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Pathogen buildup in vegetative planting material, termed seed degeneration, is a major problem in many low-income countries. When smallholder farmers use seed produced on-farm or acquired outside certified programs, it is often infected. We introduce a risk assessment framework for seed degeneration, evaluating the relative performance of individual and combined components of an integrated seed health strategy. The frequency distribution of management performance outcomes was evaluated for models incorporating biological and environmental heterogeneity, with the following results. (1) On-farm seed selection can perform as well as certified seed, if the rate of success in selecting healthy plants for seed production is high; (2) when choosing among within-season management strategies, external inoculum can determine the relative usefulness of 'incidence-altering management' (affecting the proportion of diseased plants/seeds) and 'rate-altering management' (affecting the rate of disease transmission in the field); (3) under severe disease scenarios, where it is difficult to implement management components at high levels of effectiveness, combining management components can be synergistic and keep seed degeneration below a threshold; (4) combining management components can also close the yield gap between average and worst-case scenarios. We also illustrate the potential for expert elicitation to provide parameter estimates when empirical data are unavailable. [Formula: see text] Copyright © 2017 The Author(s). This is an open access article distributed under the CC BY-NC-ND 4.0 International license .

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.

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 the 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.

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.

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 involved. 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.

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 for 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 to optimize BCA application strategies.

ABSTRACT Disease dynamics of Cercospora leaf spot (CLS) of sugar beet was analyzed at two hierarchical scales: as vertical profiles within individual plants and in relation to disease on neighboring plants. The relative contribution of different leaf layers to increase in CLS was analyzed using a simple continuous-time model. The model was fitted to data from two field trials in the Netherlands: one in an area with a long history of CLS, the other in an area where CLS has only recently established; in each case these were unsprayed and twice-sprayed treatments. There were differences in the relative contribution of different leaf layers to disease increase on the target leaf layer according to the CLS history and whether the plants were sprayed or unsprayed. In both field trials, parameter estimates giving the relative contribution of the target leaf layer to disease increase at that leaf layer were higher than those for the lower leaf layer. On only a few occasions the contribution of an upper leaf layer to disease increase at the target leaf layer was significant. Thus, CLS increase at the target leaf layer was determined mainly by disease severity at that leaf layer and to a lesser extent by disease at the lower leaf layer. Our continuous-time model was also used to analyze CLS increase on an individual sugar beet plant in relation to its own and its neighbor's level of disease in field trials at five locations in the two CLS areas over two years. In all field trials, the contribution of the target plant itself to disease increase (auto-infection) was larger than that of its neighboring plants (allo-infection). The overall analysis in the two CLS areas also indicated a larger contribution of the target plant to its disease increase than of neighboring plants, and this pattern was also apparent in a pooled analysis across all sites. Thus, CLS increase on a sugar beet plant was mainly determined by the disease severity on that plant and to a lesser extent by its within-row neighboring plants.

ABSTRACT Two, 4-year studies on summer epidemic progress of apple scab were conducted at Randwijk, the Netherlands, from 1998 until 2001 and at Eperjeske, Hungary, from 2000 until 2003. Disease assessments were made on scab-susceptible cv. Jonagold. A range of nonlinear growth functions were fitted to a total of 96 disease progress curves (3 treatment classes x 2 plant parts x 2 disease measures x 4 years x 2 locations) of apple scab incidence and severity. The three-parameter logistic model gave the most consistent fit across three treatment classes in the experiment (integrated, organic-sprayed, and organic-unsprayed). Parameters estimated or calculated from the three-parameter logistic function were used to analyze disease progress. These were disease incidence and severity on the day of the first assessment (Y(s)); final disease incidence or upper asymptote for incidence (Y(if)) or severity (Y(sf)); fruit incidence and severity on day 40, after which no new lesions on fruits appeared (Y(40)); leaf incidence and severity on day 75, at which shoot growth stopped (Y (75)); relative (beta) and "absolute" (theta) rates of disease progress; inflection point (M); and area under the disease progress curve (AUDPC(S)) standardized by the duration of the total epidemic. Comparisons among disease progress curves were made by correlation and factor analysis followed by Varimax rotation. There were large differences but high positive correlations among the parameters Y(s), Y(f), theta, and AUDPC(S) across the three treatment classes. In the factor analysis, two factors accounted for more than 85% of the total variance for both incidence and severity. Factor 1 gave an overall description of epidemic progress of both scab incidence and severity and included the parameters Y(f), Y(40), Y(75), theta, and AUDPC(S). Factor 2 identified a relationship between the relative rate parameter (beta) and the inflection point (M) for severity and a relationship between disease incidence and severity. For an integrated or an organic orchard, theta, AUDPC(S), and one of Y(f) or Y(75) (because of the link with host phenology) can characterize apple scab epidemics during summer. Based on these findings, improved scab management approaches were provided for integrated and organic apple production systems.

