Epidemiological analysis of the effects of biofumigation for biological control of root rot in sugar beet

Abstract

The effects of biofumigation using a Brassica juncea (mustard) cover crop on the dynamics of rhizoctonia root rot of sugar beet were recorded in two field trials in 2007 and 2008, and analysed using epidemiological modelling. Differences between partial biofumigation, involving the pulling up of mustard plants, and complete biofumigation, involving the crushing and incorporation of mustard residues into the soil, were compared with bare soil treatment. An epidemiological model was used that includes rates of transmission of primary and secondary infection, pre-emergence damping off, and expression of wilting symptoms (above-ground disease) due to infected roots (below-ground disease). The model indicated that biofumigation reduces the transmission of primary infections but affects secondary infections in a variable pattern between field trials. Likewise, the proportion of infected plants expressing wilting was significantly reduced, by 28%, in the partial and complete biofumigation treatments compared with bare soil in the trial of 2007 but not in 2008. It is suggested that the effects of biofumigation on secondary infection and the expression of disease are more variable than those on primary infection, and that this is probably due to an interplay between pathogen, antagonists, host, and environmental factors. These interactions may or may not offset the benefits afforded by a reduction in primary infection and account for the overall variable success of biofumigation to control disease.

Introduction

The epidemiological processes involved in the spread of a soilborne plant pathogen are now well-defined (Gilligan, 2002). Typically, they involve a phase of primary infection as the pathogen spreads from particulate inoculum to nearby roots or plants. During this process the rate of primary infection may decline in response to decaying inoculum or to the spatial limitations of pathogen transmission. This may be followed by a phase of secondary infection if the pathogen spreads from root to root or from plant to plant. The rate of secondary infection might be constant over time or might be described by a more complicated function in response to temporal changes in pathogen infectivity, host susceptibility, the soil environment or the spatial distribution of the host population (Otten et al., 2003; Bailey et al., 2009). Pathogen dynamics involving distinct phases of primary and secondary infection are typically characterized by two plateaux, one at the end of primary infection and, if time permits before crop harvest, a second at the end of secondary infection (Bailey et al., 2009) (Fig. 1).

Figure 1.  Schematic of the dynamics of infection (I) and disease (D) over time for an epidemic of Rhizoctonia solani in sugar beet. The effects of biofumigation are examined with respect to rates of primary infection (1), final levels of pre-emergence damping off (2), rates of secondary infection, (3) and the proportion of infected plants expressing disease at harvest (4).

Rhizoctonia solani is a soilborne fungal pathogen that is widespread and destructive across an extensive range of host species (Sneh et al., 1996). A combination of high pathogenicity in susceptible crops and high competitive saprotrophic ability to colonize dead organic material makes this one of the most economically important crop pathogens worldwide. Rhizoctonia solani is also a major pathogen of sugar beet for which the epidemiology is poorly understood. For the anastomosis group (AG) AG2-2, the disease can present firstly as pre-emergence damping off, then as post-emergence damping off, and finally as root and crown rot on mature plants (Herr, 1996). However, the timing and the relative contributions of epidemiological processes (primary and secondary infection) in relation to the stages of the disease (pre- and post-emergence damping off and crown rot) are not yet known.

Biofumigation is increasingly considered as an effective alternative to synthetic chemicals for the control of soilborne pests and disease (Matthiessen & Kirkegaard, 2006). Biofumigation involves the growth and then shredding and incorporation of the residues into the soil of a cover crop grown during the intercrop period between commercial crops. Brassica crops, and in particular Brassica juncea (Indian mustard), are of particular interest for biofumigation because they contain significant levels of glucosinolates that, on hydrolysis by a myrosinase enzyme released during the shredding process, are converted into fungitoxic isothiocyanates (ITC). The ITC can reduce activity of pathogen inoculum in the soil and hence the magnitude and severity of disease epidemics in the subsequent crop of beet (Motisi et al., 2009b). The growth and incorporation of a mustard crop for the control of R. solani in sugar beet has been described as having two key phases (Motisi et al., 2010). First, in the cropping phase a small dose of glucosinolates may be delivered into the soil from the Brassica crop, via root exudates along with a living root population, and be converted into ITC by soil microflora which exerts a myrosinase-type activity (Gimsing et al., 2007). Secondly, in the residue phase the above ground biomass of the Brassica crop is crushed and incorporated into the soil along with the dead roots, releasing larger quantities of ITC together with large volumes of plant biomass, which tends to increase antagonism between soil microbial populations (Mazzola et al., 2007; Yulianti et al., 2007; Motisi et al., 2009a). The contribution of the two phases to the success or failure of biofumigation has not been examined. Depending on many factors, such as the net pathogen inhibition due to the ITC and antagonism, and pathogen growth on living or dead plant biomass, either of the two phases can lead to a reduction or amplification in pathogen inoculum with consequences for epidemic development in the subsequent sugar beet crop (Motisi et al., 2010).

