*To whom correspondence should be addressed.†Present address: Julianastraat 145, 6707 DD Wageningen, The Netherlands (e-mail: firstname.lastname@example.org).
The effect of temperature on latent period and aeciospore production of Puccinia lagenophorae on Senecio vulgaris was determined in small-scale experiments under controlled conditions. A clear effect of temperature on latent period was demonstrated. Latent period decreased exponentially with increasing temperature. Both total aeciospore production and net reproductive number increased linearly with increasing temperature in a range from 10 to 22°C. The three parameters were incorporated in models to determine the effect of temperature on epidemic development. The present study suggests an increase in the exponential growth rate, r, and the velocity of focus expansion, V, with temperature. This increase in epidemic development was caused mainly by the effect of temperature on latent period and on net reproductive number. The effect of temperature on the sporulation curve appeared to be less important.
Senecio vulgaris (Asteraceae) is a self-compatible and strongly self-pollinating annual plant species originating from southern Europe (Kadereit, 1984). It is a significant weed, especially in horticulture where frequent cultivations occur (Paul et al., 1993). The rust fungus Puccinia lagenophorae infects S. vulgaris and is known to reduce the competitive ability of the weed towards crops and other weeds (Paul & Ayres, 1987; Paul & Ayres, 1990). It has therefore been proposed as a potential biological control agent for the weed (Müller-Schärer & Frantzen, 1996; Frantzen & Hatcher, 1997). The rust fungus colonizes leaves, stems and capitula of S. vulgaris. Although teliospores are produced, this spore stage does not play a role in the infection cycle. Plants appear to be infected only via aeciospores in Europe. Puccinia lagenophorae probably originates from Australia, and was observed throughout the UK and Europe in the early 1960s (Mayor, 1962; Viennot-Bourgin, 1964; Wilson et al., 1965).
In the field, P. lagenophorae infections are most severe in late summer and autumn, but sometimes infected seedlings are found in the spring (Müller-Schärer & Frantzen, 1996). The absence of sufficient epidemic levels to reduce growth, reproduction and survival of S. vulgaris in spring limits its applicability as biocontrol agent. The limited disease levels in spring are due to two factors. First, and most important, is the low through-winter survival of the pathogen. Puccinia lagenophorae survives as mycelium within overwintering host plants (Frantzen & Müller-Schärer, 1999). Overwintering of S. vulgaris is infrequent, however, as it is an annual plant. Moreover, survival of S. vulgaris plants in winter is greatly reduced by P. lagenophorae (Paul & Ayres, 1986a, Paul & Ayres, 1986b; Frantzen & Müller-Schärer, 1999). Therefore from the epidemic the previous year only a limited amount of inoculum survives to start an epidemic the next spring. The second cause of low epidemic severity in spring is found under adverse climatic conditions, though very little quantitative information is available for P. lagenophorae. In most fungal plant diseases, infection, latent period, lesion development and sporulation depend on temperature, humidity, leaf wetness duration and solar radiation (Zadoks & Schein, 1979). Several authors also mention the effect of pre-inoculation temperature on epidemic parameters (Brown & Shipton, 1964; Ramage & Sutherland, 1995; Gijzen et al., 1996). The effect of climatic variables on P. lagenophorae and its epidemics is not well studied.
This paper describes the effects of temperature on epidemic parameters of this disease, firstly by assessing (i) postinfection temperature on the latent period; (ii) postinfection temperature on total number of spores produced; (iii) postinfection temperature on the sporulation curve; and (iv) possible interactions of pre- and postinfection temperature on these epidemic parameters. Secondly, the effect of temperature on epidemic development was studied. An experimental approach to these population-level effects of temperature requires large-scale, multi-year field experimentation. Instead, the epidemic development parameters were calculated on the basis of measurements at the individual level, by studying the effect of temperature on (i) the exponential rate of increase, r, using the Euler equation (Roughgarden, 1979); and (ii) the velocity of focus expansion, V, using the model developed by Van den Bosch et al. (1988a, 1988b). Both models have gone beyond the theoretical/construct stage and are intensively used by ecologists and epidemiologists (Buiel et al., 1989; Van den Bosch et al., 1988c; Van den Bosch et al., 1992) and have been extensively verified (reviewed by Zadoks & Van den Bosch, 1994).
