A nonlinear model for temperature-dependent development of Erysiphe necator chasmothecia on grapevine leaves


E-mail: vittorio.rossi@unicatt.it


Production and development of the chasmothecia of Erysiphe necator on Vitis vinifera leaves were studied using potted plants in controlled and outdoor environments and grapevines in a vineyard. The optimum temperature for ascocarp production was 20°C; fewer chasmothecia were produced at 15°C and even fewer at 25°C; at 10 and 30°C, no or very few chasmothecia were observed, and none reached maturity. Nonlinear equations describing ascocarp development as a function of time and temperature were developed, parameterized with data from experiments at constant temperatures, and evaluated under fluctuating temperatures. Goodness-of-fit showed high agreement between observed and predicted data: the model efficacy ranged from 0·74 to 0·97 (1·0 indicates a perfect fit), and the root mean square error ranged from 0·001 to 0·01 (zero indicates a perfect fit). The high proportion of the observed variability accounted for by these equations (R2 = 0·83–0·98) supported the hypothesis that temperature has a predominant role in ascocarp development under natural conditions, when all environmental factors interact. The equations tended to overestimate the production of mature chasmothecia (the coefficient of residual mass was −0·23), but this inconsistency mainly occurred when rainfall apparently washed the mature chasmothecia from leaves during the logarithmic phase of the ascocarp developmental curve. Results from this work will be useful for predicting the development of chasmothecia in a vineyard and for timing the use of natural products, fungicides or biocontrol agents for reducing the population of chasmothecia, which are all more effective when they are applied to immature chasmothecia.


Erysiphe necator (syn. Uncinula necator) is the causal agent of powdery mildew of grapevine (Vitis vinifera), a disease that affects all green tissues of the grapevine including leaves and berries. On both the upper and lower surfaces of leaves, the fungus appears as a white or greyish-white powder; leaves severely affected may become dull, desiccate and drop prematurely. Infected berries are covered by a white or dark powder or dust and sometimes shrivel or crack. Erysiphe necator produces small spherical ascocarps (chasmothecia, formerly cleistothecia; Braun et al., 2002) on the surface of infected tissue. When chasmothecia are mature, they are dispersed by splashing rain (Gadoury & Pearson, 1988; Cortesi et al., 1995) and deposited on the bark of the vine trunk, the soil, or leaf litter on the soil surface, where they overwinter. Ascocarp survival, however, is consistently higher on exfoliating bark than on the other substrates (Gadoury & Pearson, 1988). Ascospores are repeatedly released mainly between budbreak and bloom (Munshi et al., 1996; Rossi et al., 2010) and cause primary infections on leaves (Gadoury & Pearson, 1990). Primary infections caused by ascospores trigger powdery mildew epidemics, which are then driven by the asexual infection cycles.

Despite the initial debate among scientists on the role of the chasmothecia in powdery mildew epidemics on grapevine, ascospores are now considered a source of primary inoculum, either alone or in addition to mycelia in the dormant buds, depending on the viticultural area (Pearson & Gadoury, 1987; Gadoury & Pearson, 1988; Cortesi et al., 1997; Magarey et al., 1997; Jailloux et al., 1998; Schneider et al., 1998; Steinkellner & Redl, 1998a; Halleen & Holz, 2000; Hoffmann & Virányi, 2007). The number of chasmothecia produced can be very large. In northern Italy, as many as 15 ascocarps per cm2 of bark surface were observed, which means 18–40 million chasmothecia per hectare of vineyard, depending on the trellis system (Rossi et al., 2011). Preventing infections caused by ascospores requires treatments that prevent formation or maturation of chasmothecia during the grape-growing season, or that reduce their number during winter. For instance, lime sulphur can reduce the number of chasmothecia on dormant grapevines (Gadoury et al., 1994).

