The sensitivity of the epidemic growth rate to weather variables, with an application to yellow rust on wheat

ABSTRACT We first show how to estimate the exponential epidemic growth rate, r, for different combinations of three weather variables. Then we derive a method to quantify the sensitivity of r to a weather variable as a function of the pathogen life cycle variables of latent period, basic reproductive number, and the mean and standard deviation of the sporulation curve. The method can be used to identify the most important weather variable and pathogen life cycle component in terms of epidemic progress. The method is applied to yellow rust, caused by Puccinia striiformis, on winter wheat. We conclude that the most important weather variable for the progress of yellow rust is temperature, followed by dew period and light quantity. By far, the most important pathogen life cycle component is the basic reproductive number, especially at low and high temperatures. This disagrees with the general view that latent period is the most important variable at low temperatures. We discuss explanations of this.     

Effects of initial epidemic conditions, sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics

ABSTRACT A stochastic model that simulates the spread of disease over space and time was developed to study the effects of initial epidemic conditions (number of initial inocula and their spatial pattern), sporulation rate, and spore dispersal gradient on the spatio-temporal dynamics of plant disease epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). The rate of temporal increase in disease incidence (beta(I), per day) was influenced jointly by mu and by the sporulation rate lambda (spores per lesion per day). The relationship between beta(I) and mu was nonlinear: the increase in beta(I) with increasing mu was greatest when mu was small (i.e., when the dispersal gradient was steep). The rate of temporal increase in disease severity of diseased plants (beta(S)) was affected mainly by lambda: beta(S) increased directly with increasing lambda. Intraclass correlation (kappa(t)), the correlation of disease status of plants within quadrats, increased initially with disease incidence, reached a peak, and then declined as disease incidence approached 1.0. This relationship was well described by a power-law model that is consistent with the binary form of the variance power law. The amplitude of the model relating kappa(t) to disease incidence was affected mainly by mu: kappa(t) decreased with increasing mu. The shape of the curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. Generally, the relationship of spatial autocorrelation (rho(t,k)), the correlation of disease status of plants at various distances apart, to disease incidence and distance was well described by a four-parameter power-law model. rho(t,k) increased with disease incidence to a maximum and then declined at higher values of disease incidence, in agreement with a power-law relationship. The amplitude of rho(t,k) was determined mainly by initial conditions and by mu: rho(t,k) decreased with increasing mu and was lower for regular patterns of initial inocula. The shape of the rho(t,k) curve was affected mainly by initial conditions, especially the spatial pattern of the initial inocula. At any level of disease incidence, autocorrelation declined exponentially with spatial lag; the degree of this decline was determined mainly by mu: it was steeper with decreasing mu.     

河南小麦白粉病逐年春季流行时间动态

1980－1997年对河南小麦白粉病春季流行的时间动态进行了系统分析。结果表明：（1）逐年春季流行程度波动较大,中度以上流行年份有9年,但流行程度之间没有明显的周期性。（2）逐年春季流行的时间动态有明显差异,特大流行年份白粉病发病特早,指数增长期和逻辑斯蒂期比其它年份长30d以上,表观侵染速率达0.16以上;大流行年和中度流行年份的始发期相同,表观侵染速率前者达0.16,后者只有0.12-0.14;轻度流行年始发期晚,指数增长期和逻辑斯蒂期短,表观侵染速率低,导致最终病情指数低。（3）小麦越冬返青期的降水量、雨日、水份积分指数、相对湿度对白粉病的始发期有显著影响,但白粉病的最终流行程度主要取决于小麦拔节孕穗期的水份积分指数、温雨系数、降水量、雨日和温度。     

Effect of temperature on epidemiological parameters of Puccinia lagenophorae

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.     

Sporulation of Pyrenopeziza brassicae (light leaf spot) on oilseed rape (Brassica napus) leaves inoculated with ascospores or conidia at different temperatures and wetness durations

