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Effective use of biocontrol agents (BCAs) is a potentially important component of sustainable agriculture; recently, there has been a trend for combined use of several BCAs, with an expectation of synergistic interactions among them. A previous numerical study suggested that, under homogenous conditions in which two BCAs occupied the same host tissue as the pathogen, combined use of two BCAs with different biocontrol mechanisms resulted, in most cases, in efficacies similar to using he more efficacious one alone; this result is consistent with published experimental results. The present study investigates whether combined use of a mycoparasitic and a competitive BCA leads to greater efficacy than that expected when the model is modified to allow for fluctuating temperature regimes and the effects of temperature on the pathogen and BCAs. Within the range of parameter values considered, combined use of two BCAs is shown to be less effective than that expected under the assumption of Bliss independence, and to result in a level of efficacy similar to that achieved by the more efficacious component used alone, indicating antagonistic interactions between the two BCAs. Nevertheless, combined use of two BCAs resulted in a slightly longer delay in epidemic development than did individual use of BCAs. Stochastic variability in simulated hourly temperatures did not result in a high level of variability in efficacy among replicates; nevertheless, the among-replicate variability appeared to be greater for the combined use of BCAs than for individual BCAs used alone. In contrast, there were greater effects of varying BCA-temperature relationships and application time (reflected in the temperature profile) on efficacy, suggesting the importance of characterizing the relationship between BCA activity and environmental conditions in future research. [ABSTRACT FROM AUTHOR]

Effective use of biological control agents (BCAs) is a potentially important component of sustainable agriculture. Recently, there has been an increasing interest among researchers in using combinations of BCAs to exploit potential synergistic effects among them. The methodology for investigating such synergistic effects was reviewed first and published results were then assessed for available evidence for synergy. Correct formulation of hypotheses based on the theoretical definition of independence (Bliss independence or Loewe additivity) and the subsequent and statistical testing for the independence-synergistic-antagonistic interactions have rarely been carried out thus far in studies on biocontrol of plant diseases. Thus, caution must be taken when interpreting reported "synergistic" effects without assessing the original publications. Recent theoretical modeling work suggested that disease suppression from combined use of two BCAs was. in general, very similar to that achieved by the more efficacious one, indicating no synergistic but more likely antagonistic interactions. Only in 2% of the total 465 published treatments was there evidence for synergistic effects among BCAs. In the majority of the cases, antagonistic interactions among BCAs were indicated. Thus. both theoretical and experimental studies suggest that, in combined use of BCAs, antagonistic interactions among BCAs are more likely to occur than synergistic interactions. Several research strategies, including formulation of synergy hypotheses in relation to biocontrol mechanisms, are outlined to exploit microbial mixtures for uses in biocontrol of plant diseases. Additional keywords: hypothesis testing. [ABSTRACT FROM AUTHOR]

Effective use of biocontrol agents is an important component of sustainable agriculture. A previous numerical study of a generic model showed that biocontrol efficacy was greatest for a single biocontrol agent (BCA) combining competition with mycoparasitism or antibiosis. This study uses the same mathematical model to investigate whether the biocontrol efficacy of combined use of two BCAs with different biocontrol mechanisms is greater than that of a single BCA with either or both of the two mechanisms, assuming that two BCAs occupy the same host tissue as the pathogen. Within the parameter values considered, a BCA with two biocontrol mechanisms always outperformed the combined use of two BCAs with a single but different biocontrol mechanism. Similarly, combined use of two BCAs with a single but different biocontrol mechanism is shown to be far less effective than that of a single BCA with both mechanisms. Disease suppression from combined use of two BCAs was very similar to that achieved by the more efficacious one. As expected, a higher BCA introduction rate led to increased disease suppression. Incorporation of interactions between two BCAs did not greatly affect the disease dynamics except when a mycoparasitic and, to a lesser extent, an antibiotic-producing BCA was revolved. Increasing the competitiveness of a mycoparasitic BCA over a BCA whose biocontrol mechanism is either competition or antibiosis may lead to improved biocontrol initially and reduced fluctuations in disease dynamics. The present study suggests that, under the model assumptions. combined use of two BCAs with different biocontrol mechanisms in most cases only results in control efficacies similar to using the more efficacious one alone. These predictions are consistent with published experimental results, suggesting that combined use of BCAs should not be recommended without clear understanding of their main biocontrol mechanisms and relative competitiveness, and experimental evaluation. [ABSTRACT FROM AUTHOR]

