Model implementation: mathematical representation and parameterisation of

component models

After providing the agronomic context against which the weed population is developing, the proceeding sections relate to the biological processes within the lifecycle of an annual weed. Each section contains a brief overview of the key factors that need to be modelled, the mathematical representation of the processes and is completed with the parameterisation. Component input sources are either set by the weed management scenarios (e.g. crop rotation length is 4 years), by species-specific parameters or parameter files embedded in the component or by other components.

2.5.1

Nomenclature

ECOSEDYN distinguishes state, rate and driving variables (Rabbinge and de Wit, 1989). The state variables represent a quantitative measure at any given time of the population characteristic that is modelled, in this case numbers of seeds (S), pre- emerged seedlings (G), plants (P) and the weight of plants (W). Subscripts are used to identify the status and position of seeds (S) in the soil and the size-cohorts of plants (P); e.g. the total amount of seeds in the surface layer is indicated by Stot-1, and the

number of emerged seedlings until the 2nd true leaf stage is represented by P1

Driving variables are environmental variables that regulate important processes; e.g. plant growth is regulated by solar radiation and temperature, seed germination by temperature and soil moisture. They will be indicated with capital letters (e.g. effective day-degrees, EDD).

. To acknowledge that weed seedlings are separated into different weed cohorts and that within a crop different habitats are characterised, the notation for plants and seeds will be followed by the characteristic ‘c’ and/or ‘h’ between brackets whenever required.

A year in ECOSEDYN runs for 365 simulation days (no leap years) from the 1st of October to the end of September to accommodate the farming activities associated with growing winter wheat, which is sown in October and harvested in August the next year. A random simulation day is represented by dsim whereas specific days such

2.5.2

Dormancy evolution

2.5.2.1 Background

Only recently have researchers started to include dormancy in models of population dynamics. One of the reasons is that the factors influencing the dormancy status of seeds pre- and post dispersal are not fully understood for most species. The dormancy status is not simply a binary condition but rather is measured on a continuous scale; the temperature range over which germination can occur increases during dormancy release and reduces during dormancy induction (Vleeshouwers et al., 1995; Baskin and Baskin, 2006). An essential feature of dormancy is that it prevents a viable seed from germinating even if the actual environmental conditions (temperature, soil moisture) would allow successful germination. For some species, germination may be restricted more by environmental conditions rather than internal conditions. Although this model aimed to have a generic purpose, without the detailed data it was impossible to create a generic component for dormancy. Instead species-specific accounts of the biology were created and implemented into simple mathematical equations.

In representing dormancy in ECOSEDYN, the intent was not to represent the relevant processes at the mechanistic level, e.g. factors that control phytochrome changes in seeds which cause the seeds to be more or less sensitive to light (Hartmann et al., 2005). However, key aspects that impact on the probability of germination were implemented to reflect their importance. Neither S. media nor T. inodorum displays an annual dormancy cycle but rather a decrease in dormancy over time.

A recent review on the outcome of day-time as compared to night-time cultivations showed that, although the results are very variable, S. media and T. inodorum belong to a small subset of species where germination is more often than not reduced by night-time cultivations (Juroszek and Gerhards, 2004). Seeds of both species display temporally variable levels of light requirement, a manifestation of dormancy. Whereas the ability to germinate in light relates to seeds located in the top surface layer, a flash of light as received during cultivation can trigger germination at any depth. The ability to germinate after so-called short duration light exposure (SDLE) is included as well to account for germination after cultivation.

In the species account of S. media below the parts of the review that address the implementation of the principles, based on findings of the literature as discussed in the preceding part of the text, are indented for clarity.

2.5.2.2 Species specific parameterisation: S. media

The germinability of seeds from S. media is determined by two processes and both act upon young seeds only: an afterripening requirement to germinate and cold stratification that can either reduce or enhance germination in dark or light.

Many studies have shown that fresh seeds of Stellaria media are primary dormant (Roberts and Lockett, 1975; Baskin and Baskin, 1976; van der Vegte, 1978; Froud Williams et al., 1984; Grundy, 1997). When tested over a range of temperatures, fresh seeds collected in May, June or October did not germinate in dark and a maximum of 5% germinated in light (Roberts and Lockett, 1975). Grundy (1997) found that after 6 weeks of dry storage at laboratory temperatures only 40% of seeds germinated. After 5 weeks of storage at room temperature followed by 8 months of cold storage (over which the percentage germination did not change) 95% of fresh seeds germinated both in light and dark (Noronha et al., 1997).

Afterripening

Wesson and Wareing (1969) noticed some inhibition of germination in 1 month old seeds germinated in light (≈25%) as compared to dark (≈40%) and the same response can be observed in seeds from two of the three populations in the study by Milberg and Andersson (1998); percentage germination in dark / light was 51 / 38, 29 / 18, and 98 / 97 respectively after 7 weeks of dry storage. Population variability and seasonal differences are likely to play a role in the germinability (capacity to germinate) of fresh seeds. Perhaps populations differ in the rate with which they afterripen and growing plants from different populations in a common environment could shed light on this issue. Interestingly, in both populations where germination was high (afterripening completed) (Noronha et al., 1997; Milberg and Andersson, 1998) there was no appreciable difference between germination in light and dark. It is assumed therefore that the inhibition to germinate in light is alleviated once afterripening is completed.

Roberts and Lockett (1975) showed that afterripening was complete after 14 weeks for seeds shed and buried in May and June but not for those in October. Baskin and Baskin (1976; 1986) showed that there is a clear relationship between temperature and afterripening; high temperatures increase the rate and extent of afterripening but below 10 ˚C afterripening was inhibited.

afterripening requires a certain ‘heat sum’, the accumulated day degrees above a base temperature of 10.0 ˚C. It was further assumed that dormancy loss is a linear function of accumulated day degrees.

Roberts and Lockett (1975) tested germinability of seeds after 4 and 14 weeks of burial; after 4 weeks, only about 50% seeds germinated but after 14 weeks all seeds germinated over a broad range of temperatures. Quite possibly afterripening was already completed earlier.

It was assumed that the minimum period in which the heatsum could be reached was after 9 weeks. The interval that spans the period with highest temperatures in England roughly starts the 1st

To account for the initial inhibition of germination in light, separate equations for the proportion of the population that can germinate in dark and light were generated, approximately reflecting the results as observed by Milberg and Andersson (1998) and Wesson and Wareing (1969); 20% and 5% of freshly shed seeds can germinate in dark and light respectively and this increases to a maximum of 95%, the rate a function of accumulated DD.

of July. The number of accumulated day-degrees above 10.0 ˚C over the 9 weeks was determined for each of the 17 weather years used for the climate scenarios (see Chapter 5, Section 5.3). The average value (471 DD) was then calculated and this taken as the reference heatsum to complete afterripening.

Van der Vegte (1978) showed that fresh seeds from plants grown at 7 ˚C had higher dormancy than seeds grown at 20 ˚C which suggests that the temperature whilst seeds are still on the motherplant contributes to the heatsum as well.

Therefore the heatsum should be initiated two weeks before seed shedding (i.e. the heatsum is initiated on the day of seed shedding as the accumulated heatsum over the previous two weeks). The linear functions of the germinability of seeds in dark and light against accumulated degrees then become: