A new tool for entry and analysis of virulence data for plant pathogens

Abstract

The methods of Habgood (1970) and Gilmour (1973) for the assignment of pathogen race names are discussed and the advantages of a reversed octal system, based on Gilmour's octal code, are emphasized. A new spreadsheet, ‘HaGiS’, exploits these two designation systems to provide user‐friendly and fast access to some routine steps in the analysis of virulence data for plant pathogen populations. It produces graphs and tables for frequency distributions (of pathotypes, isolate complexities and cultivar susceptibilities); sorted lists (e.g. of the races ranked by predominance); indices (of sample diversity and of pathogenicity for each differential cultivar); and coloured proximity matrices. Use of HaGiS requires knowledge of only a few basic functions of MS Excel 97^®. All graphs, tables, indices and matrices are generated automatically and displayed by switching to the corresponding worksheet. In addition to data analysis, the spreadsheet is convenient for the entry of experimental data, allowing for all commonly used assessment scales.

Introduction

Physiological races of plant pathogens are routinely characterized by their spectrum of pathogenicity for a defined set of differential host cultivars and various methods of naming the races have been developed. The system proposed by 5) and particularly its modification by 2) are considered to be useful because the race name produced contains coded information for the virulence of the race. Utilizing these codes, a spreadsheet, HaGiS (Habgood–Gilmour), was produced in MS Excel 97^® for the entry and evaluation of pathogenicity data and is available free of charge upon request.

The major properties of the two naming systems are summarized, emphasizing the advantages of Gilmour's octal code. The main features of the new spreadsheet, which aims at standardizing and simplifying some frequently recurring steps in virulence analysis of plant pathogens, are also described.

Habgood's designation method

In the simplest case, pathogenicity can be rated on a dichotomous scale, assigning 0 for avirulence on a differential and 1 for virulence. Each pathogen isolate is classified by its disease reactions on a given differential set, resulting in a sequence of 0s and 1s, the ‘pathotype vector’. 5) proposed that the series of zeros and ones can be regarded as a binary number, whose value is converted into its decimal (decanary) representation, giving a binary/decanary code. The number derived in the decanary conversion then serves as a race name for that particular pathotype and translation back to the binary code reveals the spectrum of virulence.

Habgood originally suggested listing the cultivars of the differential set from right to left, i.e. with the lowest numbered differential on the right, and calculating the binary value of the observed virulence in the conventional manner as the inner product P^→ · W^→ of the pathotype vector P^→ and the weight vector W^→ = (2^{(n − 1)}, …, 2¹, 2⁰) of proper dimension. Following 8) we prefer a modified but equivalent notation, in which the order of weights is reversed, i.e. w^→ = (2⁰, 2¹, …, 2⁽ⁿ⁻¹⁾), and the list of cultivars is presented in the ‘more natural’ order, written from left to right. Given a differential set of n = 12 cultivars A, B, C, …, L, for example, in which all cultivars except D, E, K and L are susceptible to an isolate, i.e. we obtain the pathotype vector p^→ = (1, 1, 1, 0, 0, 1, 1, 1, 1, 1, 0, 0) and assign ‘999’ as race name, because the corresponding inner product p^→ · w^→ equals 1.2⁰ + 1.2¹ + 1.2² + 0.2³ + 0.2⁴ + 1.2⁵ + 1.2⁶ + 1.2⁷ + 1.2⁸+ 1.2⁹ + 0.2¹⁰ +  0.2¹¹ = 999. The short race name ‘999’ carries the same information as the lengthy pathotype vector p^→.

The binary/decanary nomenclature of 5) eliminated several drawbacks of earlier notations ( 3). Some of its merits are: (1) isolates of different pathotypes are readily distinguishable by name and easily sorted numerically; (2) neither specific mechanisms nor knowledge of the genetics underlying host–pathogen interactions is required; (3) results from different surveys employing the same differentials are fully compatible; (4) for each race, the associated susceptibility pattern can be recovered completely from its coded name; (5) once the set of differentials and their linear arrangement are fixed, the naming system is exhaustive, i.e. names are provided for all possible races that can be diagnosed within the differential set; (6) differential sets can be extended, although race names will change for isolates virulent to newly added cultivars.

Generalization to more than two categories

Sometimes it is desirable to avoid the restrictions of dichotomous rating of virulence into only two classes and to expand the scale into three, where differentials are classified as resistant, intermediate or susceptible, or into more classes for a more precise record of observed infection types. The binary/decanary code can easily be generalized in this direction by substituting the power‐of‐two weights by power‐of‐three or higher weights. To indicate the number of categories in the rating scale, binary/‐, tertiary/‐ and quaternary/decanary classifications can be proposed. Where there are three classes, pathotype vectors with 0s, 1s and 2s, e.g. vector (1, 2, 1, 2, 0) would receive the reverse tertiary/decanary race name 70, because 1.3⁰+ 2.3¹+ 1.3²+ 2.3³+ 0.3⁴ = 70. It is clear that this number could also arise in a two‐celled classification system. In order to avoid ambiguities the underlying code should always be stated explicitly.