In controlled environment experiments, sporulation of Pyrenopeziza brassicae was observed on leaves of oilseed rape inoculated with ascospores or conidia at temperatures from 8 to 20°C at all leaf wetness durations from 6 to 72 h, except after 6 h leaf wetness duration at 8°C. The shortest times from inoculation to first observed sporulation ( l ₀), for both ascospore and conidial inoculum, were 11–12 days at 16°C after 48 h wetness duration. For both ascospore and conidial inoculum (48 h wetness duration), the number of conidia produced per cm² leaf area with sporulation was seven to eight times less at 20°C than at 8, 12 or 16°C. Values of Gompertz parameters c (maximum percentage leaf area with sporulation), r (maximum rate of increase in percentage leaf area with sporulation) and l ₃₇ (days from inoculation to 37% of maximum sporulation), estimated by fitting the equation to the observed data, were linearly related to values predicted by inserting temperature and wetness duration treatment values into existing equations. The observed data were fitted better by logistic equations than by Gompertz equations (which overestimated at low temperatures). For both ascospore and conidial inoculum, the latent period derived from the logistic equation (days from inoculation to 50% of maximum sporulation, l ₅₀) of P. brassicae was generally shortest at 16°C, and increased as temperature increased to 20°C or decreased to 8°C. Minimum numbers of spores needed to produce sporulation on leaves were ≈25 ascospores per leaf and ≈700 conidia per leaf, at 16°C after 48 h leaf wetness duration.     

Coupling Disease-Progress-Curve and Time-of-Infection Functions for Predicting Yield Loss of Crops

ABSTRACT A general approach was developed to predict the yield loss of crops in relation to infection by systemic diseases. The approach was based on two premises: (i) disease incidence in a population of plants over time can be described by a nonlinear disease progress model, such as the logistic or monomolecular; and (ii) yield of a plant is a function of time of infection (t) that can be represented by the (negative) exponential or similar model (zeta(t)). Yield loss of a population of plants on a proportional scale (L) can be written as the product of the proportion of the plant population newly infected during a very short time interval (X'(t)dt) and zeta(t), integrated over the time duration of the epidemic. L in the model can be expressed in relation to directly interpretable parameters: maximum per-plant yield loss (alpha, typically occurring at t = 0); the decline in per-plant loss as time of infection is delayed (gamma; units of time(-1)); and the parameters that characterize disease progress over time, namely, initial disease incidence (X(0)), rate of disease increase (r; units of time(-1)), and maximum (or asymptotic) value of disease incidence (K). Based on the model formulation, L ranges from alphaX(0) to alphaK and increases with increasing X(0), r, K, alpha, and gamma(-1). The exact effects of these parameters on L were determined with numerical solutions of the model. The model was expanded to predict L when there was spatial heterogeneity in disease incidence among sites within a field and when maximum per-plant yield loss occurred at a time other than the beginning of the epidemic (t > 0). However, the latter two situations had a major impact on L only at high values of r. The modeling approach was demonstrated by analyzing data on soybean yield loss in relation to infection by Soybean mosaic virus, a member of the genus Potyvirus. Based on model solutions, strategies to reduce or minimize yield losses from a given disease can be evaluated.     

PANCRIN, a prototype model of the pandemic cultivar-race interaction of yellow rust on wheat in China

The pandemic of yellow rust on wheat in China, including cultivar-race interactions at the population level, is described by a prototype model (PANCRIN). As the framework of this model, the main epidemic system of wheat yellow rust in China was divided into 11 epidemiological regions. The major parameters are R, the rate of epidemic progress of each region in each month, determined by regional climatological factors and cultivar-race interactions; DIL, the dilution coefficient of inter-regional longdistance dissemination of this disease, determined mainly by distance; and F, fitness values of the pathogen on different cultivar-race combinations. With cultivar deployment, initial disease amount, and initial race frequency as inputs, this model can output the disease amount on each cultivar and the race frequencies of each region. Results of preliminary simulation experiments tallied with some historical situations such as the breakdown of disease resistance of some important cultivars Weak points of this model are also discussed.     

The effects of dispersal gradient and pathogen life cycle components on epidemic velocity in computer simulations

ABSTRACT The velocity of expansion of focal epidemics was studied using an updated version of the simulation model EPIMUL, with model parameters relevant to wheat stripe rust. The modified power law, the exponential model, and Lambert's general model were fit to primary disease gradient data from an artificially initiated field epidemic of stripe rust and employed to describe dispersal in simulations. The exponential model, which fit the field data poorly (R (2) = 0.728 to 0.776), yielded an epidemic that expanded as a traveling wave (i.e., at a constant velocity), after an initial buildup period. Both the modified power law and the Lambert model fit the field data well (R(2) = 0.962 to 0.988) and resulted in dispersive epidemic waves (velocities increased over time for the entire course of the epidemic). The field epidemic also expanded as a dispersive wave. Using parameters based on the field epidemic and modified power law dispersal as a baseline, life cycle components of the pathogen (lesion growth rate, latent period, infectious period, and multiplication rate) and dispersal gradient steepness were varied within biologically reasonable ranges for this disease to test their effect on dispersive wave epidemics. All components but the infectious period had a strong influence on epidemic velocity, but none changed the general pattern of velocity increasing over time.     