Whilst it is now generally accepted that epidemiological modelling of transmissible disease data, which requires the use of non-linear models, offers a means of improving our understanding of the processes involved in the spread of disease (Gilligan, 1990b), the difficulties in collecting data constrain the use of such techniques for soilborne plant pathogens. Surrogate observations of aerial symptoms of below-ground infection such as changes in plant height, leaf colour and turgor offer an alternative measure of disease progress. The key is then to establish the relationship between the above-ground expression of disease symptoms and the below-ground epidemic. It should be noted that the relationship itself might be subject to the effects of biofumigation.

The aim of this work is to use a parsimonious epidemiological model that includes terms for primary and secondary infection, and links, in a simple way, the above-ground disease symptoms (wilting) with below-ground disease (measured twice; at plant emergence and at harvest) in order to analyse the effects of biofumigation on R. solani infection of sugar beet. Specifically, this study quantifies partial biofumigation (growing the mustard crop only) and complete biofumigation (growing the mustard crop and incorporating its residues in the soil) on primary and secondary infection using data on below-ground diseased plants (pre-emergence damping off and diseased roots at harvest) and on the proportion of diseased plants that express wilting during the cropping season (Fig. 1).

Materials and methods

Experimentation

Observations were made in two field trials as described in Motisi et al. (2009b). Data quantifying post-emergence disease (wilting) over time and the number of below-ground diseased plants at harvest were obtained from the observation of epidemics in 2007 (trial 2007) and 2008 (trial 2008) conducted at the INRA Experimental Domain at Epoisses, Côte-d’Or, France (5°05′56″E; 47°14′20″N).

The trials are described briefly here (for further details refer to Motisi et al., 2009b). The two field trials involved a sugar beet–wheat rotation pre-inoculated with R. solani, AG2-2 IIIB isolate G6 in 2006. Sugar beet (cv. Alpage; five seeds linear m⁻¹; 97% germination rate) was grown in 2007 in trial 2007, and in 2006 and 2008 in trial 2008 (with observation of disease to inform modelling in 2008 only). In each trial, mustard was grown as a late-summer cover crop during the intercrop period between the wheat and sugar beet crops. A complete, randomized block design was used in each trial allowing four replicate plots for three treatments of intercrop management: partial biofumigation involving mustard pulled out at flowering (named MP in Motisi et al., 2009b), complete biofumigation with mustard crushed and incorporated into the soil at flowering (MC in Motisi et al., 2009b), and no biofumigation with bare soil (BS in Motisi et al., 2009b) plots used as baseline. Each plot in each treatment measured 18 m in length and 6 m wide.

Below-ground diseased plants were counted on two occasions: (i) as pre-emergence damping off (Pre-DO), defined as the difference between the number of viable seeds (Table 1) and the number of emerged plants at harvest; and (ii) as post-emergent diseased plants, evaluated by visually assessing the sugar beet roots in the six (18 m long) central rows of each plot (corresponding to about 540 sugar beets per plot) after destructive sampling at harvest (Motisi et al., 2009b). Hereafter, below-ground diseased plants are defined as being infected and infectious, I. Post-emergence diseased plants were counted by assessing above-ground symptoms of crown rot resulting in leaf wilting. This monitoring was done on the whole surface of each plot over time, weekly from 24 April 2007 to up to 3 weeks before harvest (23 August 2007) in trial 2007, and from 7 May 2008 until harvest (17 September 2008) in trial 2008. Hereafter, wilted plants are defined as being diseased and infectious, D.