Processes underlying the development of chasmothecia are thus pertinent from both epidemiological and disease management perspectives. Erysiphe necator is heterothallic, i.e. the ascocarps form when two opposite mating types contact and mate (Smith, 1970). This process is density dependent: the higher the disease severity, the higher is the probability that the two mating types will be in contact so that mating can occur (Schnathorst, 1965; Gadoury & Pearson, 1988). Environmental factors determine the rates of growth of both mating types and, therefore, directly influence the probability of mating. Once initiated, the chasmothecia are small and white; as they mature they increase in size and become yellow, then brown, and finally black. During maturation, chasmothecia are attached to the powdery mildew colony by anchorage hyphae; when they are mature, the anchorages break down and the chasmothecia are dispersed. Initiation of chasmothecia and their subsequent growth are two different processes (Gadoury & Pearson, 1988). Gadoury & Pearson (1988) studied the effect of some factors on ascocarp development and concluded that only temperature and host resistance affect the growth of chasmothecia once they are initiated. These results were obtained under controlled environmental conditions at constant temperatures between 8 and 32°C, and no information has been published on the effect of fluctuating temperature on ascocarp development under natural conditions.

The objective of this work was to investigate the dynamics of ascocarp production and development under a wide range of temperatures, both in controlled and natural environments.

Materials and methods

Plant and fungal materials

Green cuttings of the grapevine cultivar Barbera, which is susceptible to E. necator (Rossi et al., 2006), were grown in a greenhouse (at 18–26°C, photoperiod of 12–14 h light) in 10- × 10-cm pots containing a mixture of sand, peat and soil. When the plants reached the growth stage of four to six unfolded leaves, the adaxial leaf surface was inoculated by dusting conidia produced by leaves severely affected by E. necator (these leaves were collected in different commercial vineyards of Emilia-Romagna, northern Italy, and therefore probably contained a mixture of E. necator strains); 80–120 conidia were uniformly deposited per cm2 of leaf. After the inoculation, the potted plants were kept in the greenhouse at 20 ± 4°C, and high humidity was provided by covering the plants with transparent plastic bags for 48 h after inoculation. About 1 month after inoculation, the leaves were uniformly covered by powdery mildew colonies and the first ascocarp initials appeared. Three groups of potted plants were managed as previously described, in October 2008, March 2009 and September 2009, and used in experiments 1, 2 and 3, respectively.

Ascocarp development on potted plants at constant temperature (experiment 1)

Experiment 1 was carried out from November 2008 to February 2009. When the first ascocarp initials appeared on the cuttings prepared as previously described, the cuttings were separated into five groups of six replicate plants, and each group was kept in a controlled-environment chamber at one of five constant temperatures (10, 15, 20, 25 or 30°C) in a saturated atmosphere (with no condensation of water on leaves) and with a 12-h photoperiod using Philips Master Tl-D 90 Deluxe 18W/950 lamps. The plants were supplied with water every other day.

Leaves were observed every other day for 35 days with a stereomicroscope (×40 magnification). All the chasmothecia on the leaves were enumerated and classified based on their development stage as follows (Gadoury & Pearson, 1988): (i) yellow, spherical, immature ascocarps (hereafter referred to as ‘yellow’); (ii) brown, spherical, immature ascocarps (hereafter referred to as ‘brown’); and (iii) dark brown or black, concave–convex, mature ascocarps (hereafter referred to as ‘black’). At the end of the experiment, the area of each leaf was measured using an area meter (Li-Cor 3000; Licor Biosciences Inc.), and chasmothecia were expressed as numbers per cm2 leaf. Experiment 1 was repeated once (trials 1 and 2).

A factorial analysis of variance was performed on numbers of chasmothecia (total and black) as affected by temperature and trial. Numbers of ascocarps cm−2 leaf were transformed using the natural logarithm function to reduce the heterogeneity of the variance. Because neither trial (= 0·30 and 0·24 for total and black chasmothecia, respectively) nor the trial × temperature interaction (= 0·47 and 0·54, respectively) significantly influenced the numbers of chasmothecia, the data from both trials of experiment 1 were pooled for further analysis.