Materials and methods
Origin of plants and rust
Plants of S. vulgaris line ELS 1 originate from a plant collected in Unterehrendingen, Switzerland in 1993. Selection and cultivation of S. vulgaris lines is described by Wyss (1997). Seeds used in the experiments are the fourth generation of line ELS 1 and were collected between 23 September and 15 October 1997 from plants grown in a climate chamber at the University of Fribourg. Seeds were stored in paper bags until use.
Aeciospores of P. lagenophorae strain ELS used in this experiment originate from a single-sorus isolate of P. lagenophorae, collected from S. vulgaris in an organic seedling cultivation at Unterehrendingen. The isolate was collected in 1993 and maintained using methods described by Wyss (1997).
Seeds were germinated in shallow trays filled with nutrient-amended peat (Floragard TKS 2), placed in incubators with a day temperature of 10, 16 or 22°C and a night temperature of 8°C, a 16 h photoperiod, and relative humidity fluctuating between 70 and 80%. Seedlings at the second- and third-leaf stage were transplanted to 9-cm-diameter plant pots (one plant per pot) and returned to the incubators. Plants grown for determination of spore production were directly sown in 9 cm pots, grown under conditions described above, and thinned to one plant per pot before inoculation, in a separate experiment. The temperature treatments were randomly allocated over the incubators in each experiment.
To test whether the temperatures at which the plants are grown before inoculation affect epidemiological parameters, three pre-inoculation temperatures were used: 10, 16 and 22°C. Plants grown at these pre-inoculation temperatures are referred to as groups I, II and III, respectively. From each of these groups, equal numbers of plants were subjected to the various postinoculation temperatures.
Plants of each group were inoculated when 50% of the plants had, on average, three fully developed leaves (44, 29 and 25 days after sowing for groups I, II and III, respectively). Aeciospores were evenly distributed over S. vulgaris plants using a settling tower. The plants were removed from the settling tower and 10 plants from each group were grown at postinoculation temperatures of 10, 13, 16, 19 or 22°C during the day and 8°C at night. Immediately after inoculation, plants were covered with plastic for 15 h to provide the high humidity needed for infection.
Plants were examined each day for the presence of open aecia. The latent period was determined for each plant as the number of days between inoculation and appearance of the first open aecium.
The data on latent period were analysed with pre-inoculation temperature as factor, in which groups I, II and III represent pre-inoculation temperatures of 10, 16 and 22°C, respectively. The effect of pre-inoculation temperature on latent period was tested by anova. An exponential function relating postinoculation temperature, T (°C), and latent period, p(T) (days), was fitted to the data:
where f and g are shape parameters.
Plants from groups I, II and III were inoculated 70, 40 and 28 days after sowing, respectively, in a separate experiment as described above. Ten plants from each group were placed at either 10, 16 or 22°C during the day and 8°C at night, after inoculation.
Aeciospore production was determined by collecting aeciospores from each individual plant every 2 days after the latent period. Aluminium foil (9 × 9 cm) was placed below the first leaf pair when the first symptoms appeared. Flowers were removed from the plants to prevent contamination of collected aeciospores with pappus and seed. Aeciospores were collected by brushing them from the leaves with a paint brush into a snap-cap bottle. Aeciospores on the foil were collected and added to the bottle. The number of aeciospores collected was assessed using a haemocytometer. Demineralized water (5 mL) and two drops of Tween 20 were added to each bottle. The bottles were shaken until all aeciospores were suspended in the solution. An aliquot (0·064 µL) was placed in a haemocytometer, and all aeciospores present were counted. Ten aliquots were sampled from each snap-cap bottle. Aeciospore collection was stopped when no visible aeciospore production occurred.