Table 1. Estimated (i) mean proportion (over four plots) of pre-emergence damping off (showing mean number of viable seeds in parentheses); (ii) parameters in the rate functions of primary infection (α₁, α₂); (iii) parameters in the rate functions of secondary infection (β₁, β₂, β₃); and (iv) proportion of infected plants expressing disease (γ) for epidemics of root rot in sugar beet caused by Rhizoctonia solani, in trial 2007 and trial 2008 for the treatments control bare soil, partial biofumigation and complete biofumigation. The rate of primary infection is described by an exponential decline (Eqn 4) and the rate of secondary infection is described by a log-normal rise and fall (Eqn 5) over time

Point estimates	Parameter	Unit	Trial 2007			Trial 2008
			Control bare soil	Partial biofum.	Complete biofum.	Control bare soil	Partial biofum.	Complete biofum.
(i) Pre-emergence damping off	Pre-DO	1	0·20 (1108)	0·18 (1108)	0·15 (1084)	0·04 (1069)	0·03 (1069)	0·01 (1069)
(ii) Primary infection	α1	1/°C day	2·0 × 10^−3	2·0 × 10^−3	1·9 × 10^−3	1·4 × 10 ^−3	2·4 × 10^−4	1·3 × 10^−4
	α2	1/°C day	8·4 × 10^−3	9·7 × 10 ^−3	1·1 × 10^−2	3·4 × 10^−2	6·3 × 10^−3	8·3 × 10^−3
(iii) Secondary infection	β1	1/°C day	5·9 × 10^−7	4·0 × 10^−7	3·6 × 10^−7	1·1 × 10^−6	9·0 × 10^−7	1·4 × 10^−6
	β2	1	2·5 × 10^−1	3·4 × 10^−1	3·0 × 10^−1	6·0 × 10^−1	5·3 × 10^−1	4·5 × 10^−1
	β3	°C day	1396	1450	1480	1482	1432	1498
(iv) Proportion of infected plants expressing disease (wilting)	D/I plants (γ)	1	0·64	0·46	0·46	0·37	0·36	0·34

Epidemiological model

Changes in the number of susceptible, S, infected, I, and diseased, D, plants over time, t, are described by a set of linked differential equations that define the SI(D) model:

Susceptible plants

• (1)

Infected plants

• (2)

Diseased plants

• (3)

Primary infection

• (4)

Secondary infection

• (5)

Disease is initiated by primary infection from particulate inoculum, X, at a rate α(t) (Eqn 2). As a response to the declining infection efficiency of the inoculum, the rate of primary infection, α, reduces exponentially over time from an initial level, α₁, and at a rate, α₂ (Eqn 4). The density of particulate inoculum, X, at the onset of an epidemic was not estimated experimentally and, without loss of generality, is fixed at 1·0; this means that the value of X is absorbed into the amplitude of α(t), which is estimated from the epidemiological data. The pathogen spreads by secondary infection from infected to susceptible plants with rate β(t). Following previous work involving R. solani (Otten et al., 2003; Filipe et al., 2004) and initial inspection of the data, a log-normal model for β(t) (Eqn 5) was used to accommodate a delay in the onset of secondary infection, followed by a rise and a subsequent decrease in the rate of secondary infection over time. The parameters β₁, β₂ and β₃ of the log-normal function define the maximum, width, and location of the curve describing β over time. The proportion of infected plants, I, expressing disease, D, is given as γ. For simplicity, the parameter γ is considered constant over time, and is calculated from experimental data at harvest in trial 2008; for trial 2007, γ is estimated in the fitting of the model to data, as the number of plants expressing wilting symptoms at harvest was not measured. Disease progress curves are interpreted according to changes in the rates of primary and secondary infection given by α(t) and β(t).

Statistical analysis

Levels of Pre-DO were calculated from differences between the number of sugar beets at harvest and the estimated number of viable seeds sown. The effects of treatment (partial and complete biofumigation and bare soil) on the previously defined proportions of plants with Pre-DO and above-ground disease were assessed by analysis of variance (anova), using a linear regression model with treatment and year and their interaction as explanatory variables.

Model fitting

For epidemics in trial 2007, six parameters, α₁, α₂, β₁, β₂, β₃ and γ, were estimated via maximum likelihood, whilst for trial 2008 the same parameters were estimated except for the proportion of infected plants expressing disease, γ, which was calculated directly from the data at harvest.