Ascocarp development on potted plants at fluctuating temperatures (experiments 2 and 3)

Experiment 2 was carried out in April–May 2009 and experiment 3 was carried out in October–November 2009. Cuttings of cv. Barbera were inoculated with E. necator about 1 month before the beginning of each experiment, and managed in a greenhouse to favour colony growth and production of ascocarp initials as described earlier. When the first ascocarp initials appeared, the plants were moved to one of four environments: A (a glasshouse), B (a corridor of the glasshouse complex, with natural light from windows and no temperature control), C (outside, in the shade and under a roof) or D (outside, fully exposed and unshaded). There were four potted cuttings per environment, and the plants were maintained in the environments for about 40 days. Temperatures in environments A to C were registered by a data logger (Tinytag Plus 2; Gemini Data Loggers Ltd), while both temperature and rainfall in environment D were monitored with a weather station (Vantage Pro2; Davis Instruments) adjacent to the potted plants. Average, minimum and maximum temperatures for the 40-day period are shown in Table 1. After 40 days in the environments, chasmothecia were counted and classified as described for experiment 1 on four leaves per plant.

Table 1.   Temperature data recorded in the two experiments in which potted grapevine plants inoculated with Erysiphe necator were incubated in different environments for 40 days
EnvironmentaExperiment 2bExperiment 3c
T dTmineTmaxfTTminTmax
  1. aEnvironments were: A (greenhouse), B (open corridor), C (outside, in the shade and under a roof) and D (outside).

  2. bExperiment 2 was carried out in April–May 2009.

  3. cExperiment 3 was carried out in October–November 2009.

  4. dMean daily temperature (average of 24 hourly values).

  5. eMinimum daily temperature.

  6. fMaximum daily temperature.


Ascocarp development in the vineyard

Ascocarps were assessed in a vineyard of cv. Trebbiano Romagnolo located in Travazzano (northern Italy, 44°51′33′′N, 9°47′40′′E, 275 m a.s.l.). The susceptibility of this cultivar to powdery mildew is equivalent to that of cv. Barbera used in experiments 1, 2 and 3 (Rossi et al., 2006). The vines were 15 years old and were high-wire cordon-trained with a 1·8- × 2·0-m spacing. A plot of four rows with about 25 plants per row (about 90 m2) was selected and not sprayed against powdery mildew for the entire season. Starting from early August 2009, i.e. when chasmothecia usually begin to form in this grape-growing area (Rossi et al., 2011), 12 leaves (four in the basal, four in the median and four in the apical part of the shoot) were randomly collected from the entire plot every 5–9 days until the end of November, when leaf fall was complete. Two circles of 2·0 cm diameter were drawn on the upper surface of each leaf, and the yellow, brown and black chasmothecia in the circles were counted with a stereomicroscope (×40) and expressed as numbers cm−2 leaf.

Air temperature and rainfall were recorded by a weather station (Vantage Pro2) in the vineyard.

Modelling ascocarp development at constant temperature

A model describing the effect of time and temperature on the development of chasmothecia, either yellow, brown or black, was developed by a four-step procedure. In the first step, original data on the development of chasmothecia over time at each temperature were fitted with S-shaped curves; in the second step, the estimated parameters of these curves were fitted against temperature by using a bell-shaped curve; in the third step, the two curves were combined so that the predicted development of chasmothecia was a function of both time and temperature; in the fourth step, the predicted data were compared with the original ones.

In the first step, the numbers of chasmothecia found on each sampling date were summed over time, separately for each of the three ascocarp developmental stages (yellow, brown and black) and for each of the five temperature regimes (10, 15, 20, 25 or 30°C in experiment 1). These cumulative numbers were divided by the total number of chasmothecia found at the end of experiment 1 and were expressed as percentages. The cumulative percentages were then regressed over time. In a preliminary analysis, the following equations were used: logistic, monomolecular and Gompertz in the forms shown by Campbell & Madden (1990). The equation parameters were estimated using the nonlinear regression procedure of spss (ver. 15; SPSS Inc.), which minimizes the residual sums of squares using the Marquardt algorithm. The following were used as indicators of goodness-of-fit: the magnitude of the standard errors of the model parameters, the coefficient of determination adjusted for the degrees of freedom, the number of iterations required by the Marquardt algorithm to converge on parameter estimates, and the magnitude and distribution of residuals (data not shown). The best fits were obtained using the equation of Gompertz, which describes the S-shaped curve of the dependent variable over time:


where: y is the cumulative percentage of ascocarps; A is the equation parameter accounting for the lag of the ascocarp progress curve; B is the rate parameter; C is the asymptotic parameter; and x is the time expressed in number of days after the appearance of ascocarp initials.