For each pre- and postinoculation temperature combination, a gamma density (Mood et al., 1974) was used to describe aeciospore production, I(t):
where Γ(η) is the gamma function, Itot is the total number of aeciospores produced, and η and β are constants of the gamma density with dimensions 1 and T−1, respectively. After logarithmic transformation, Eqn 2 becomes:
where y = ln(I), x1 = ln(t), x2 = t, α = ln [Itotβη/Γ(η) ], δ1 = η−1, and δ2 = –β. The mean of the gamma density, µ, can be interpreted as the mean time required to produce a randomly selected spore after the latent period. In terms of the parameters of the gamma density:
The standard deviation of the gamma distribution, ν, is interpreted as the standard deviation of the time required to produce a randomly selected spore. In terms of the parameters of the gamma density:
Parameters α, δ1 and δ2 were estimated using linear least-squares regression on the means for each pre- and postinoculation temperature combination.
The net reproductive number, R0, depends on total spore production per lesion, Itot in Eqn 2, and the infection efficiency of a spore. Assuming that the infection efficiency of aeciospores of P. lagenophorae under optimal humidity conditions is not affected by temperature, the net reproductive number, R0, and the total aeciospore production per plant, Itot, are linearly related, R0 = cItot, where c is a calibration constant. The total number of aeciospores produced was determined for each pre- and postinoculation temperature combination. A linear relation between total aeciospore production, Itot, and temperature was fitted to the data, Itot = a + bT, in which T is the average temperature (°C) and a and b are parameters. The total number of new aecia caused by one aecium during the entire sporulation period, the net reproductive number R0, is then given by R0 = c(a + bT). To calibrate this relation, a net reproductive number of 383 in a field of S. vulgaris at an average temperature of 16·33°C (J. Frantzen, University of Friburg, Switzerland, personal communication) was used. From this, the next step gives:
The net reproductive number was calculated for each pre- and postinoculation temperature combination, using the average of temperature during day and night.
Calculating exponential growth rate and velocity of focus expansion
In the initial phase of an epidemic, with few lesions in a virtually uninfected population, the number of lesions increases exponentially in time at a rate known as the exponential growth rate, r. The exponential growth rate in an age-structured population is given by:
This formula is an extended version of the well known relation r≈ln(R0) / (p + µ) often used in entomology, and first derived from the Lotka integral equation for an age-structured population (Roughgarden, 1979) by Keyfitz (1968). The exponential growth rate, r, was calculated for each pre- and postinoculation temperature combination. The value of p was calculated from Eqn 1.
The velocity of focus expansion, V, expressed in centimetres per day, was calculated for each pre- and postinoculation temperature combination using Equation A1 from Van den Bosch et al. (1988b):
where λ is a shape parameter of the wave front, α = β2, V* = Vη/βσ and p* = pβ/η. For this calculation the standard deviation of the spatial distribution of daughter lesions around a mother lesion, σ, has to be measured. This parameter was not determined in the present experiment. The velocity of focus expansion, however, is linearly dependent on the parameter σ (Minogue & Fry, 1983; Van den Bosch et al., 1988a). Therefore the velocity was expressed as:
The latent period decreased with increasing postinoculation temperature (Fig. 1). No significant (anova, P = 0·68) effect of pre-inoculation temperature on latent period was demonstrated, and an exponential curve was fitted through the combined data set. Fitting the equation p(T) = fe−gT to the data resulted in estimates of f = 40·32 (SE = 0·70) and g = 0·058 (SE = 0·001) and R2 was 0·95. The expected length of the latent period at a postinoculation temperature of 10, 16 and 22°C, based on the values of f and g, was 22·6, 15·9 and 11·3 days, respectively.
Aeciospore production was described well by the gamma distribution (Fig. 2). The curves underestimated the maximum aeciospore production, but standard errors of the estimated parameter values were small and, except for a postinoculation temperature of 10°C in group II, R2 was higher than 0·85 (Table 1). Aeciospore production was not affected by pre-inoculation temperature (Fig. 2). The mean, µ, and standard deviation, ν, of the time required to produce a randomly selected spore after the latent period, decreased with increasing postinoculation temperature in all groups (Table 1). Total aeciospore production per plant increased with increasing postinoculation temperature in all but one group (Table 2). The total aeciospore production at a postinoculation temperature of 22°C was very low in group I. Regression analyses of the relationship between average postinoculation temperature and total aeciospore production, Itot, resulted in estimates of a = 0 and b = 1·43 × 106 (SE = 2·45 × 105), R2 was 0·81, and calibration factor c = 1·64 × 10−5. The net reproductive number increased with increasing postinoculation temperature in all but one group (Table 2).