Comparison of disease progress curves

The effects of complete biofumigation and partial biofumigation on the processes (groups of parameters) of primary infection (α₁ and α₂), secondary infection (β₁, β₂ and β₃), and, only for trial 2007, linkage between infection and disease (γ), were analysed by parallel curve analysis (Gilligan, 1990a). Briefly, the statistical analysis of the effects of treatments (compared in pairs) on the above processes is based on comparing two versions of the fitted model that differ in the number of parameters allowed to differ between treatments. The statistical significance of differences between model versions was assessed using the residual sum of squares, i.e. the squared residual difference between model prediction and data summed over data points. In the simplest model version a common curve (CC) was fitted to the data of the two treatments (MP and MC); six parameters α₁, α₂, β₁, β₂, β₃, γ and five parameters α₁, α₂, β₁, β₂, β₃ were estimated jointly for trial 2007 and trial 2008, respectively. In the model version with the most free parameters, separate curves (SC_MP and SC_MC) were fitted without any common parameters to the data of each treatment MP and MC (2 × 6 and 2 × 5 parameters were estimated for each pair of treatments for trial 2007 and trial 2008, respectively). These models were compared with intermediate models (X) in which only some of the parameters for primary infection or secondary infection were allowed to differ between treatments. The statistical comparison of the treatments was performed using F-tests as proposed by Gilligan (1990a) that allow determination of the processes that contribute most to the differences between treatments:

• (6)

where RSS is the residual sum of squares and df the degree of freedom of each model. All statistical analyses were performed with R software (R Development Core Team, 2008).

Results

Pre-DO and disease symptoms (wilting)

In each trial, the mean proportion of Pre-DO was higher, although not significantly (P = 0·72), in the untreated plots than in the treated plots (Table 1). In trial 2007, the proportion of Pre-DO was 0·2, 0·18 and 0·15 in the bare soil, partial biofumigation and complete biofumigation treatments, respectively. Pre-DO in trial 2008 epidemics was identical in ranking to those in trial 2007, with mean proportion of 0·04, 0·03 and 0·01 Pre-DO in bare soil, partial biofumigation and complete biofumigation treatments, respectively. However, Pre-DO was significantly lower (P < 0·001) in trial 2008 than in trial 2007 (Table 1).

In trial 2007, disease symptoms (wilting) appeared on average 349 degree-days (using a base temperature of 4°C below which R. solani growth is zero) after sowing, rising to an initial plateau after 800 degree-days. At 885 degree-days there were approximately 10, five and two diseased sugar beet plants for plots treated with bare soil, partial biofumigation and complete biofumigation, respectively (Fig. 2a). In the bare soil plots, the average numbers of wilting plants then increased to a second plateau of about 84 plants at 2366 degree-days after sowing. Growing mustard as an intercrop (partial biofumigation) reduced the level of the second plateau to 48 diseased plants (anova, P < 0·001), whilst crushing and incorporation of mustard residues (complete biofumigation) reduced the final levels of disease still further to about 34 affected plants (anova, P < 0·001) (Fig. 2a).

Figure 2.  Epidemic data (dots) and fitted disease progress curves (lines) on the spread of sugar beet root rot for trial 2007 (a, b, c & d) and trial 2008 (e, f, g & h). a and e: changes in the number of diseased plants over time; b and f: changes in the number of infected plants over time; c and g: changes in the rates of primary infection; d and h: changes in the rates of secondary infection. Epidemic data and model curves are presented for bare soil plots (BS, black dots and solid lines), partial biofumigation plots (MP, grey dots and long dash), and complete biofumigation plots (MC, white dots and short dash).

Similar to trial 2007, in trial 2008 disease was first observed after about 300 degree-days after sowing. Unlike trial 2007, fewer diseased (wilted) plants were detected during the early part of the epidemics, which limited the evidence of an initial disease plateau. Notably during this period, fewer diseased plants were recorded for the bare soil plots than for those with either a partial or complete biofumigation treatment (Fig. 2e solid line vs 2e broken lines). However, at harvest the average number of diseased plants in bare soil plots had increased markedly to 76 whilst in partial and complete biofumigation plots it had only increased to 44 and 38 diseased plants, respectively (both of which were significantly different from the bare soil treatment, anova, P < 0·001). No second plateau was detected and the number of diseased plants was continuing to increase over time when the crop was harvested.