In the second step of model development, the equation parameters A, B and C estimated by Eqn 1 at 10, 15, 20, 25 and 30°C for each developmental stage of chasmothecia were regressed against temperature by using a generalized beta equation (Analytis, 1977), which describes a bell-shaped response of the dependent variable to temperature:


where: N is either A, B or C of Eqn 1; K is a constant; D and F are the equation parameters accounting for height and width of the bell-shaped curve; E determines the temperature at which the curve reaches the apex; and Teq are temperature equivalents calculated as:


where: T is the temperature regime; Tmin and Tmax are minimum and maximum temperatures, respectively, at which chasmothecia of a particular stage developed. Tmin and Tmax were considered as equation parameters and estimated accordingly (Xu, 1996).

In the third step, the estimated percentages of ascocarps in any developmental stage were calculated by the following equations, which combine the Eqns 1 and 2:


where the model parameters a to n have the same meaning as in Eqns 1 and 2.

An example of this set of equations is given in Figure 1 for the ascocarps in the yellow stage. Estimation of the parameters a, b and c as a function of temperature and based on Eqns 3.2 to 3.4 is provided in Figure 1a–c, while estimation of the percentage of ascocarps based on Eqn 3.1 is shown in Figure 1d.

Figure 1.

 Estimation of the percentage of Erysiphe necator ascocarps in the yellow stage as a function of time (days after ascocarp initials first appeared) and temperature (T). Curves in (a), (b) and (c) estimate the parameters a, b and c of Eqn 3.1 that generated the graph in (d), by using the temperature-dependent Eqns 3.2, 3.3 and 3.4, respectively. Points are the values of the parameters A, B and C of Eqn 1 calculated for the percentages of yellow ascocarps observed in experiment 1, which was carried out at constant temperatures between 10 and 30°C. Parameter values are shown in Table 2.

In the fourth step of model development, predicted values were regressed against observed data, and the properties of the linear model were examined; the null hypotheses that ‘a’ (intercept of regression line) was equal to 0 and that ‘b’ (slope of regression line) was equal to 1 were tested using a t-test. If the t-tests for ‘a’ and ‘b’ were not significant, then both null hypotheses were accepted and the equation was considered a statistically accurate predictor of the real data (Teng, 1981). Regression analysis can lead to misinterpretation when predicted data are very close to the observed ones (Rossi et al., 1997). Therefore, additional indices of goodness-of-fit (Nash & Sutcliffe, 1970) that avoid problems of regression analysis (Green & Stephenson, 1986) were evaluated: the Nash & Sutcliffe model efficacy (NS) as the ratio of the mean square error to the variance in the observed data, subtracted from unity (when the error is zero, NS = 1 and the equation provides a perfect fit); the W index of agreement as the ratio between mean square error and total potential error (W = 1 represents a perfect fit); the root mean square error (RMSE) as the square root of the mean square error (RMSE represents the average distance of real data from the fitted line); model efficiency (EF) as a dimensionless coefficient that takes into account both the index of disagreement and the variance of the observed values (when EF increases toward 1, the fit increases); and the coefficient of residual mass (CRM) as a measure of the tendency of the equation to overestimate or underestimate the observed values (a negative CRM indicates a tendency of the model toward overestimation).

Estimated versus observed ascocarp development at fluctuating temperatures and in the vineyard

Cumulative percentages of yellow, brown and black chasmothecia produced under fluctuating temperatures were calculated. These observed values were compared with the predicted ones. Predicted percentages of yellow, brown and black chasmothecia were calculated by a rate summation procedure (Hau et al., 1985). First derivatives of Eqn 3.1, whose parameters a, b and c were estimated by Eqns 3.2, 3.3 and 3.4, respectively, were summed daily, with T = Tm, where Tm is the average temperature of the day. To make time uniform for data from experiments 2 and 3 and from the vineyard, Eqn 3.1 was calculated with x as the number of days after ascocarp initiation / 35 days (35 days was the length of experiment 1). Goodness-of-fit was evaluated as described earlier.