Table 1. Estimates and standard error (in parentheses) of parameters of a gamma functiona fitted to the data of aeciospore production of Puccinia lagenophorae on Senecio vulgaris for different postinoculation temperatures
a Gamma function fitted in the form of y = a + δ1x1 + δ2x2 (see Eqn 3).
b Mean time required to produce a randomly selected aeciospore after the latent period has ended, µ = [(δ1 + 1) / –δ2].
c Standard deviation of aeciospore production, .
Table 2. Estimates and standard error (in parentheses) of total aeciospore production, Itot, and calculated net reproductive number, R0, of Puccinia lagenophorae on Senecio vulgaris for different postinoculation temperatures
Exponential growth rate and velocity of focus expansion
The exponential growth rate increased threefold when postinoculation temperature increased from 10 to 22°C for group III plants (Table 3). Velocity of focus expansion, expressed as V′, also increased with increasing postinoculation temperature (Table 3). At 22°C the velocity was about three times as fast as at 10°C. Despite the low value of R0 at 22°C in group I, values of both V′ and r also increased with increasing temperature in group I. This increase of both V′ and r was caused by the temperature effect on latent period.
Table 3. Estimates of relative velocity of focus expansion, V′, and exponential growth rate, r, of Puccinia lagenophorae on Senecio vulgaris for different postinoculation temperatures
Pre-inoculation temperature group
Relative velocity of focus expansion, V′ (cm cm−1 day−1)a
Exponential growth rate, r (lesion lesion−1 day−1)
aV′ = V/σ where V is the velocity of focus expansion in cm day−1 and σ is the standard deviation of the spore dispersal distribution.
A clear effect of temperature on the latent period of P. lagenophorae was demonstrated. The confounding effect of incubators appeared to be negligible, because the relationship between temperature and latent period was almost equal on plants grown both for determination of the latent period and for determination of spore production (data not presented). The use of five temperatures to determine the relationship between temperature and latent period enabled a reliable fit. In the temperature range between 10 and 22°C, the latent period decreased exponentially with temperature. As discussed by several authors, the relationship between latent period and temperature is often asymmetrically U-shaped (Shearer & Zadoks, 1972; Zadoks & Schein, 1979). In this light it is very likely that the latent period of P. lagenophorae will increase at temperatures not included in the experiments reported here. The latent period of P. lagenophorae has been previously reported to be ≈10 days at 20°C (Paul & Ayres, 1984; Wyss, 1997). In the present study the latent period at that temperature was 11·3 days, on average. The slightly longer latent period recorded in this study is probably due to the lower night temperature used. The latent period of P. lagenophorae is moderately sensitive to temperature compared to Puccinia hordei on barley (Simkin & Wheeler, 1974), Puccinia arachidis on groundnut (Wadia & Butler, 1994), and Melampsora lini on Linum marginale (Burdon & Elmqvist, 1996).
Production of aeciospores gradually increased to a maximum, followed by a gradual decrease with time in all treatments. This pattern has been observed in several other fungal species including Puccinia recondita on wheat (Eyal & Peterson, 1967; Mehta & Zadoks, 1970) and Pyricularia oryzae on rice (Kato & Kozaka, 1974). The gamma distribution fitted the sporulation curves reasonably well, although the fit was not as good for low temperature (10°C). The gamma distribution underestimated the maximum aeciospore production per plant per day in all treatments, which is due to the logarithmic transformation used to enable the use of linear-least-squares as a fitting procedure. However, aeciospore production was estimated well by the gamma distribution.
The effect of temperature on the sporulation curves of P. lagenophorae was similar to, but less extreme than, that seen on sporulation curves of P. oryzae on rice (Kato & Kozaka, 1974; Van den Bosch et al., 1988b). An increase in temperature during the day resulted in an increased relative spore production at the beginning of the infectious period. This shape of the sporulation curve is reflected in the quotient of the mean, µ, and standard deviation, ν, of the time required to produce a randomly selected spore after the latent period. The value of v/µ of P. lagenophorae decreased slightly with increasing temperature.