A previously published generic mathematic model has been used in a numerical study to understand the dynamics of foliar pathogens in relation to mechanisms, and timing and coverage of biocontrol agent (BCA) applications. With the model parameter values used, it was demonstrated that a BCA possessing either competition or induced resistance as the main mechanism of biological control was more effective in reducing disease development than a BCA with either mycoparasitism or antibiosis as its mechanism. Application coverage, ranging from 50 to 90%, had little effect on biocontrol efficacy, particularly for a BCA with competition and induced resistance as the main mechanism of biocontrol Conversely, delayed application of BCA had more profound effects on biocontrol efficacy for those with competition or induced resistance as their main mechanism than those with mycoparasitism and antibiosis. Biocontrol efficacy was greatest for a single BCA combining competition with mycoparasitism or antibiosis. The efficacy for a single BCA combining induced resistance with competition critically depended on application time; the efficacy was greatly reduced lot delayed applications. The present study suggests that development of an effective strategy for BCA application is critically dependent upon our quantitative understanding of several key biocontrol processes and their interactions. Without reliable quantitative estimation of these processes, it is impossible to make quantitative predictions about biological control and hence Io optimize BCA application strategies [ABSTRACT FROM AUTHOR]

Spatial pattern, an important epidemiological property of plant diseases, can be quantified at different scales using a range ol methods. The spatial heterogeneity (or overdispersion) of disease incidence among sampling units is an especially important measure of small-scale pattern. As an alternative to Taylor's power law for the heterogeneity of counts with no upper bound, the binary power law (BPL) was proposed in 1992 as a model to represent the heterogeneity of disease incidence (number of plant units diseased out of n observed in each sampling unit, or the proportion diseased in each sampling unit). With the BPL, the log of the observed variance is a linear function of the log of the variance for a binomial (i.e., random) distribution. Over the last quarter century, the BPL has contributed to both theory and multiple applications in the study of heterogeneity of disease incidence. In this article, we discuss properties of the BPL and use it to develop a general conceptualization of the dynamics of spatial heterogeneity in epidemics; review the use of the BPL in empirical and theoretical studies; present a synthesis of parametei estimates fiom over 200 published BPL analyses from a wide range of diseases and crops; discuss model fitting methods, and applications in sampling, data analysis, and prediction; and make recommendations on reporting results to improve interpretation. In a review of the literature, the BPL provided a very good fit to heterogeneity data in most publications. Eighty percent of estimated slope (b) values from field studies were between 1.06 and 1.51, with b positively correlated with the BPL intercept parameter. Stochastic simulations show that the BPL is generally consistent with spatiotemporal epidemiological processes and holds whenever there is a positive correlation of disease status of individuals composing sampling units. [ABSTRACT FROM AUTHOR]

The binary power law (BPL) has been successfully used to characterize heterogeneity (overdispersion or small-scale aggregation) of disease incidence for many plant pathosystems. With the BPL, the log of the observed variance is a linear function of the log of the theoretical variance for a binomial distribution over the range of incidence values, and the estimated scale (κ) and slope (b) parameters provide information on the characteristics of aggregation. When b = 1, the interpretation is that the degree of aggregation remains constant over the range of incidence values observed: otherwise, aggregation is variable. In two articles published in this journal in 2009, Gosme and Lucas used their stochastic simulation model, Cascade, to show a multiphasic (split-line) relationship of the variances, with straight-line (linear) relationships on a log-log scale within each phase. In particular, they showed a strong break point in the lines at very low incidence, with b considerably >1 in the first line segment (corresponding to a range of incidence values usually not observed in the field), and b being ≈1 in the next segment (corresponding to the range of incidence values usually observed). We evaluated their findings by utilizing a general spatially explicit stochastic simulator developed by Xu and Ridout in 1998, with a wide range of median dispersal distances for the contact distribution and number of plants in the sampling units (quadrats), and through an assessment of published BPL results. The simulation results showed that the split-line phenomenon can occur, with a break point at incidence values of ≈0.01; however, the split is most obvious for short median dispersal distances and large quadrat sizes. However, values of b in the second phase were almost always >1, and only approached 1 with extremely short median dispersal distances and small quadrat sizes. An appraisal of published results showed no evidence of multiple phases (although the minimum incidence may generally be too high to observe the break), and estimates of b were almost always >1. Thus, it appears that the results from the Cascade simulation model represent a special epidemiological case, corresponding primarily to a roughly nearest-neighbor population-dynamic process. Implications of a multiphasic BPL property may be important and are discussed. [ABSTRACT FROM AUTHOR]

There has been a trend for combined use of several biocontrol agents (BCAs) with an expectation of synergistic interactions among BCAs. However, previous modeling studies suggested that, under homogeneous and temporal-fluctuating conditions, combined use of two BCAs, in most cases, only results in efficacies similar to the more efficacious one used alone; a result consistent with published experimental data. The present modeling study investigated whether combined use of two mycoparasitic BCAs, two competitive BCAs, or a mycoparasitic and a competitive BCA leads to synergistic interactions under spatially heterogeneous conditions. In the model, there were two patches with varying relative sizes and two BCAs differentially adapted to the two patches. Within the range of model parameter values considered, combined use of two BCAs is more effective than the more efficacious BCA used alone in 72% of the simulated cases. There was also a considerable proportion (≈21%) of model simulations in which combined use of two BCAs led to synergy (i.e., efficacy was greater than expected under the assumption of Bliss independence, especially when each of the two BCAs can only survive in one [different] patch). Combined use of a mycoparasitic BCA with a competitive one is more likely to result in synergy than the other two BCA combinations. When biocontrol activities of individual BCAs are low or moderate, biocontrol efficacy arising from combined use of two BCAs does not depend greatly on biocontrol mechanisms. However, for high BCA activities, combined use with at least one competitive BCA resulted in better control than combined use of two mycoparasitic BCAs. The present modeling study emphasized the need for understanding the degree of spatial patchiness and quantitative relationships between biocontrol activities and external conditions in order to apply commercial BCAs effectively.