Infected plants I, and rates of primary and secondary infection

Fitting the model (Table 1) jointly to infection data (number of Pre-DO and below-ground diseased plants at harvest; Fig. 2b,f) and disease data (number of wilted plants; Fig. 2a,e) predicted the underlying changes in the numbers of infected plants over time (Fig. 2b,f). For trial 2007, the model outcome exhibited two plateaux for which the use of biofumigation showed significant reductions in the numbers of diseased (Fig. 2a) and infected (Fig. 2b) plants, particularly for the complete biofumigation treatment (Fig. 2b). The initial plateaux in the model peaked at 220, 200 and 180 infected plants for bare soil treatment, partial biofumigation and complete biofumigation, respectively (Fig. 2b). The second plateaux peaked at 355, 317 and 247 infected plants for bare soil treatment, partial biofumigation and complete biofumigation, respectively (Fig. 2b). For trial 2008, the model predicted the presence of an initial plateau in the number of infected plants that occurred at a similar time (about 300 degree-days) to that in the epidemics of trial 2007 (Fig. 2e). The magnitude of the initial plateau in trial 2008 was lower than that in trial 2007, but with identical ranking, peaking at 55, 50 and 18 infected plants for the bare soil, partial biofumigation and complete biofumigation treatments, respectively (Fig. 2f). For trial 2008, the model did not reach a second plateau in infection over the time the crop was grown.

The emergence of two phases in the predicted numbers of infected plants over time resulted from the temporal shape of the rates of primary infection (Fig. 2c,g) and secondary infection (Fig. 2d,h). Rates of primary infection declined to zero after 500 degree-days (after sowing), and were followed by rates of secondary infection that increased from 0 at 500 degree-days to a maximum at about 1500 degree-days before decreasing again. Statistical analysis (Tables 2 & 3) revealed that differences in epidemic behaviour between treatments were associated with differences in the estimated rates of primary infection, which had the highest significant F-values (except for the comparison between partial biofumigation and bare soil treatment in trial 2007). The rates of primary infection (Fig. 2c,g) were reduced by partial biofumigation in relation to bare soil; the model with varying parameters α₁, α₂ differed from the simplest model and the model with all parameters differing between these treatments (P < 0·01, F = 23·6 and 40·1 for trial 2007 and trial 2008, respectively; Tables 2 & 3). The rates of primary infection were further reduced by complete biofumigation compared with bare soil in both trial 2007 and trial 2008; parameters α₁, α₂ also differed from the simplest model and the model with the most free parameters (P < 0·01, F = 61·3 and 72·2 for trial 2007 and trial 2008, respectively; Tables 2 & 3). The effects of biofumigation on the rates of secondary infection (parameters β₁, β₂ and β₃) were also significant in both trials (F tests, P < 0·01; Tables 2 & 3), but were less consistent between the trials than the effects of biofumigation on primary infection. In fact, in trial 2007, both primary infections and secondary infections explained a significant part of the differences between treatments; the model with varying α₁, α₂, β₁, β₂ and β₃ is different from the model with varying α₁, α₂ for complete biofumigation compared with bare soil (P < 0·01, F = 4·7), for partial biofumigation compared to bare soil (P < 0·05, F = 3·1), and for partial biofumigation compared to complete biofumigation (P < 0·05, F = 3·2; Table 2). However, whilst in trial 2008 the largest part of the differences between treatments were explained by primary infections, the model with varying α₁, α₂, β₁, β₂ and β₃ is not significantly different from the model with varying α₁, α₂ when comparing the three treatments two by two (F = 1·3, 0·6 and 0·2 for partial biofumigation against bare soil, complete biofumigation against bare soil, and partial biofumigation against complete biofumigation, respectively; Table 3). As such, secondary infections contributed less to the differences between treatments in trial 2008 than in trial 2007.

Table 2. Comparison of disease progress curves for trial 2007. Calculated F-values (see text for details) higher than the critical value, F (significance level, degree of freedom of numerator, degree of freedom of denominator), indicate that the processes tested (group of varying parameters) contribute to significant differences between the treatments shown

