptibility/virulence. Writing the cultivar list horizontally, the cultivar on the right hand end of the list represented the lowest number and that on the left hand end the highest. The row of zeros and ones indicating resistance or susceptibility then appeared as a binary number. In the system of 2) this binary number was translated into a decanary number, and in that of 1) groups of three cultivars were used to produce octal numbers. These were used for naming the races of the pathogen. Both these original proposed systems used the normal numerical convention of having units on the right and higher order numbers to the left of this. The octal system is easy to remember in this normal order ( Table 1). 3) described a method for assigning names to races, biotypes or pathotypes of pathogens whose populations consist of variants detected by their differential virulence on selected sets of host cultivars. They developed a spreadsheet with capabilities of assigning the names for races. and analysing some attributes of the pathogen populations. Thus the programme has the practical objective of helping those who have the challenge of analysing such populations. They developed the program to use binary/decanary and binary/octal designations and emphasized the advantages of the latter. Unfortunately, in developing the programme, they chose to reverse the numerical notation for their race analysis. This is an option that seems unnecessary and unhelpful to those wishing to use the spreadsheet. They advanced the argument that, because the normal convention is to write a horizontal list from left to right, it is normal to write the lowest numbered differential on the left, and therefore, that it is preferable to reverse the numerical system also. It should be noted that, when a normal number is written, it is written from left to right across the page, but that, nonetheless, the units are on the right. The whole number is kept in mind to permit it to be written correctly. For example, the number 569 would be written from left to right and would normally be read as five hundred and sixty-nine. If, however, the numerical convention was reversed, this number would have to be read as nine hundred and sixty-five. To reverse the direction of reading the number would clearly be a source of possible confusion. The same risk of confusion arises by the reversal of the binary numbering system proposed by 3) for their spreadsheet, to produce a reverse octal system ( Table 2). To insist on reversing the numerical system simply because a list is normally written from left to right (when written horizontally) seems to indicate a psychological preoccupation with the conventional system of Western writing, at the expense of the normal system of writing numbers. A reverse binary system is more difficult to remember than a normal binary system. It seems particularly unnecessary to reverse the numerical system when devising a spreadsheet, in which the calculations are controlled by entry of an appropriate formula, and data can be entered in any order appropriate for that formula. A spreadsheet could just as easily produce a normal binary/octal number as a reverse number. The use of normal binary notation is preferable for these pathogen assignation systems, as originally proposed by 2) and 1), and reversal of the code seems more complicated and is unnecessary. Although the paper by 3) came to my attention through my activities as Senior Editor of this journal, my reaction to the paper arises from my long-term professional interest in the challenge of accurate analysis of the type of pathogen populations they refer to.