ABSTRACT The general Kermack and McKendrick epidemic model (K&M) is derived with an appropriate terminology for plant diseases. The epidemic dynamics and patterns of special cases of the K&M model, such as the Vanderplank differential-delay equation; the compartmental healthy (H), latent (L), infectious (S), and postinfectious (R) model; and the K&M model with a delay-gamma-distributed sporulation curve were compared. The characteristics of the disease cycle are summarized by the basic reproductive number, R(0), and the normalized sporulation curve, i(tau). We show how R(0) and the normalized sporulation curve can be calculated from data in the literature. There are equivalences in the values of the basic reproductive number, R(0), the epidemic threshold, and the final disease level across the different models.However, they differ in expressions for the initial disease rate, r, and the initial infection, Q, because the values depend on the sporulation curve. Expressions for r and Q were obtained for each model and can be used to approximate the epidemic curve by the logistic equation.

ABSTRACT The development of Pyrenopeziza brassicae (light leaf spot) apothecia was studied on petiole debris from artificially infected oilseed rape leaves incubated at temperatures from 6 to 22 degrees C under different wetness regimes and in 16 h light/8 h dark or continuous darkness. There was no significant difference between light treatments in numbers of apothecia that developed. Mature apothecia developed at temperatures from 5 to 18 degrees C but not at 22 degrees C. The rate of apothecial development decreased as temperature decreased from 18 to 5 degrees C; mature apothecia were first observed after 5 days at 18 degrees C and after 15 days at 6 degrees C. Models were fitted to estimates of the time (days) for 50% of the maximum number of apothecia to develop (t(1); model 1, t(1) = 7.6 + 55.8(0.839)(T)) and the time for 50% of the maximum number of apothecia to decay (t(2); model 2, t(2) = 24.2 + 387(0.730)(T)) at temperatures (T) from 6 to 18 degrees C. An interruption in wetness of the petiole debris for 4 days after 4, 7, or 10 days of wetness delayed the time to observation of the first mature apothecia for approximately 4 days and decreased the number of apothecia produced (by comparison with continuous wetness). A relationship was found between water content of pod debris and electrical resistance measured by a debris-wetness sensor. The differences between values of t(1) predicted by model 1 and observed values of t(1) were 1 to 9 days. Model 2 did not predict t(2); apothecia decayed more quickly under natural conditions than predicted by model 2.

ABSTRACT A continuous-time and deterministic model was used to characterize plant virus disease epidemics in relation to virus transmission mechanism and population dynamics of the insect vectors. The model can be written as a set of linked differential equations for healthy (virus-free), latently infected, infectious, and removed (postinfectious) plant categories, and virus-free, latent, and infective insects, with parameters based on the transmission classes, vector population dynamics, immigration/emigration rates, and virus-plant interactions. The rate of change in diseased plants is a function of the density of infective insects, the number of plants visited per time, and the probability of transmitting the virus per plant visit. The rate of change in infective insects is a function of the density of infectious plants, the number of plants visited per time by an insect, and the probability of acquiring the virus per plant visit. Numerical solutions of the differential equations were used to determine transitional and steady-state levels of disease incidence (d*); d* was also determined directly from the model parameters. Clear differences were found in disease development among the four transmission classes: nonpersistently transmitted (stylet-borne [NP]); semipersistently transmitted (foregut-borne [SP]); circulative, persistently transmitted (CP); and propagative, persistently transmitted (PP), with the highest disease incidence (d) for the SP and CP classes relative to the others, especially at low insect density when there was no insect migration or when the vector status of emigrating insects was the same as that of immigrating ones. The PP and CP viruses were most affected by changes in vector longevity, rates of acquisition, and inoculation of the virus by vectors, whereas the PP viruses were least affected by changes in insect mobility. When vector migration was explicitly considered, results depended on the fraction of infective insects in the immigration pool and the fraction of dying and emigrating vectors replaced by immigrants. The PP and CP viruses were most sensitive to changes in these factors. Based on model parameters, the basic reproductive number (R(0))-number of new infected plants resulting, from an infected plant introduced into a susceptible plant population-was derived for some circumstances and used to determine the steady-state level of disease incidence and an approximate exponential rate of disease increase early in the epidemic. Results can be used to evaluate disease management strategies.