The total aeciospore production per plant, and thus the net reproductive number, R0, increased by almost 50-fold when temperature increased from 10 to 22°C. The relationship between temperature and net reproductive number was affected by the low aeciospore production of plants grown at 22°C in group I. Due to this treatment, the value of the calibration constant, c, was probably underestimated.
Application of the methods to calculate the exponential growth rate, r, and the velocity of focus expansion, V′, made it possible to determine the extent to which the effect of temperature on epidemiological parameters of individual lesions contributes to effects at the population level. Van den Bosch et al. (1988b, 1990) demonstrated that a decreased latent period, p, as well as an increased standard deviation of the infectious period, ν, at a fixed mean, µ, a decreased µ at a fixed ν, and/or an increased net reproductive number produces an increased velocity of focus expansion. The relationship between temperature and velocity of focus expansion (V′) of P. lagenophorae appears to be caused mainly by the effect of temperature on latent period and on net reproductive number. Both the relative growth rate and the velocity of focus expansion were affected to the same degree by temperature, suggesting that the disease gradient (the decline in infections over distance; Campbell & Madden, 1990) is not affected by temperature as might be expected.
Only a few estimates of velocity of focus expansion are presented in the literature. Zadoks & Van den Bosch (1994) presented a list with some empirical records for focal epidemics. Downy mildew on spinach, caused by Peronospora farinosa, can be indicated as a slowly expanding disease, spreading 2·3 cm day−1 (Van den Bosch et al., 1988c). On the other hand, the rust fungus Puccinia coronata on oats, spreading with a velocity of ≈50 cm day−1, is a fast-expanding disease (Berger & Luke, 1979). Stripe rust on wheat, caused by Puccinia striiformis, spreads with a velocity of 8 cm day−1 (Van den Bosch et al., 1988c), which is comparable with the spread of Uromyces fabae on broad bean, Uromyces appendiculatus on French bean, and P. recondita on wheat (Zadoks & Van den Bosch, 1994). Buiel et al. (1989), however, reported a velocity of 3 cm day−1 for P. striiformis and explained this low velocity, compared to the findings of Van den Bosch et al. (1988c), by unfavourable weather conditions. The findings reported here support this explanation.
Estimates of velocity of focus expansion of P. lagenophorae are not available in the literature, but an estimate for the distribution kernel, σ = 28 cm, was obtained from field data (J. Frantzen, University of Friburg, Switzerland, personal communication). Including this value in Eqn 10 results in an estimated velocity between 3·5 cm day−1 at 10°C and 8·0 cm day−1 at 22°C. These results suggest that the focus of P. lagenophorae infection expands slowly (Zadoks & Van den Bosch, 1994). However, further field studies on velocity of focus expansion of P. lagenophorae should be done to validate these data.
The models used in this study have been extensively verified (Levin, 1989; Zadoks & Van den Bosch, 1994). Nevertheless, field experiments are needed to test the conclusions concerning the effect of temperature on exponential growth rate, r, and velocity of focus expansion, V.
Our study demonstrates that temperature influences the velocity of focus expansion and exponential growth rate. The results showed a positive relationship between temperature and both velocity of focus expansion and relative growth rate of P. lagenophorae on a population of S. vulgaris in the temperature range between 10 and 22°C. This was caused mainly by the effect of postinoculation temperature on both latent period and net reproductive number. Aeciospores of P. lagenophorae need high humidity to germinate, and dry periods will reduce epidemic development. Effects of these and other factors, such as host diversity, plant growth stage and density on epidemics of P. lagenophorae, are not well understood and should be the subject of further research.
We thank Jos Frantzen for his advice, discussions and comments on this manuscript, and also Nigel Paul and Heinz Müller-Schärer for their comments on the manuscript. We thank Nilgün Sailer and Mathias Villiger for gathering data. IACR receives grant-aided support from the Biotechnology and Biological Sciences Research Council of the United Kingdom.