Modelling Inoculum Availability ofPlurivorosphaerella nawaein Persimmon Leaf Litter with Bayesian Beta Regression

Abstract

1 Circular leaf spot (CLS), caused by Plurivorosphaerella nawae, is a serious disease of persimmon 2 (Diospyros kaki ) inducing necrotic lesions on leaves, defoliation and fruit drop. Under Mediter-3 ranean conditions, P. nawae forms pseudothecia in the leaf litter during winter and ascospores are 4 released in spring infecting susceptible leaves. Persimmon growers are advised to apply fungicides 5 for CLS control during the period of inoculum availability, which was defined based on ascospore 6 counts under the microscope. A model of inoculum availability of P. nawae was developed and eval-7 uated as an alternative to ascospore counts. Leaf litter samples were collected weekly in L'Alcúdia 8 from 2010 to 2015. Leaves were soaked, placed in a wind tunnel, and released ascospores of P. 9 nawae were counted. Hierarchical Bayesian beta regression methods were used to fit the dynamics 10 of ascospore production in the leaf litter. The selected model, having the lowest values of DIC, 11 WAIC and LCPO, included accumulated degree days (ADD) and ADD taking into account the 12 vapor pressure deficit (ADDvpd) as fixed effects, and year as a random effect. This model had 13 a MAE of 0.042 and RMSE of 0.062. The beta regression model was evaluated in four orchards 14 for different years from 2010 to 2015. Higher accuracy was obtained at the beginning and the end 15of the ascospore production period, which are the events of interest to schedule fungicide sprays 16 for CLS control in Spain. This same modelling framework can be extended to other fungal plant 17 pathogens whose inoculum dynamics are expressed as proportion data.

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“…Temperature was expressed in ADD recorded after the 50 % blooming biofix, and PPM progression was modelled according to ADD using beta regression models (Ferrari and Cribari-Neto, 2004). As shown by previous studies using beta regression for modelling inoculum availability of Plurivorosphaerella nawae (Martínez-Minaya et al, 2019), this method overcomes the drawbacks of the traditional data transformations, allowing a direct interpretation of model parameters in terms of the original data.…”

“…Beta regression assumes that the response variable is within the interval (0,1) (Ferrari and Cribari-Neto 2004;Martínez-Minaya et al, 2019), although, in any interval (a,b) is possible, since it can be transformed easily to (0,1). As in generalized linear models (GLM), the mean ( μ i ) is linked to the linear predictor using the logit link function:…”