Ascocarp development on potted plants at constant and fluctuating temperatures (experiments 1–3)

In experiment 1, the time between the onset of the first ascocarp initials and the observation of the first chasmothecia was 16 days at 10°C, 4 days at 20 and 25°C, 7 days at 25°C and 9 days at 30°C (Fig. 2a). The total number of ascocarps increased over time until the following numbers of chasmothecia cm−2 leaf were present after 35 days (Fig. 2a): 2·5 at 10°C, 23·4 at 15°C, 38·0 at 20°C, 9·6 at 25°C and 3·2 at 30°C. No black ascocarps were observed at 10 and 30°C (Fig. 2b,f, respectively). The first black chasmothecia were observed after 21 days at 15°C (Fig. 2c), 16 days at 20°C (Fig. 2d) and 14 days at 25°C (Fig. 2e). After 35 days, the percentage of all ascocarps that were black was 22% at 15°C, 28% at 20°C and 11% at 25°C (Fig. 2c, d and e, respectively).

Figure 2.

 Dynamics over time (days after ascocarp initials first appeared) of ascocarp production and development at constant temperatures (experiment 1). (a) Total number of ascocarps of Erysiphe necator produced per cm2 of leaf at constant temperatures. The percentage of ascocarps that were yellow (light grey area), brown (dark grey area) and black (black area) at 10 (b), 15 (c), 20 (d), 25 (e) and 30°C (f).

Data on the development of the chasmothecia in potted grape cuttings at fluctuating temperatures in experiment 2 and experiment 3 were consistent with data obtained at constant temperatures in experiment 1. In experiments 2 and 3, high numbers of ascocarps were produced when the average temperature of the period ranged from 18 to 24°C (Fig. 3a–f) while very few ascocarps were produced when the average temperature was about 10°C, and none of them reached the black stage (Fig. 3g,h). Ascocarp development during the incubation period was not inhibited by a maximum temperature >30°C (Fig. 3a,b) or by minimum temperatures between 11·6 and 12·5°C (Fig. 3c–e). In environment D (i.e. outside), plants were exposed to rainfall. In experiment 2 (Fig. 3d), rainfall was 67·2 mm between days 7 and 11, and 7 mm on day 26 (data not shown); in experiment 3 (Fig. 3h), rainfall was 31·4 mm between days 19 and 20, and 15·6 mm on day 31 (data not shown).

Figure 3.

 Dynamics over time (days after ascocarp initials first appeared) of the number of yellow (…), brown (-- --) and black (—) ascocarps of Erysiphe necator produced per cm2 of leaf in environments A (a), B (b), C (c) and D (d) of experiment 2, and in environments A (e), B (f), C (g) and D (h) of experiment 3.

Ascocarp development in the vineyard

On the basal leaves in the vineyard, the first yellow chasmothecia were observed on 28 August (day 1 in Fig. 4) and the first black chasmothecia were observed on 25 September (Fig. 4a); on the median and apical leaves, the chasmothecia appeared 1 week later (Fig. 4b and c, respectively). The total number of ascocarps was largest on the basal levels, intermediate on the median leaves, and smallest on the apical leaves. Irrespective of leaf position, the production of yellow chasmothecia showed a sigmoid pattern, with a lag phase of about 20 days followed by a logarithmic increase of about 40 days (from mid-September until mid-October); no additional yellow ascocarps were found after mid-November. Similarly, the number of black chasmothecia did not markedly increase in late November (Fig. 4).

Figure 4.

 Dynamics over time (days after ascocarp initials first appeared) of the number of yellow (…), brown (-- --) and black (—) ascocarps of Erysiphe necator produced per cm2 of the basal (a), median (b) and apical (c) leaves in a vineyard in Travazzano (northern Italy). The bottom panel (d) shows temperature (T, continuous line) and rainfall (R, black bars) data recorded in the vineyard between 28 August (day 1) and 27 November 2009.

