A new mechanistic model of weather-dependent Septoria tritici blotch disease risk

Abstract

We present a new mechanistic model for predicting Septoria tritici blotch (STB) disease, parameterized with experimentally derived data for temperature- and wetness-dependent germination, growth and death of the causal agent, Zymoseptoria tritici. The output of this model (A) was compared with observed disease data for UK wheat over the period 2002-2016. In addition, we compared the output of a second model (B), in which experimentally derived parameters were replaced by a modified version of a published Z. tritici thermal performance equation, with the same observed disease data. Neither model predicted observed annual disease, but model A was able to differentiate UK regions with differing average disease risks over the entire period. The greatest limitations of both models are: broad spatial resolution of the climate data, and lack of host parameters. Model B is further limited by its lack of explicitly defined pathogen death, leading to a cumulative overestimation of disease over the course of the growing season. Comparison of models A and B demonstrates the importance of accounting for the temperature-dependency of pathogen processes important in the initiation and progression of disease. However, effective modelling of STB will probably require similar experimentally derived parameters for host and environmental factors, completing the disease triangle. This article is part of the theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: approaches and important themes'. This issue is linked with the subsequent theme issue 'Modelling infectious disease outbreaks in humans, animals and plants: epidemic forecasting and control'.

Keywords: Septoria tritici blotch; Zymoseptoria tritici; infection risk; mechanistic; modelling; weather.

Figure 1.

Schematic of models A and B. Models A0, A1 and A2 are described by experimentally derived parameters for the temperature- and leaf wetness-driven transition probabilities of spore germination (T1, W1), spore death (T2, W2), and hyphal growth (T3, W3). Model B1 is described by the temperature- and leaf wetness-driven transition probabilities between spores landing on the leaf surface and pycnidiation (T4, W4); model B2 is only described by T4 [29]. (Online version in colour.)

Figure 2.

Model A parameterization. Temperature response functions for (a) germination and (b) hyphal growth. T_min, T_opt and T_max of temperature response functions were calculated by brute force fitting of the observed data to a beta function (10 million brute force iterations), such that residual sums of squares (RSS) were minimized. RSS for (a) germination and (b) growth were calculated as 0.0141 and 9.24, respectively. Insets show representative images of Z. tritici after 15 days growth at 5°C (left) or 25°C (right). (c) Increase in proportion of cells dying during 1 h under wet (blue) and dry (red) conditions. Lines show linear regression analysis. Slope of blue line = −0.00178, s.e. = 0.069, t = −0.026, d.f. = 14, p = 0.980; slope of red line = 0.169, s.e. = 0.092, t = 1.830, d.f. = 14, p = 0.0881. (d,e) Representative images of blastospores stained with propidium iodide (d) immediately after inoculation (wet) or (e) after 4 h drying at 18°C. Fluorescence of propidium iodide within the entire cell (blue arrows), or nuclear fluorescence (white arrows) indicated cell death. Scale bars in (b) represent 100 µm; (d and e) represent 10 µm.

Figure 3.

Model B parameterization. (a) Average effect of temperature on the latent period (time elapsed from inoculation until 37% of maximum by area sporulation) of three French isolates of Z. tritici. Calculated as the inverse of equation (2.1), taken from Bernard et al. [29]. (b) Temperature-dependent relative rate of STB disease development, calculated from equation (2.1) and rescaled (0–1), allowing temperature-dependent relative rates of STB disease development to be calculated.

Figure 4.

Average trajectory of Z. tritici infection (model A) and STB disease development (model B) over the wheat-growing season (1 October–31 July). (a) Model A0: infection refers to spore cohorts that germinate and grow hyphally along the leaf surface, leading to stomatal penetration. Models B1 (b) and B2 (c): disease development refers to spore cohorts that successfully infect and subsequently sporulate on the leaf surface. Infection/STB disease development is calculated for each hour of the growing season, as the mean of all pixels for all growing seasons in the climate dataset (winter 1990/summer 1991 to winter 2015/summer 2016). Green and blue lines represent (sexual) ascospores and (asexual) pycnidiospores, respectively.

Figure 5.

Pearson's correlation between model outputs and observed STB disease (%). Predicted infection (predicted STB disease) was calculated as the average total infection (average total STB disease) in a given pixel, for each growing season. Observed STB disease was calculated as the average disease of each farm, for each growing season. (a) Model A0, r = 0.065, p > 0.05. (d) Model B1, r = 0.065, p > 0.05. (g) Model B2, r = 0.043, p > 0.05. Mean predicted infection (mean predicted STB disease) was calculated as the average total infection (average total STB disease) in a given pixel, pooled for all growing seasons. Mean observed STB disease was calculated as the average disease of all farms located in a given pixel, pooled for all growing seasons. (b) Model A0, r = 0.623, p < 0.005. (e) Model B1, r = −0.261, p > 0.05. (h) Model B2, r = −0.236, p > 0.05. Mean predicted infection (%) across the spatial scale of model A0. (f,i) Mean predicted STB disease (%) across the spatial scale of models B1 (f) and B2 (i). Values of x and y refer to longitude and latitude, respectively. (a,d,g) n = 179; (b,e,h) n = 22. Growing seasons included in (a,b,d,e,g,h) are winter 2001/summer 2002 to winter 2015/summer 2016. Growing seasons included in (c,f,i) are winter 1990/summer 1991 to winter 2015/summer 2016. Data were log₁₀-transformed prior to statistical analysis to improve fit to the underlying assumptions of Pearson's correlation test.