Relationships among measurements of fitness and disease severity in Phytophthora infestans

Several methods of estimating pathogen fitness and disease severity in the Phytophthora infestans Solanum tuberosum pathosystem were investigated. Components of fitness measured in a growth chamber were compared with area under the disease progress curve (AUDPC) measured in small field plots. The closest relationship with AUDPC was for sporulation capacity (coefficient of determination, r ²= 0.86)and the least close relationship was with infection frequency ( r ²= 001). Two different methods were compared for calculating the relative fitnesses of two isolates: (i) apparent infection rates and (ii) changes in frequency in mixed epidemics. The values obtained by the two methods were not contradictory (0.98 and 0.93 units per day for the less fit isolate, against 1 for the more fit isolate), but had wide and overlapping confidence intervals.     

Characterization of early leaf spot suppression by strip tillage in peanut

ABSTRACT Epidemics of early leaf spot of peanut (Arachis hypogaea), caused by Cercospora arachidicola, are less severe in strip-tilled than conventionally tilled fields. Experiments were carried out to characterize the effect of strip tillage on early leaf spot epidemics and identify the primary target of suppression using a comparative epidemiology approach. Leaf spot intensity was assessed weekly as percent incidence or with the Florida 1-to-10 severity scale in peanut plots that were conventionally or strip tilled. The logistic model, fit to disease progress data, was used to estimate initial disease (y(0)) and epidemic rate (r) parameters. Environmental variables, inoculum abundance, and field host resistance were assessed independently. For experiments combined, estimated y(0) was less in strip-tilled than conventionally tilled plots, and r was comparable. The epidemic was delayed in strip-tilled plots by an average of 5.7 and 11.7 days based on incidence and severity, respectively. Tillage did not consistently affect mean canopy temperature, relative humidity, or frequency of environmental records favorable for infection or spore dispersal. Host response to infection was not affected by tillage, but infections were detected earlier and at higher frequencies with noninoculated detached leaves from conventionally tilled plots. These data suggest that strip tillage delays early leaf spot epidemics due to fewer initial infections; most likely a consequence of less inoculum being dispersed to peanut leaves from overwintering stroma in the soil.     

Lesion expansion as an epidemic component

ABSTRACT A simulator for the enlargement of cohorts of circular lesions on cohorts of host tissue was used to examine five epidemiological parameters: radial rate (mm day(-1)) of lesion expansion, k (exp); maximum basic infection rate, R (m); proportion of lesion area as infectious, f; initial lesion size (mm(2)), z; and proportion of susceptible host sites, s. Based on the proportion of disease severity at day 50 and the proportion of the total disease that originated solely from lesion expansion, k(exp) was the most sensitive of the five parameters. A radial rate of only 0.1 mm day(-1) resulted in a proportion of >0.7 of the diseased area that came from lesion expansion. In an extensive survey of phytopathological literature, many plant pathogens had radial rates greater than 0.1 mm day(-1), which would result in a proportion of >0.95 of the total disease that comes from lesion expansion. Susceptible host sites, s, was a sensitive parameter, as this determined the host area into which lesions could expand. Naturally, R(m) was a sensitive parameter for the proportion of disease on day 50, as it controlled the overall speed of the epidemic. Initial lesion size was a relatively insensitive parameter, although z interacted significantly with s. The greatest proportion of disease that originated from lesion expansion occurred with fast k(exp), small z, and low values of s, R(m), and f. The model was validated with lesion numbers and severities obtained in natural epidemics of Cercospora medicaginis on alfalfa and Exserohilum turcicum on maize. We recommend that the 'epidemic quintuplet' used to describe polycyclic epidemics be expanded to the 'epidemic sextuplet' with the inclusion of k(exp), since lesion expansion is a major component of many polycyclic epidemics.     

模糊聚类分析在稻纹枯病流行动态研究中的应用

 本文引入模糊(Fuzzy)集论中基于模糊等价关系的模糊聚类分析方法,将发病数量(病害强度)、空间和时间动态的相互关系联系起来作为统一整体,研究了稻纹枯病田间流行动态。以平均发病株数(X)、聚集度指标(Ṁ/M)和发病丛率(P)作为群体动态的特征测度。从整体水平上,将对病害流行系统的考察,化成对若干亚系统(若干阶段)来研究,使复杂的系统得以简化,为深入定量研究和刻划纹枯病流行动态进行了初步尝试。作为一种新的研究方法,文中给出了具体的应用过程。     

Variability in the reaction of squash (Cucurbita pepo) to inoculation with Sphaerotheca fuliginea and methodology of breeding for resistance