Average temperature of the period (28 August–27 November) was 14·7°C, and the maximum and minimum were 26·4 and 7·3°C, respectively. During the lag and logarithmic phases of ascocarp development, the average temperature was 21·4 and 15·8°C, respectively; during the asymptotic phase, it was 9·2°C (Fig. 4d). A total of 243 mm of rain fell in three main periods. The first rainy period occurred between 14 and 21 September (82 mm) (Fig. 4d), when only a few, yellow chasmothecia were present. The second rainy period occurred during the logarithmic phase of ascocarp development, between 21 and 23 October (39 mm). The third rainy period was between 2 and 9 November (101 mm), when the mean daily temperature was always below 10°C and the number of chasmothecia did not further increase.

Model for ascocarp development

The set of equations developed for describing the development of yellow, brown and black chasmothecia at constant temperatures produced a satisfactory fit with the actual data. Standard errors of the equation parameters were low compared to the parameter values (Table 2). Regressions of estimated versus observed values showed that the equations for yellow and brown ascocarps overestimated the real values (the slope parameter b was significant) but with low standard errors of estimates (SEest ≤ 0·08) and high coefficients of determinations (R2 ≥ 0·77) (experiment 1 in Table 3). All the indices used showed a high goodness-of-fit for experiment 1: NS ≥ 0·74, W ≥ 0·93, RMSE ≤ 0·012 and EF ≥ 0·74. However, CRM was −0·36, which confirmed the tendency of the equation for brown chasmothecia to overestimate (experiment 1 in Table 3).

Table 2.   Parameters of the equations used to describe the effect of temperature on the dynamics of three developmental stages of Erysiphe necator ascocarps (see the example of Fig. 1)
Ascocarp stage (y)aTemperature (Teq)bEquation parameters and standard errorsc
  1. ay is the cumulative percentage of ascocarps, with y = 100 · c · exp [−a · exp(−b · x)]; c = k1 · [d · Teqe · (1 − Teq)]f; a = k2 · [g · Teqh · (1 − Teq)]i; b = k3 · [l · Teqm · (1 − Teq)]n; x is time expressed in number of days.

  2. bTeq is the temperature equivalent: (TTmin)/(TmaxTmin); where: T is the temperature regime; Tmin and Tmax are minimum and maximum temperatures, respectively.

  3. cParameters were estimated with the data from experiment 1, which was carried out in growth chambers at constant temperatures between 10 and 30°C. Standard error of the parameters are in italics.

Yellow(T − 5)/3010·04·060·611·460·124·681·420·371·03·320·786·57
Brown(T − 10)/2010·0-−0·070·160·126904·600·070·31·780·141·24
Black(T − 10)/20100·04·221·361·951·01·821·611·251·02·770·844·15
Table 3.   Statistics and indices used for evaluating the goodness-of-fit of the estimated percentages of yellow, brown and black ascocarps of Erysiphe necator versus the percentages observed in the three experiments and in the vineyard
Experiment and ascocarp stagenaPbPSEestR2NSWRMSEEFCRM
  1. Experiment 1 was carried out in growth chambers at constant temperatures between 10 and 30°C; experiments 2 and 3 were carried out in two periods and in four different environments with fluctuating temperatures (Table 1); the vineyard was located in northern Italy and was subjected to natural weather conditions.

  2. n, number of observations; a and b, parameters of the regression line of the predicted against observed values; P, probability level for the null hypotheses that a = 0 and b = 1; SEest, standard error of the estimates for the regression line; R2, coefficient of determination of the regression line; NS, model efficacy (Nash & Sutcliffe, 1970); W, index of agreement (Nash & Sutcliffe, 1970); RMSE, root mean square error (Nash & Sutcliffe, 1970); EF, model efficiency (Nash & Sutcliffe, 1970); CRM, coefficient of residual mass (Nash & Sutcliffe, 1970).