Drawbacks of the naming system

Because of its advantages, the binary/decanary system was well accepted and widely used, and was applied to several different fungal pathogens, e.g. rusts, mildews and potato blight ( 5; 8). However, over time several difficulties with this notation became apparent, especially in surveys with large differential sets: (1) the lack of direct correspondence between race names and susceptibility patterns makes the recovery of pathotypes cumbersome, even for medium‐sized differential sets; (2) relations within and between pathogen isolates are not easily recognized. Similarities, differences and subpatterns are not obvious from the names. Compare for example the above race ‘999’ with race ‘2023’. These are quite divergent names for two very similar pathogen races, which differ in their reaction on only one of 12 differential cultivars whereas races 2023 and 2048 appear much closer by name, but in fact differ in their virulence on 10 of 12 cultivars; (3) compatibility is poor for results from studies with extended differential sets because addition of new cultivars will change race names substantially if a virulent isolate is found; (4) for incomplete data, the binary/decanary code fails, and no meaningful name can be assigned if the disease reaction is missing for any cultivar.

Gilmour's triplet code

Fortunately, the problems encountered with Habgood's method can be overcome by a small but powerful modification. Instead of representing the binary values decimally, 2) proposed the use of octal numbers. This amounts to breaking down the series of 0s and 1s into groups of three. Consequently the binary values of all resulting triplets will fall within the range from 0 to 7, and may be represented entirely by octal digits. Table 1 lists the possible pathotypes for a cultivar triplet (A, B, C) and their reverse octal designations. For example, two virulences in a triplet can arise in three different ways, which result in the octal digits 3 (virulent on A and B), 5 (virulent on A and C), or 6 (virulent on B and C). The reverse octal system is used to keep the order of cultivars from left to right and then to reverse the corresponding weight vectors. 2) originally proposed the non‐reversed octal code; however both versions are equivalent.

Table 1. Reverse binary/octal code to combinations of virulences and avirulences in a triplet of differential cultivars (A, B, C), resulting from reversing the order of weights (see text). Virulence to a cultivar is scored as 1 in the corresponding column, while avirulence is scored as 0. The octal digits are sorted according to the number of virulences per triplet, leading to a switch of digits 3 and 4

Whilst the binary/octal code preserves all the benefits of the binary/decanary naming system, it avoids the inherent problems of the latter: (1) octal race names display relationships between races more clearly. The fictitious reverse binary/decanary races 999, 2023 and 2048, for example, are labelled 7471, 7473 and 0004 in their reverse octal form. The closeness of pathotypes 7471 and 7473, and their distance from race 0004, are now evident and well reflected in their race names; (2) the triplet‐based system allows comparisons between same‐position digits: for example, races 7471 and 7473 match in three positions indicating identical susceptibilities for three triplets, i.e. in the first nine cultivars; (3) because of this same‐position compatibility, it also becomes meaningful and often useful to sort binary/octal race names with respect to any single position of interest; (4) in the binary/octal nomenclature, only eight different patterns, shown for the reverse binary/octal code in Table 1, must be memorized in order to diagnose the original virulence reactions for each triplet, e.g. 7471 and 7473 only disagree in their last digit, which corresponds with the triplet (J, K, L). Now, reverse binary/octal ‘1’ translates into (1, 0, 0) and ‘3’ into (1, 1, 0), hence their only difference lies in cultivar K; (5) the new designation method is open‐ended, i.e. compatibility between studies is preserved, even if, in some of them, the differential sets were extended; (6) in contrast to binary/decanary, the binary/octal system accommodates missing information, as long as only a few triplets are affected (corresponding digits are then marked by underscores as defective, 3). Nondefective digits stay unchanged and can be evaluated without restrictions; (7) octal names strongly reflect the linear arrangement of differentials. 3) therefore emphasized the importance of carefully selecting the order of cultivars in the set, for which they discuss a number of valuable criteria.

The binary/octal modification ( 2) apparently constitutes a substantial improvement over the binary/decanary code, as illustrated by the advantages discussed above. Applications to rust, mildew, and leaf blotch can be found in 1) and in 3). The binary/decanary and binary/octal systems were both published in the early seventies in Nature ( 5; 2). Nevertheless, Gilmour's method still seems to be much less well known, and was therefore independently reintroduced several times in the past ( 1; 8).