Treatment comparison	Disease progress curves	RSS	df	F-value
^a(1) Separate-curve fits are compared with the single-curve fit. (2) Separate-curve fits are compared with the separate-curve fit with varying α1, α2. NS: non-significant differences at significance level 0.05.
Partial biofumigation against control bare soil	Common curve with all parameters in common	1·14E+06	122
	Separate curves with all parameters varying	7·58E+05	116
	Separate curves with α1, α2 varying | β1, β2, β3, γ in common	8·31E+05	120	23·63	>F(0·01,2,120)	(1)^a
	Separate curves with β1, β2, β3 varying | α1, α2, γ in common	8·04E+05	119	17·12	>F(0·01,3,120)	(1)
	Separate curves with γ varying | α1, α2, β1, β2, β3 in common	9·02E+05	121	36·36	>F(0·01,1,120)	(1)
	Separate curves with α1, α2, β1, β2, β3 varying | γ in common	7·70E+05	117	3·10	>F(0·05,3,120)	(2)
	Separate curves with α1, α2, γ varying | β1, β2, β3 in common	7·93E+05	119	5·74	>F(0·05,1,120)	(2)
Complete biofumigation against control bare soil	Common curve with all parameters in common	3·03E+06	122
	Separate curves with all parameters varying	1·37E+06	116
	Separate curves with α1, α2 varying | β1, β2, β3, γ in common	1·58E+06	120	61·29	>F(0·01,2,120)	(1)
	Separate curves with β1, β2, β3 varying | α1, α2, γ in common	1·63E+06	119	39·43	>F(0·01,3,120)	(1)
	Separate curves with γ varying | α1, α2, β1, β2, β3 in common	2·43E+06	121	50·65	>F(0·01,1,120)	(1)
	Separate curves with α1, α2, β1, β2, β3 varying | γ in common	1·42E+06	117	4·70	>F(0·01,3,120)	(2)
	Separate curves with α1, α2, γ varying | β1, β2, β3 in common	1·53E+06	119	4·47	>F(0·05,1,120)	(2)
Partial biofumigation against complete biofumigation	Common curve with all parameters in common	1·62E+06	122
	Separate curves with all parameters varying	1·13E+06	116
	Separate curves with α1, α2 varying | β1, β2, β3, γ in common	1·24E+06	120	19·37	>F(0·01,2,120)	(1)
	Separate curves with β1, β2, β3 varying | α1, α2, γ in common	1·22E+06	119	13·68	>F(0·01,3,120)	(1)
	Separate curves with γ varying | α1, α2, β1, β2, β3 in common	1·55E+06	121	7·09	>F(0·01,1,120)	(1)
	Separate curves with α1, α2, β1, β2, β3 varying | γ in common	1·15E+06	117	3·19	>F(0·05,3,120)	(2)
	Separate curves with α1, α2, γ varying | β1, β2, β3 in common	1·21E+06	119	3·41	NS	(2)

Table 3. Comparison of disease progress curves for trial 2008; otherwise as in Table 2

Treatment comparison	Disease progress curves	RSS	df	F-value
^a(1) Separate-curve fits are compared with the single-curve fit. (2) Separate-curve fits are compared with the separate-curve fit with varying α1, α2. NS: non-significant differences at significance level 0.05.
Partial biofumigation against control bare soil	Common curve with all parameters in common	2·12E+06	179
	Separate curves with all parameters varying	1·43E+06	174
	Separates curve with α1, α2 varying | β1, β2, β3, γ in common	1·46E+06	177	40·08	>F(0·01,2,120)	(1)^a
	Separate curves with β1, β2, β3 varying | α1, α2, γ in common	1·43E+06	176	27·87	>F(0·01,3,120)	(1)
	Separate curves with α1, α2, β1, β2, β3 varying | γ in common	1·43E+06	174	1·26	NS	(2)
Complete biofumigation against control bare soil	Common curve with all parameters in common	3·07E+06	179
	Separate curves with all parameters varying	1·67E+06	174
	Separates curve with α1, α2 varying | β1, β2, β3, γ in common	1·69E+06	177	72·18	>F(0·01,2,120)	(1)
	Separate curves with β1, β2, β3 varying | α1, α2, γ in common	1·72E+06	176	47·28	>F(0·01,3,120)	(1)
	Separate curves with α1, α2, β1, β2, β3 varying | γ in common	1·67E+06	174	0·61	NS	(2)
Partial biofumigation against complete biofumigation	Common curve with all parameters in common	1·23E+06	179
	Separate curves with all parameters varying	1·09E+06	174
	Separates curve with α1, α2 varying | β1, β2, β3, γ in common	1·09E+06	177	11·33	>F(0·01,2,120)	(1)
	Separate curves with β1, β2, β3 varying | α1, α2, γ in common	1·11E+06	176	6·57	>F(0·01,3,120)	(1)
	Separate curves with α1, α2, β1, β2, β3 varying | γ in common	1·09E+06	174	0·17	NS	(2)

Link between infected plants (I) and diseased plants (D)

Whilst reductions in the rates of primary and secondary infection account for a significant portion of the control of infection in the treatments of trial 2007, the expression of disease (wilting parameter γ) was also associated with differences between treatments. In the epidemics of trial 2007 the proportion of infected plants that expressed disease was significantly reduced, by 28%, in the partial and complete biofumigation treatments compared with bare soil. The model with varying γ is significantly different from the simplest model and the model with the most free parameters (P < 0·01, F = 36·4, 50·6 and 7·1 for partial biofumigation against bare soil, complete biofumigation against bare soil, and partial biofumigation against complete biofumigation, respectively; Table 2). In the epidemics of trial 2008, the proportion of infected plants that expressed disease did not differ among treatments (Table 1).