Reaction to inoculation with powdery mildew caused by Sphaerotheca fuliginea was observed on leaf discs and young plants of eleven representatives of seven edible cultivar groups of Cucurbita pepo. Disease intensity (i.e. number of infections per leaf) was highly correlated ( r ²=0·863, P <0·0001) with spore yield per leaf. Spore yield per leaf and frequency of sporulation on leaf disks were moderately ( r ²=0·505), but significantly correlated ( P <0·01), suggesting that frequency of sporulation can be used for initial screening against susceptibility in a breeding programme. Spore yield per leaf and spore yield per artificially inoculated leaf disc were highly correlated ( r ²=0·87, P <0·0001); this suggests that counting of spores on leaf discs, a laborious but accurate procedure, could be used on the remaining plants as a second step in selection for resistance of the variation in the response of edible C. pepo to the pathogen, 85·8% was attributed to differences between the edible groups and only 14·2% to individual cultivars within a group. Cultivars of the cocozelle and vegetable marrow groups were the most susceptible, whereas relatively resistant cultivars were found in the scallop and straightneck groups.     

Comparative analysis of flexible two-parameter models of plant disease epidemics

ABSTRACT Eleven previously published models of plant disease epidemics, given as differential equations with a rate and a shape parameter, are compared using general model characteristics as well as their usefulness in fitting observed data. Six out of the eleven models can be solved analytically resulting in epidemic growth functions, while the others can be solved only numerically. When all 11 differential equations were fitted to two data sets, all models showed a similar goodness of fit, although the shape parameter in some models could not be estimated very precisely. With respect to useful characteristics (exponential population growth at the beginning, ability to generate monomolecular disease progression, and flexibility of the inflection point), the models of Fleming, Kosman-Levy, Birch, Richards and Waggoner, and Rich are recommended. Formulas were established to calculate the point of inflection as well as the weighted absolute and relative rate, respectively, depending on the shape and rate parameter. These formulas allow transformation of the parameter values of one model into those of another model in many cases. If the two models are required to have the same temporal position of the disease progress curve, then the initial disease level at the start of the epidemic or the time when the inflection point is reached have to be transformed.     

Analyzing and Modeling Temporal Disease Progress of Barley yellow dwarf virus Serotypes in Barley Fields

ABSTRACT Population dynamics of Padi avenae (PAV), Macrosiphum avenae (MAV), and Rhopalosiphum padi (RPV) virus serotypes of Barley yellow dwarf virus (BYDV) and of their main aphid vectors were studied in winter barley (Hordeum vulgare) fields for three successive years in western France. An epidemiological model of the spread of viruses in the field was developed based on vector populations as forcing variables and the population dynamics of each virus serotype. This model accurately simulated the kinetics of the epidemic for PAV serotypes, which are the most common ones. For RPV and to some extent for MAV, the results were less satisfactory. The occurrence and spread of PAV and MAV serotypes in the field was clearly and easily related to that of their main vector species. Conversely, the spread of RPV serotypes showed no consistent relationships with the dynamics of their vectors. Incidence of PAV in 1989 to 1990 and 1990 to 1991 showed a bimodal distribution, with maximums in fall (December) and spring (May) that were linked to fall infestations by R. padi and spring infestations by three (R. padi, Sitobion avenae, and Metopolophium dirhodum) or two (S. avenae and M. dirhodum) aphid species. In 1991 to 1992, the PAV infection curve was monomodal and mainly due to a primary spread of the virus by very large populations of alate R. padi. MAV incidence was low in fall and winter and reached a maximum in spring 1990 and 1991 related to the occurrence of S. avenae and M. dirhodum. RPV incidence was low every year, despite the abundance of its vector, R. padi. Mixed infections were more frequent than expected by chance and were assumed to be partly related to heterologous encapsidation. The occurrence of each serotype is discussed in relation to the time of crop infection and possible damage.     