Experiment 1
 Brown 0·022<0·0010·79<0·0010·030·770·740·930·0050·74−0·36
 Black 0·0040·280·990·930·030·870·850·960·0030·85−0·15
Experiments 2 and 3
 Brown 0·009<0·0010·81<0·0010·020·840·860·960·0020·86−0·03
 Black 0·0090·091·160·910·070·870·740·950·0100·74−0·23
 Brown 0·0080·0010·930·020·010·960·960·990·0010·96−0·07
 Black 0·0310·020·990·950·060·830·750·940·0080·75−0·23

When the above-mentioned equations were used to estimate ascocarp development on potted plants at fluctuating temperatures, the goodness-of-fit did not change substantially (experiments 2 and 3 in Table 3). The fit of the data for brown ascocarps improved (in particular, the tendency to overestimate diminished, with CRM = −0·03), while that for black ascocarps declined somewhat. In particular, the tendency to overestimate the observed values for black ascocarps increased from −0·15 to −0·23. For instance, in environment C of experiment 2, black chasmothecia were overestimated between days 29 and 36 (Fig. 5a). In environment D (i.e. outside) of experiment 2, overestimation was greater (Fig. 5b) than in environment C on the three samples between days 29 and 33; in this case, 7 mm of rain fell on day 26 (data not shown), which may have washed the mature chasmothecia from the leaves. In environment B of experiment 3, black ascocarps were correctly estimated (Fig. 5c).

Figure 5.

 Observed and estimated frequency (%) of yellow, brown and black ascocarps in environments C (a) and D (b) of experiment 2 and in environment B (c) of experiment 3. Observed frequencies are indicated by symbols: □ yellow, ⋄ brown and • black ascocarps. Estimated frequencies (generated by the equations in Table 2) are indicated by lines: … yellow, -- -- brown and — black ascocarps.

When the equations developed for constant temperatures were used to estimate the development of chasmothecia under vineyard conditions, the goodness-of-fit was the same as described for fluctuating temperatures in experiments 2 and 3 (see Vineyard in Table 3), with some overestimation of the black chasmothecia during their logarithmic increase (Fig. 6, data for basal leaves); as before, this overestimation might be explained by rain during that period (Fig. 4d).

Figure 6.

 Observed and estimated frequency (%) of yellow, brown and black ascocarps on the basal leaves in a vineyard in Travazzano (northern Italy). Observed frequencies are indicated by symbols: □ yellow, ⋄ brown and • black ascocarps. Estimated frequencies (generated by the equations in Table 2) are indicated by lines: … yellow, -- -- brown and — black ascocarps.


In this work, both the production and development of E. necator chasmothecia were influenced by temperature. The optimum temperature for ascocarp production was 20°C, fewer chasmothecia were produced at 15°C and especially at 25°C, and no or very few were observed at 10 and 30°C. At 10 and 30°C, none of the produced ascocarps reached maturity. These results are consistent with those of Gadoury & Pearson (1988), who also reported that few or no ascocarps were produced and that none reached maturity at 10 and 32°C. The present results, however, differ from those in the latter study with respect to the optimum temperature for ascocarp production. Although Gadoury & Pearson (1988) found that ascocarps matured more slowly at 25 than at 20°C, they reported that ascocarp production was greater at 25 than at 20°C. As noted, the optimum temperature for ascocarp production in the current study was 20°C, and many fewer ascocarps were produced at 25 than at 20°C. The difference between the two reports with respect to production of ascocarps at 25°C is difficult to explain. From an ecological perspective, greater production and faster maturation of chasmothecia at lower temperatures (as found in this work at 15 and 20°C) seems an adaptation to the late-season production of ascocarps, which has been widely documented in the literature (Schnathorst, 1965; Diehl & Heintz, 1987; Gadoury & Pearson, 1988, 1990; Pezet & Bolay, 1992; Munshi et al., 1996; Cortesi et al., 1997; Steinkellner, 1998b). Other powdery mildews (E. polygoni, E. cichoracearum and Mycosphaera penicillata) also produce fewer ascocarps at 25°C than at lower temperatures (Smith, 1970).

In this work, the development of E. necator chasmothecia was expressed as a function of time and temperature through a set of nonlinear equations, which were parameterized with data from experiments carried out at constant temperatures between 10 and 30°C. These equations were then used to estimate ascocarp development on potted plants under fluctuating temperatures in the range of 7·1–30·7°C and in the vineyard. Xu (1996) discussed possible problems arising from using equations derived from data collected in controlled environments to predict developmental processes under varying temperatures. These problems involve mathematical properties of the nonlinear functions and possible physiological mechanisms operating at low and high temperatures. The developed equations were reasonable, however, as demonstrated by the results of goodness-of-fit tests. For example, the model efficacy (NS) ranged between 0·74 and 0·97, and the root mean square error (RMSE) ranged between 0·001 and 0·01; when the fit is perfect, NS is equal to 1·0, and RMSE is close to 0·0 (Nash & Sutcliffe, 1970). Therefore, the equations developed in this work may be considered an accurate representation of the effect of temperature on the ascocarp development in E. necator.

