The study consisted of two experimental works. The f irst experiment, based on sown plots, was aimed to develop the model. The second one, performed in two commercial cereal fields located in climatically contrasting North and South Spain, was intended to validate it.

 

Experiment in sown plots: model development

A controlled experiment was conducted in an experimental field at La Rábida Campus of the University of Huelva, in Huelva Province, Andalusia, south-western Spain (37º12ʹ10''N, 6º55ʹ05''W). Mature caryopses of P. brachystachys (hereafter seeds) were collected in June 2006 from a wheat field near Huelva, and stored in airtight containers at 4°C until needed. Ten 25 × 25 cm plots were randomly established and the soil up to 5 cm deep was replaced by a substrate. The substrate was a mixture of 50% Kekkilä garden peat, 25% sand, and 25% local sandy clay soil. After autoclave sterilization to suppress viability of existing seeds, the volume of substrate to be added to each plot was thoroughly mixed with 200 seeds of P. brachystachys and placed on topsoil on 27th November 2007. Seed losses to soil surface-foraging predators were prevented by placing 2-mm mesh nets over 0.4 m diameter, 0.1 m height PVC fences placed encircling the plots. An additional, similarly arranged plot with substrate lacking seeds was established to support sensors connected to a datalogger set to record at hourly intervals temperature (Hobo TMC6-HD, Onset Computer Corp., USA) and electrical conductivity (Hobo EC-20, 20-cm length blade) at 5 cm depth. Numbers of emerged seedlings were recorded and thereafter removed at weekly intervals, from sowing until end of seedling emergence (mid-April).

 

Experiments in commercial cereal fields: model validation

Seedling emergence was monitored in two climatically contrasting commercial wheat fields with clay-rich soils located c. 780 km apart, in South and North Spain. The southern field (durum wheat cv. 'Amilcar'), was located in Huelva (37º 18' N, 6º 55'W; 17 m a.s.l.) and sampled in the 2007-2008 season. The climate is typically Mediterranean, with a mean annual temperature of 16.6 °C and mean annual rainfall of 555 mm, mainly distributed between October and April. The crop season of winter cereals in the southern area encompasses from late November-early December (crop sowing) to late May-June (crop harvest). The northern field (bread wheat cv. 'Berdun') was located in Arazuri, Navarra, (42º 49’ N, 1º 43’ W; 395 m a.s.l.) and sampled in the 2006-2007 season. The climate is temperate with cool summers with abundant rainfall. The mean annual temperature is 12.3 °C and the mean annual rainfall is 750 mm. In this area cereal sowing takes place in October and harvest occurs in July. In both fields, emergence data were collected weekly, from crop sowing until the end of seedling emergence by mid-April, from 20 randomly distributed 50 × 50 cm permanent quadrats.

 

The calculation of hydrothermal time

Climatic variables were obtained from meteorological stations located less than 10 km from the commercial fields. Soil temperature (T; ºC) and water potential (ψ; MPa) at 5 cm depth were estimated using the STM2 software (Spokas & Forcella, 2009) and used to calculate the HT accumulated in soil in day t, HT(t), using the following equation (Schutte et al., 2008):

 

H(t) = 1 when the actual water potential at day t, ψ(t), is larger than or equal to the base water potential (ψb), i.e. the highest value of soil water potential that prevents germination of P. brachystachys seeds, otherwise H(t) = 0, and

 

where T(t) is the average soil temperature at day t and Tb the base temperature for seed germination. Cumulative hydrothermal time (CHT) starting at crop sowing up to day n is defined as follows:

 

For P. brachystachys, Tb = 0.8 °C and ψb =−1.50 MPa (M. J. Sánchez del Arco, pers. comm.).

 

 

Model development and evaluation

Cumulative seedling emergence (C) in response to CHT was modeled by the Logistic function (Gonzalez-Andujar et al., 2016a),

 

where K is the maximum emergence predicted by the mo-del, b is the rate of increase in the emergence, M is cumu-lative HT at the point of inflection (50% emergence).

Model performance was assessed by calculating the root mean-square error (RMSE), sum of the residuals (SRES) and sum of the absolute residuals (SARES). In conjunction, they are useful measures for estimating va-riation and bias in a model. These measures are defined by the following equations:

 

where xi and yi represent observed and predicted cumu-lative percentage seedling emergence, respectively; ABS is absolute value of the number within parentheses and n is the number of observations. A small RMSE value suggests close agreement between simulated and obser-ved values. The SRES and SARES expressions are use-ful in determining how errors in the model cancel out. If SRES is small compared to SARES, errors in the model will tend to cancel out. If SRES and SARES are large and SRES is positive, the model tends to underestimate the observed value. However, if SRES is negative and lar-ge in comparison to SARES then the model will tend to overestimate the observed value. Model parameters were estimated by nonlinear least-squares regression using the Marquard-Levenberg algorithm in SigmaPlot v.11 (Systat Software, Inc). Multiple initial values were used to ensure that the solution was global rather than local.

For model validation, we compared the models’ esti-mates of cumulative emergence against the independent data set obtained in the experiments under commercial field conditions. Prediction accuracy was evaluated by the coefficient of determination (R2) of the linear regres-sion of predicted against observed cumulative seedling emergence.