The new spreadsheet

The Habgood–Gilmour Spreadsheet (HaGiS) is designed as a tool for the convenient entry of pathogenicity data by personal computer (PC). Entered raw data are immediately converted into pathotype vectors, and associated reverse binary/octal and reverse binary/decanary race names are calculated. At the same time, HaGiS provides selected characteristics of the given data set. The program currently offers 12 different sheets, labelled according to their function, e.g. ‘data‐entry’, ‘print SG’, ‘Fig. C’, or ‘conv’. The user starts in ‘data‐entry’ by specifying the range of the assessment scale and its partition into categories. For instance an assessment scale from 0 to 4 is usually partitioned into the classes avirulent (0, 1 or 2) and virulent (3 or 4). At least two classes are required, and up to four (quaternary) may be defined. The program can handle such commonly used assessment scales as 0–4, 0–9, or 0–100. The maximum size of the differential set is currently limited to 25 cultivars, but no restrictions apply to their linear arrangement. Two rows in the data table are reserved for entry of cultivar names, one column for isolate names, and one column on the right end of the table for a control line or successful infection check. User input is only permitted in specifically marked (green) areas. All input undergoes a consistency check, and detected inconsistencies are reported through error messages (e.g. no value outside the corresponding user‐defined range will be accepted).

Once the data are entered into the data‐entry sheet various tables, figures and statistics describing the sample can be viewed in other sheets. The table toolbar at the bottom of the screen displays the names of all available sheets. In some sheets, the user will find the tables and graphs derived from the data set already produced. In other sheets, the corresponding features will be generated as soon as the sheet is selected.

The sheets labelled with the prefix ‘print’ supply different tables in printable form:

•print SG documents the original susceptibility raw data with corresponding reverse binary/octal race names and associated virulence complexities

•print SH contains the same information, but with reverse binary/decanary race names

•print PG lists the pathotype vectors (derived according to the user‐defined categories) together with their reverse binary/octal race names and complexities

Sheets labelled with the prefix ‘Fig.’ display frequency distributions in graphs and tables, supplemented with appropriate indices (means, standard errors, or diversity measures):

•Fig. C shows the sample distribution of complexities as a histogram and a table. Sample mean, standard deviation and standard error are provided

•Fig. S displays the susceptibility distribution of cultivars as a histogram and a table. Various indices are provided

•Fig. P(all) contains, in graphical and tabular form, the distribution of all pathotypes (races) found in the sample, as well as the values of several diversity indices and a table where races are ranked according to their predominance

•Fig. P(gt1) displays the same features as Fig. P(all), but excludes all races with fewer than two occurrences in the sample

The third group of sheets is concerned with comparisons between pathotypes or cultivars:

•virdif provides another option to compare races by determining their departure from the pathotype pattern of the most frequent race in the given sample

•pairw generates a proximity matrix for pairs of pathotypes. The user can select different proximity measures, such as Dice or Russell‐Rao. An additional colouring option helps to identify pairs of pathotypes with extremely low or extremely high similarity

Sometimes only the race name of a pathogen is known but one is interested in the associated virulence pattern. A conversion sheet is therefore included:

•conv decodes reverse binary/octal (or reverse binary/decanary) names back to the underlying pathotype vectors; it also converts between the octal and decanary names. The ‘conv’ sheet also provides an additional tool for converting binary/octal to reverse binary/octal names

Discussion

The introduction of binary/decanary classification ( 5) significantly simplified the representation and analysis of pathogenicity data. 11) used this code and developed the computer program VIRULA (VIRULence Analysis), specifically designed to process virulence data. VIRULA is a DOS‐based program, written in Turbo Pascal, that performs various descriptive and inference‐statistical procedures. As intended by its authors, VIRULA has contributed in the past to the unification of methodological approaches in the analysis of virulence data. However, since the publication of VIRULA, hardware and software of PCs has improved significantly and it now seems worthwhile to design a new program that takes greater advantage of the latest developments in PC technology. The HaGiS program is such an attempt, to provide a tool for entry and analysis of pathogenicity data.

HaGiS is developed in Microsoft Excel 97, which combines the user‐friendly interface of Windows with the benefits of a spreadsheet and was chosen primarily because of its widespread availability. Consequently no special HaGiS commands have to be learned to handle the software; familiarity with a few basic functions of Excel is sufficient. The program is designed to be as flexible as possible with respect to assessment scale, scale partitioning, and sample size, as well as to the number and order of differential hosts. The development of HaGiS in Excel allows users to make many adjustments to serve their individual needs.