Epidemiology and chemical control of take-all on seminal and adventitious roots of wheat

ABSTRACT Epidemiological modeling is used to examine the effect of silthiofam seed treatment on field epidemics of take-all in winter wheat. A simple compartmental model, including terms for primary infection, secondary infection, root production, and decay of inoculum, was fitted to data describing change in the number of diseased and susceptible roots per plant over thermal time obtained from replicated field trials. This produced a composite curve describing change in the proportion of diseased roots over time that increased monotonically to an initial plateau and then increased exponentially thereafter. The shape of this curve was consistent with consecutive phases of primary and secondary infection. The seed treatment reduced the proportion of diseased roots throughout both phases of the epidemic. However, analysis with the model detected a significant reduction in the rate of primary, but not secondary, infection. The potential for silthiofam to affect secondary infection from diseased seminal or adventitious roots was examined in further detail by extending the compartmental model and fitting to change in the number of diseased and susceptible seminal or adventitious roots. Rates of secondary infection from either source of infected roots were not affected. Seed treatment controlled primary infection of seminal roots from particulate inoculum but not secondary infection from either seminal or adventitious roots. The reduction in disease for silthiofam-treated plants observed following the secondary infection phase of the epidemic was not due to long-term activity of the chemical but to the manifestation of disease control early in the epidemic.     

Development of a Downy Mildew Advisory Model Based on Downcast

A downy mildew advisory model for use in practical onion growing was constructed according to DOWNCAST, an existing downy mildew forecasting model. The model was empirically improved after comparison between observed and calculated disease development. Onion plants grown in pots were placed as trap plants in artificially inoculated onion fields (one in 1995, three in 1996 and one in 1997) for 1–7 days, then removed and incubated outdoors in a sheltered place at 1km distance from the onion field. Symptom development was observed. Hourly measurements of leaf wetness, temperature and relative humidity were taken in the crop and hourly data on rainfall were obtained from a nearby automatic weather station. Sporulation of the fungus was visually observed in the onion crop in the morning on several days in all three years. Sporulation-infection periods and sporulation as predicted by the model were compared with symptom development on the trap plants and observations on sporulation in the field. The initial model corresponded to the trap plant observations in only 18 out of 42 and to visual sporulation in 25 out of 40 occasions. Criteria in both the sporulation and infection submodels of the advisory model were subsequently calibrated to obtain a best fit between the model and observations. In 30 out of 42 occasions the improved model corresponded with trap plant observations while 30 out of 40 sporulation observations were now calculated correctly. The improved model needs to be evaluated with additional and independent data.     

玉米大豆条带间作根系分布模式

在土壤剖面上冲洗根系,观测玉米/大豆条带间作模式下根系的生长分布及动态变化规律;使用二次曲线和修正的Logistic函数拟合根系下扎深度和侧向伸展距离与播后天数(DAS)的关系;引入根系的相对侧向伸展距离(RLD)与相对深度(RD)两个概念,将根系下扎深度和侧向伸展距离归一化,利用高斯函数拟合RLD与RD的关系,建立根系分布函数.结果表明,该根系分布函数对玉米大豆间作模式下的根系生长分布状况有很好的模拟性.     

不同温度下的豌豆蚜实验种群生命表研究

在6种温度(12、15、18、21、24℃和27℃)和相对湿度为80%的条件下,研究了温度对豌豆蚜发育和增殖的影响。组建了生命表,并统计出种群内禀增长率、净增殖率、世代平均周期、种群加倍时间和周限增长率等种群动态参数。结果表明,在试验温度范围内,豌豆蚜的发育历期随温度升高而缩短。种群的内禀增长率在24℃条件下最大(rm=0.281 0),相应的种群净增殖率(R0)、周限增长率(λ)、平均世代周期(T)和种群加倍时间(t)分别为17.030 9、1.324 5、10.089 3 d和2.466 7 d。     

Interactive Effects of Host, Pathogen and Mineral Nutrition on Grey Leaf Spot Epidemics in Uganda

Grey leaf spot incited by Cercospora zeae-maydis is a new devastating foliar disease of maize in East Africa. For effective control, elucidation of the most critical elements of the grey leaf spot disease pyramid is important. This study investigated the role of mineral nutrition, pathogen variability and host resistance in the epidemic. Trials were conducted under field and controlled environments. The 28 isolates used in the controlled environment varied significantly (P 0.05) in parasitic fitness measured indirectly as disease efficiency, but no infection pattern could be attributed to known C. zeae-maydis pathotypes. Data from field trials showed that host resistance and mineral nutrition significantly (P 0.05) affected disease efficiency, with highest disease development occurring in nitrogen-augmented plots. Exclusive phosphorus application had no clear effect on grey leaf spot epidemics but combined application with nitrogen significantly (P 0.05) reduced the predisposition effects of nitrogen to the disease. Overall, treated plots had less disease than unfertilised plots. Fertiliser application had no effect on sporulation capacity, while cultivars significantly affected it. Geographic differences in amount of disease were observed, suggesting environment influences on grey leaf spot incidence. The results suggest that the current grey leaf spot epidemics in East Africa are due to favourable cultivars, poor mineral nutrition and environmental interactions.