When applied as single factors under environmentally controlled conditions in previous works, neither day length (Gadoury & Pearson, 1988), nor cyclical wetting of leaves, nor reduced humidity (Gadoury & Pearson, 1988; Gee et al., 2000) affected the density of chasmothecia or their rate of maturation. When environmental conditions were not controlled and all environmental factors acted simultaneously in the current work, the high proportion of the observed variability accounted for by the temperature-based equations (R2 = 0·83–0·98) confirmed that ascocarp development was largely determined by temperature.

There were, however, some differences between data predicted by the equations and observed data for leaves that were exposed to rain. Thus, in environment D of experiments 2 and 3 and in the vineyard, the coefficients of residual mass (CRM) of these equations showed an overestimation of the black ascocarps (Table 3); in detail, the equations overestimated the numbers when there was rainfall during the logarithmic stage of the ascocarp curve (Figs 5b & 6). It is well known that when ascocarps are mature, the hyphae that anchor them to the colony degrade, and the chasmothecia can then be washed from the leaves by rainfall (Gadoury & Pearson, 1988; Cortesi et al., 1995). The inconsistency between observed and estimated black ascocarps may therefore be explained, at least in part, by the removal of mature chasmothecia from leaves by rain.

The model developed in this work could be useful for predicting the developmental course of chasmothecia in a vineyard and for making decisions about actions for reducing the population of chasmothecia. Reducing the number of chasmothecia formed in a season is the first step for controlling powdery mildew epidemics in the following season (Magarey, 2010).

Such a reduction can be obtained by preventing high levels of leaf (or berry) infection at the end of the season (Carisse et al., 2009), which may require management of mildew until veraison or beyond (Hed & Travis, 2007). Eradication of powdery mildew colonies, as well as reduction in ascocarp numbers, has been obtained with both natural products and fungicides (Schilder et al., 2008; Avila et al., 2010). What is not clear, however, is when these products should be applied (Schilder et al., 2008). Treatments that are applied too late are of limited value if earlier infections are not controlled, because these infections are likely to have already produced many chasmothecia (Wilcox, 2002), and mature chasmothecia are generally not affected by fungicide sprays (Madge, 2010). Timing is also critical for biocontrol by the hyperparasitic fungi belonging to the genus Ampelomyces, which are able to parasitize the chasmothecia of E. necator (Cortesi et al., 1995; Falk et al., 1995). Field applications of these fungi reduced the production of chasmothecia in late season (Zanzotto et al., 2005) and the severity of the ascosporic infections in the next spring (Caffi et al., 2010). Because Ampelomyces parasitizes the chasmothecia only during their early development, i.e. before the chasmothecial wall darkens (Falk et al., 1995), application of this biocontrol agent must be well timed.

Because natural products, fungicides and biocontrol agents must be applied to immature chasmothecia to be effective, the results of this work, which enables the prediction of chasmothecial development in a vineyard, should help pest managers decide if and when actions are needed to reduce the number of chasmothecia that mature and overwinter. This is an evolution of the concept expressed by Gadoury & Pearson (1988), who suggested that pest managers should use the ‘minimum degree-day accumulation necessary for ascocarp maturation’ to estimate whether chasmothecia could mature sufficiently to survive the winter. Further studies are needed to evaluate the feasibility and the practical impact of timing control measures against chasmothecia based on the temperature-dependent equations developed in this work. In particular, research is needed to determine the time when these equations should begin to be applied in a season, i.e. to determine when ascocarp initials appear in the vineyard.


This study was co-funded by the Emilia-Romagna Region and coordinated by CRPV. SEL carried out this work within the Doctoral School on the Agro-Food System (Agrisystem) of the Università Cattolica del Sacro Cuore (Italy).