The purpose of HaGiS is dual. It is convenient for data entry; and it offers a first overview of the data by means of graphical and numerical representation. Without elaborate programming or other time‐consuming preparations, the user can instantly browse through various readily available sheets displaying the input data and offering a choice of distinct figures, tables, indices, and statistics. Currently, descriptive methods dominate the selection, but in the future it is intended to implement additional inference‐statistical procedures. For more complex analytical procedures the entered data set can be transferred easily to other appropriate software packages.

HaGiS can be requested by E‐mail from [e-mail]‐giessen.de or downloaded from the web site http://www.uni‐giessen.de/∼gh75/hagis.htm, where a short, illustrated manual provides further explanations and instructions. Users are encouraged to send us their comments and suggestions by E‐mail.

Acknowledgements

We gratefully acknowledge Lothar Langer, Rod Snowdon, Santani Teng and Jörn Pons‐Kühnemann for their valuable assistance and critical reading of the manuscript.

Appendix

The following section provides additional definitions, references and information concerning the set of indices and coefficients utilized in the HaGiS program. We start by introducing some notation used in subsequent formulas:

Ntotal number of isolates in the sample

Dnumber of differentials

MAXupper limit of the (user‐defined) assessment scale

a_{δ j}assessment rating of the pathogenicity of isolate j against differential δ

Rnumber of distinct races (pathotypes) detected in the sample

n_iobserved number of isolates of race i in the sample

P_i = n_i/Nproportion of isolates of race i in the sample

ln xnatural logarithm of x

The Fig. S‐sheet calculates for each differential δ (with δ = 1, 2, …, D) the corresponding Pathogenicity Index PI%, where PI_δ = Σa_δj (MAX.N), i.e. with respect to a differential δ the assessment ratings a_δj of isolates j = 1, 2, …, N are summed, then divided by the product MAX times N. See 12).

The P(all)‐sheet contains the following five commonly used diversity indices:

1 the Simple Index Q = R/N.

2 the Gleason Index G = (R − 1) ln N.

3 the Shannon Index H = −ΣP_i. ln P_i, i = 1, 2, …, R. The values of H can range from 0 to ln R.

4 the Evenness Index EH = H ln R, i.e. the normalized version of Shannon's H, obtained by division through H_max = ln R.

5 the Simpson Diversity Index S = 1 − Σ(n²_i − n_i)/(N² − N), i.e. the probability of obtaining two distinct pathotypes when randomly drawing two isolates from the sample.

The concept of diversity incorporates several aspects, two of which are ‘richness’ (i.e. the total number of distinct races) and ‘evenness’ (i.e. the degree of predominance of some races). In that sense Q and G measure only richness, and EH only evenness, while H and S each measure a combination of both aspects of diversity. With respect to sample size, Q and H are highly sensitive, and therefore not recommended for comparisons between samples of substantially divergent sizes. A detailed discussion can be found in 4) and in 10), for more recent developments, see 9) and 7).

The virdif‐sheet provides for each race i the virulence difference V_i, defined as the number of disagreements in pathogenicity between race i and the sample's most frequent (dominant) race i₀. For any dichotomous scale, pathotype vectors may be coded by sequences of zeros and ones, i.e. all vector components are 0s or 1s. The corresponding virulence difference can therefore be calculated by V_i = Σ ∣ p_δ − q_δ ∣, where p_δ and q_δ, with δ = 1, 2, …, D, denote the components of the pathotype vectors p and q of races i and i₀, respectively.

The pairw‐sheet generates a proximity matrix for all pathotype pairs. HaGiS offers a choice of six proximity measures (coefficients), each based on the same 2 × 2‐contingency table with the following entries: cell a (cell d) contains the number VV (AA) of differentials to which both races i and j are virulent (avirulent), cell b (cell c) contains the number AV (VA) of differentials to which race i is avirulent (virulent) and race j is virulent (avirulent), respectively. Note that D = VV + AV + VA +AA. The available measures are defined as follows, see e.g. 6):

1 the Dice coefficients

D ₁% = 100.2AA/(AV + VA + 2AA) and

D ₂% = 100.2 VV/(2VV + AV + VA).

2 the Russell–Rao coefficients

RR ₁% = 100.AA/D and RR₂% = 100.VV/D.

3 the Simple match and Simple mismatch coefficients

S_ma% = 100.(VV + AA)/D and

S_mis% = 100.(AV + VA)/D.

The displayed sample averaged– is calculated by d– = (1/N²) Σ_i,jf_i.f_j.d(i, j) where d(i, j) is the proximity value of races i and j computed according to the formula of the selected coefficient, f_i and f_j are the number of occurrences of races i and j, respectively.