Discussion

This study analysed, through the application of epidemiological modelling, the effects of partial and complete biofumigation on epidemics of root rot of sugar beet caused by R. solani. In the partial biofumigation treatment, the mustard crop was grown to flowering and then pulled up, while the complete biofumigation treatment involved crushing and incorporation of the aerial portion of the cover crop residues into the soil along with the roots. The model included rates of infection by primary and secondary inoculum. The model also distinguished between pre-emergence damping off and expression of wilting symptoms (above-ground disease) due to infected roots (below-ground disease).

The modelling results indicated that biofumigation affects mainly primary infections of R. solani in sugar beet and suggests, for the first time, that biofumigation can also significantly affect the rate of secondary infection. This last result supports the hypothesis that the variability in the effectiveness of biofumigation observed among studies, as discussed by Motisi et al. (2010), can be explained by the variability in the control of secondary infections (see below).

The results of this analysis suggest fundamentally different types of epidemic across the two trials in this study. In the 2007 trial, the epidemics were characterized by relatively high levels of primary infection and Pre-DO, and relatively low levels of secondary infection. There was also a clear reduction (quenching) in the rates of secondary infection towards harvest. In contrast, in the 2008 trial, there were lower levels of primary infection and Pre-DO, and higher levels of secondary infection, with little evidence of quenching towards harvest. Yet, despite these differences in epidemic development, consistent trends were detected in the effects of partial biofumigation and complete biofumigation. In both trials, the two treatments resulted in a reduction in primary infection, with complete biofumigation providing more disease control than partial biofumigation. In trial 2008, Pre-DO was the likely cause of the apparent inconsistency in the ranking of treatment impacts on the number of diseased plants during the primary infection phase (i.e. bare soil treatment showed less diseased plants than biofumigation treatments up to 600 degree-days). The interpretation is that in the 2008 trial there was a flush of Pre-DO in the bare soil plots that resulted in fewer emerged, infected plants capable of developing early disease symptoms. By accounting for the flush in Pre-DO in bare soil treatment, and assuming that this infected dead seedlings that were still capable of transmitting disease, the model was able to account for the reversal in the ranking of treatment impacts on disease at harvest (Fig. 2e, 2564 degree-days).

That the growth of mustard alone (partial biofumigation) should provide a significant reduction in primary infection is worthy of notice. In fact, the isothiocyanates (ITC) produced in the rhizosphere of a biofumigant crop are unlikely to directly affect soilborne pathogens because they are produced in too small quantities (Watt et al., 2006). However, as discussed by Motisi et al. (2010), these molecules, or other compounds released by the roots of plants of the Brassicaceae, may influence and change the structure of the microbial communities present in the rhizosphere, which can indirectly affect the pathogen populations through changes in the competitiveness of pathogens (Rumberger & Marschner, 2004) or an increase in populations of pathogen antagonists (Kirkegaard & Matthiessen, 2004). That the complete biofumigation treatment further increased the control of primary infection is probably due to the addition of ITC released from the breakdown of glucosinolates after crushing and incorporation of mustard leaves and stems into the soil. The volatile ITC released when mustard residues are mixed into the soil are well known to reduce both the viability of pathogen inoculum as well as the rate of mycelial growth (Kirkegaard et al., 1996; Sarwar et al., 1998), two key components of primary infection (Gilligan & Bailey, 1997). This suggests that the crushing and incorporation of mustard crop residues into the soil is an important component for successful disease control.