ABSTRACT Over 4 years, the environmental conditions and the causal agents of Fusarium head blight (FHB) disease of wheat were determined in field sites in four European countries: Hungary, Ireland, Italy, and the United Kingdom. Polymerase chain reaction-based methods were used to detect each species causing FHB and quantify its DNA (as a measurement of fungal abundance) in the samples. Canonical correspondence analysis (CCA) was used to determine the relationship of the incidence and abundance of each species with weather variables. CCA indicated that little variability in the species prevalence data was explained by the weather variables. In contrast, a greater proportion of variability in abundance data was accounted for by the weather variables. Most samples contained two or more species and statistical analysis suggested that these species tended to coexist at field sites. CCA also indicated that there were differences in the relationships of the prevalence and abundance of the six FHB species with environmental variables. Fusarium poae was associated with relatively drier and warmer conditions, whereas F. graminearum was associated with warmer/humid conditions. F. avenaceum and F. culmorum were both associated with niches of cooler/wet/humid conditions. Two Microdochium species were associated with regions of relatively cool/moderate temperatures and frequent rainfalls of short duration. The results also suggested that environmental conditions differentially affect the infection and colonization processes, and the comparative abundance of the six species.

ABSTRACT The spatiotemporal spread of plant diseases was simulated using a stochastic model to study the effects of initial conditions (number of plants initially infected and their spatial pattern), spore dispersal gradient, and size and shape of sampling quadrats on statistics describing the spatiotemporal dynamics of epidemics. The spatial spread of disease was simulated using a half-Cauchy distribution with median dispersal distance mu (units of distance). A total of 54 different quadrat types, including 23 distinct sizes ranging from 4 to 144 plants, were used to sample the simulated epidemics. A symmetric form of the binary power law with two parameters (alpha, beta) was fitted to the sampled epidemic data using each of the 54 quadrats for each replicate simulation run. The alpha and beta estimates were highly correlated positively with each other, and their estimates were comparable to those estimated from observed epidemics. Intraclass correlation (kappa) was calculated for each quadrat type; kappa decreased exponentially with increasing quadrat size. An asymmetric form of the binary power law with three parameters (alpha (1), beta(1), beta(2)) was used to relate kappa to the disease incidence (p); beta1 was highly correlated to beta: beta1 approximately beta - 1. In general, initial conditions and quadrat size affected alpha, beta, alpha(1), beta(1), and beta(2) greatly. The parameter estimates increased as quadrat size increased, and the relationships were described well by a linear regression model on the logarithm of quadrat size with the slope or intercept parameters dependent on initial conditions and mu. Compared with initial conditions and quadrat size, the overall effects of mu and quadrat shape were generally small, although within each quadrat size and initial condition they could be substantial. Quadrat shape had the greatest effect when the quadrat was long and thin. The relationship of the index of dispersion (D) to p and quadrat size was determined from the alpha and beta estimates. D was greatest when p was 0.5 and decreased when p approached 0 or 1. It increased with quadrat size and the rate of the increase was maximum when p was 0.5 and decreased when p approached 0 or 1.

ABSTRACT This article investigates the relationships between various statistical measures that are used to summarize spatial aspects of disease incidence data. The focus is on quadrat data in which each plant in a quadrat is classified as diseased or healthy. We show that spatial autocorrelation plays a central role via the mean intraclass correlation, rho, which is defined as the average correlation of the disease status of all pairs of plants within the quadrat. The value of rho determines the variance of the number of infected plants in the quadrat and, if this variable follows a beta-binomial distribution, the heterogeneity parameter of the beta-binomial distribution is directly related to the mean intraclass correlation. We consider in detail a model in which the spatial autocorrelation depends only on the distance between the plants. For illustration, we consider a specific autocorrelation model that was derived from simulated data. We show that this model leads, approximately, to the binary form of the power law relating the variance of the number of infected plants per quadrat to the mean. Using an approximation technique, we then show how the index of dispersion is related to quadrat size and shape. The index of dispersion increases with quadrat size. The rate of increase is dependent on quadrat shape, but the effect of quadrat shape is small in comparison to the effect of quadrat size. Finally, we note that if the spatial autocorrelation depends on the relative orientation of the plants, as well as the distance between them, there are connections with distance class methods.

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.