Seed set model development

Photothermal time models integrate temperature and photoperiod information over time using a function such as the one below (Borthwick et al., 1943; Thomas and Raper, 1976).

Photothermal model of seed development rate over time x, is integrated from the point of bolting a, up to the point of first seed maturity, b. This permits the calculation of T_h, the total thermal time experience required to achieve the production of mature seeds. In variable environments, it is necessary to approximate the above integral with a summation of the function over discrete time intervals. The summation function becomes as follows:

where θ(t) is the thermal time accumulated at time t, and T_h is the cumulative total between bolting at t = 1, and seed maturity t = n. If T_h is known in advance, this concept can be used to determine the value of n, and hence the time required to produce mature seeds in any particular environment. To develop the best model of developmental rates of Col-0 seed set was measured in multiple temperature regimes (Figure 1) and photoperiod regimes (Figure 1—figure supplement 1). The thermal time model was as follows:

where θ(t) is the number of thermal time units accumulating during the hour beginning at time t, T(t) is the average temperature during hour t, and Tb is the genotype-specific base temperature. We also compared a photothermal time model:

where θ(t) is the number of photothermal time units for the hour beginning at time t, T(t) is the average temperature (°C) during the time interval, and Tb is the base temperature, which is a genotype-specific constant. P(t) is a measure of daylight.

In order to parameterise the models seed was set under laboratory conditions at a range of temperatures between 8°C and 25°C, and at photoperiods between 8 hr light periods and 16 hr light periods (Figure 1A). Optimal parameters were calculated using the fit function of MATLAB. The performance of each model was evaluated by comparing the predictions of seed development times with nine independent recorded seed development times in the field. These data were collected between October 2011 and July 2013 and closely matched the predictions for each model. The photothermal model (R² = 0.28) did not outperform the simple thermal time model (R² = 0.42): therefore, we elected to use a simple thermal time model of Arabidopsis seed set (Figure 1).