Water availability shifts the optimal temperatures for seed germination: A modelling approach
Introduction
The timing of important life history events may have large fitness consequences for most species (Miller-Rushing et al., 2010). In plants, germination timing is one of those important events in determining the future suitability of environment for seedling growth and survival (Fenner and Thompson, 2005). Seed germination is largely regulated by temperature and water content of the seedbed (see chapter 7 in Bewley et al., 2013). Hence the hydrothermal time model (HTT) has been used widely to describe the dynamics of seed germination in response to water potential Ψ and temperature. In the basic version of the HTT model, germination time is proportionally related to the magnitude of water potential (Ψ) and temperature (T) above two thresholds, namely base water potential Ψb (in MPa) and base temperature Tb (in °C) where, at or below these thresholds, no germination will occur (Gummerson, 1986, Bradford, 2002):where θHT is the hydrothermal time (MPa °C h or MPa °C d) and t(g) is the time to reach a given seed germination fraction g (in h or d). While θHT and Tb are assumed constant for all seeds, i.e. g fractions, in the population (Gummerson, 1986), the variation in time for any fraction of the seed population to germinate is determined by seed-to-seed variability in Ψb (shown by subscript g as Ψb(g)), which has almost always been assumed to follow a Normal distribution with mean Ψb(50) and standard deviation σΨb (Bradford, 1990, Gummerson, 1986). As θHT is a constant, increasing the ambient water potential (i.e. Ψ approaching 0 MPa) or temperature, above their respective Ψb(g) and Tb thresholds, will reduce time to germination, t(g). The model further assumes that parameters Tb and Ψb(g) are independent of water and temperature respectively.
The model has been applied successfully at suboptimal temperatures to predict the time course of germination for a wide range of species (e.g. Kochy and Tielborger 2007). Model inadequacy, however, has been reported because of the violation of some assumptions, particularly when making predictions at super-optimal temperatures. For example, Kebreab and Murdoch (1999) reported an interaction between temperature and water, such that Ψb(g) and Tb changed systematically in response to temperature and water potential respectively. Similarly, an interacting effect of water and temperature was found by Larsen et al. (2004) to reduce the ability of the hydrothermal time model to predict germination of three grass species. To make the model applicable to the super-optimal range, Alvarado and Bradford (2002) modified Eq. (1) by linearly adjusting Ψb(g) to higher values as temperature increased above the optimal temperature To (the T at which germination is fastest), and by not continuing to accumulate thermal time over the range of supra-optimal temperatures. This model, however, makes a number of assumptions which may not be necessarily true: (1) the shift in Ψb(g) to higher values only happens when T exceed To, (2) To is constant among seed fractions and across water potentials which would give a triangle shape when germination rate (GR) is plotted against T (To occurs at the convergence of two straight lines), and (3) Ψb(g) follows a Normal distribution as does the ceiling temperature Tc (the T at or above which germination is inhibited).
A modified version of this approach was therefore suggested by Rowse and Finch-Savage (2003) to model seed germination in cases where there is a curved relationship between GR and T around To. Their model also accounts for the variation in To amongst seeds within the population. These features were accommodated by allowing Ψb(g) to increase linearly as T exceeds a temperature threshold known as Td (sensu Rowse and Finch-Savage, 2003), which is near but below To, as well as accumulating thermal time when T > To. A review by Watt and Bloomberg (2012) supports some assumptions of this model where for most species the relationship between GR and T was curvilinear and To varied discernibly among percentiles (g). However, neither of the above studies, nor their alternative versions (e.g. Bloomberg et al., 2009, Hardegree et al., 2015) has provided a closed analytical solution for calculating To (and Tc), quantifying their variability among seed sub-populations or their changes in response to the availability of water. Most studies report To values for seeds germinating under moist conditions (Ψ ≈ 0 MPa), but how the water availability can affect To has largely been overlooked and not quantified. In addition, most modelling approaches have also assumed a Normal distribution for variation in Ψb(g) with most emphasis being paid to changes in Ψb(g) over the super-optimal range. However, Watt et al. (2010) reported that the use of the Normal distribution in their hydrothermal model temperatures provided less accurate and more biased estimates of Ψb(g) and germination dynamics than when using the Weibull distribution. Similarly, our evaluation of eight distributions on four plant species concluded that the Normal distribution can be the worst candidate to be used in the hydrotime analysis of seed germination, and in most cases a log-logistic distribution provided better fits (Mesgaran et al., 2013).
The objectives of this paper were therefore: 1) to develop a HTT model that will work at both sub- and super-optimal temperature ranges by considering the thermoinhibition of germination at high temperatures; 2) to provide mathematical solutions for the estimation of cardinal temperatures, as affected by water potential; and 3) to determine whether there any systematic changes in cardinal temperatures with water availability and subpopulations.
Section snippets
Material and methods
Our model was developed in an interactive way, starting with a log-logistic version of the hydrotime model that quantifies the germination response to water potential alone (Mesgaran et al., 2013). This hydrotime model was then fitted to cumulative germination data of two weed species at each of six temperatures individually. Next, those parameter estimates from the hydrotime model that were clearly temperature-dependent were used to upgrade the model to account for both temperature and water
Results
For both species the log-logistic hydrotime model (Eq. (5)) provided better fits to data for most single temperatures tested (see Tables 1s and 2s, Supplementary materials). For both species there were clear trends in responses of Ψb(50) (i.e. μ + σ) and θH to temperature but not for other parameters. Parameter Ψb(50) increased linearly and approached zero with increase in temperature (Fig. 1A,B) while the response of θH was nonlinear and almost leveled off at higher temperatures (Fig. 1C,D).
The
Discussion
The HTT models developed in this paper gave a good description of the germination dynamics of both species in response to temperature over sub- and super-optimal ranges at various water potentials. We also provided mathematical closed solutions to the problem of calculating cardinal temperatures within a hydrothermal time modelling framework; this has not been addressed previously. The modelling approach we introduced in this paper not only inherited the useful attributes of previous models
Acknowledgements
MBM was supported by a University of Melbourne John McKenzie Fellowship and appreciates Sara Ohadi and Ahmad Zare for their assistance with lab work.
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