Whilst the effects of partial and complete biofumigation on rates of primary infection were consistent across trials, rates of secondary infection showed a variable pattern. In this model, the rate of secondary infection is described by a curve that rises from zero to a maximum before declining again. These curves are characterized by the timing, duration and amplitude of the peak. In the 2007 trial, both biofumigant treatments significantly reduced the contribution of secondary infection, most notably the amplitude (Fig. 2d), suggesting some longer-term effect of biofumigation that might be attributed simply to growing a mustard crop. This extended effect of biofumigation has been recognized previously (Motisi et al., 2009b) and could be associated with changes in soil physical conditions caused by the growing roots, known to affect the growth dynamics of R. solani (Otten & Gilligan, 1998, 2006) or indeed, to the balance between the pathogen and its antagonists in the rhizosphere (Motisi et al., 2009a). However, the longer-term effect of biofumigation might also be attributed to the proliferation of antagonists of R. solani onto mustard residues incorporated in the soil as suggested by Mazzola et al. (2007) and Cohen et al. (2005). In this context one may assume that secondary infection would be strongly inhibited by biofumigation when longer-term modifications to soil biology are the major mechanism of action. At the same time, one may assume that primary infection would be strongly inhibited when short-term ITC effects are the major mechanism of action.

As well as modifying the soil environment, biofumigation can also lead, through changes in soil nutrition and water retention, to larger beet roots, and perhaps to less susceptible hosts (Motisi et al., 2009b). In the 2008 trial, biofumigation significantly affected secondary infection (Fig. 2h), but with different ranking of treatments compared with the 2007 trial (Fig. 2d). Specifically, the rate of secondary infection was higher in the complete biofumigation treatment than in the bare soil treatment. In addition, the dry biomass of mustard was 1·5 times higher in the 2008 than in the 2007 trial (see results in Motisi et al., 2009b). One particular feature of R. solani is its high saprotrophic capability (Weinhold et al., 1972). This means that the pathogen is capable of reinfestation of the soil, particularly after the addition of the organic debris of the mustard crop once the effects of the ITC have subsided (Yulianti et al., 2007). This potential reinfestation may augment the transmission of the pathogen between infected and susceptible plants, thereby increasing secondary infection and potentially offsetting the control afforded by changes in soil physical or biological conditions, or by a reduction in primary infection.

Based on this modelling analysis, it is hypothesized that the variability in the control of secondary infections can partly explain the variability in the effectiveness of biofumigation found among studies (Motisi et al., 2010). A possible scenario is that if mustard did not efficiently reduce primary infections (corresponding, for example, to a low reduction in the initial rate of primary infection, α₁) and if the rate of secondary infection was unchanged, then disease incidence could increase faster during the secondary infection phase and reach or even exceed levels observed in fields where no mustard has been cropped. As such, it is suggested that biofumigation needs to provide sufficient control of primary infections to allow adequate reduction in late-season disease.

Biofumigation reduced the expression of disease (wilting) in the 2007 but not in the 2008 trial. A reduction in disease expression may be attributed to the pathogen’s reduced ability to colonize the host plant, changes in the soil environment (water availability), or the size of the host. In this model it was assumed, for simplicity, that a fixed proportion of infected (below-ground diseased) plants will express disease (wilting). More realistically, the disease could be considered to develop on a growing beet plant such that the ability of the beet to take up sufficient water would be impaired at some threshold level of disease severity, and consequently show wilting. Motisi et al. (2009b) showed that biofumigation reduces disease severity. Hence, if appropriate data were available, one could represent the diseased roots as a separate model component for which susceptible roots follow transitions through infected to diseased roots (wilting symptoms), in order to disentangle the effects of biofumigation on disease severity and wilting.

In conclusion, by combining epidemiological modelling with experimentation, this study has demonstrated consistent control of primary infection and variable control of secondary infection and disease expression afforded simply by growing mustard as a cover crop, and removing it at flowering. Crushing the mustard leaves and stems and incorporating them into the soil significantly enhanced the control of primary infection whilst providing variable control over the secondary infection phase of the epidemics. The effects of biofumigation on secondary infection and disease expression through modification of the soil biotic and abiotic environment warrant further investigations.

Acknowledgements

The final revision of this article was submitted after the premature and tragic death from cancer of our colleague and co-author Doug Bailey. The authors are very grateful to Doug for his deep insight and long-term guidance that were central to the development of this project. The authors thank P. Farcy, E. Lemarchand, P. Chamoy, M. Prunier, P. Delarue, P. Hamon, S. Bensidhoum and N. Romillac for assistance with these experiments and T. Guinet for providing mustard seeds and advising for mustard crop management. This research was partly supported by Endure, a Network of Excellence financed by the European Union and was partly funded by the Institut Technique français de la Betterave industrielle (ITB). J. Filipe and C. A. Gilligan were funded by the UK’s Biotechnology and Biological Sciences Research Council (BBSRC).