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2 Simulation of growth

2.1 Competition for maximum yield potential

Logistic growth

Growth of the different species are modelled with sigmoid growth curves where the response variable is dry matter production in tons ha^-1 and the predictor is time in days. The model uses a time step of one day per calculation (dt).

The following equation generates a sigmoid growth curve for each species when it is integrated over time:

Y_t+1 is dry matter production from day t to day t+1.

g is the relative growth rate per day.

Y_t is dry matter production up to time t

Y_max is the maximum achievable biomass production ha^-1 for the species

Y_total is the accumulated biomass produced ha^-1 of all species in the model

Restrictions

Furthermore, each growth function has the restriction that the species stops growing when Y_Total > Y_Max , in order to avoid negative growth. This makes the total biomass produced in the model equal to Y_Max of the species with the highest potential biomass production which in most agricultural systems is the crop.

Yield potential

One question immediately arose: Was it acceptable to have this restriction on the total biomass production of the system? Trenbath (1974) analysed data from 344 mixture experiments and grouped the yield of the mixture into either 1) a yield below the yield of the lowest biomass yielding species to the average yield of the two species in monoculture or 2) a yield from the average of the monocultures to above the yield of the highest biomass yielding species in monoculture. He found that more than 60% of the experiments went into category 2.

To ensure ourselves that this restriction was appropriate for a mixture of crops and weeds, we conducted an experiment in the greenhouse in which we planted oilseed rape or spring barley in monoculture and in mixtures with two weeds.

Experimental methods

Spring barley (Alexis), spring oilseed rape (Global), Stellaria media and Chenopodium album were sown on 8 July 1996 in 0.12 m² pots in the following combinations: A) All species in monoculture. B) spring oilseed rape (Global): Stellaria media: Chenopodium album. C) Spring barley: Stellaria media: Chenopodium album and D) Stellaria media: Chenopodium album. Plant densities species^-1 pot^-1 were for all combinations: Spring barley: 36, spring oilseed rape: 10, Stellaria media: 350 and Chenopodium album: 250. There were 3 replications and 6 harvest times: 24 July, 31 July, 7 August, 14 August, 21 August and 28 August. Fresh weight and dry weight were recorded at all harvest times.

Results

The experiment showed that the crop-weed mixtures had a tendency to over-yield compared to the monocultures. However, this over-yielding in the mixtures was not significantly different from the crop yield in monoculture. This implies that the over-yielding could be explained by random variation in the data.

Conclusion In conclusion, this experiment does not reject the assumption, that yield of the mixtures of crop and weeds is likely to be similar to the yield of the crop in monoculture.

2.2 Growth of crops

The individual growth curves are essentially results of a two parameter function, a growth rate and a maximum biomass. This simplification puts restrains on the possible curves, and consequently they are considered to follow the logistic curve, which is symmetric around the point of inflection. Experimentally obtained growth curves for the crops could be found in the literature. However, usable growth curves were not available for the chosen weeds. Growth curves for the latter were therefore based on a subjective estimate. Crops and volunteers have identical growth parameters, likewise for sensitive and resistant weeds of the same species.

Winter oilseed rape

Dawkins and Almond (1984) conducted an experiment in which they measured the above ground biomass of two winter varieties of oilseed rape over time and the data shown in figure 2.4 are average values of the varieties Elvira and Jet Neuf. The English data show a higher biomass level during the winter time than the model, but otherwise the simulated curve describes the steep part of the growth.

Wheat