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Neil S. Mattson, Elizabeth M. Lamb, Brian Eshenaur, and John Sanderson

greenhouse insects and diseases from living specimens, or being able to practice water and media sample testing. In response, our team developed a hands-on workshop model for educational sessions that we termed Integrated Pest Management In-Depth. The

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Paul R. Fisher, Jinsheng Huang, and William R. Argo

Limestone is incorporated into horticultural substrates to neutralize substrate acidity, increase pH buffering capacity, and provide calcium and magnesium. Limestones differ in their rate of pH change, equilibrium pH, and proportion of unreacted “residual”? lime. In horticulture, lime reactivity is currently measured empirically in batch tests, whereby limestone is incorporated into a batch of substrate and pH change is measured over time. Our objective was to develop a quantitative model to describe reaction of lime over time. The lime reaction model predicts the substrate-pH based on lime acid neutralizing capacity, lime type (calcitic, dolomitic, or hydrated), lime particle size distribution, application concentration, and the non-limed pH and neutralizing requirement (buffering) of the substrate. Residual lime is calculated as the proportion of lime remaining following gradual neutralization of the substrate acidity (by subtraction of reacted lime from total applied lime).

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Meriam G. Karlsson and Royal D. Heins

The relative progression of lateral shoot elongation from pinch to flower of chrysanthemum [Dendranthema grandiflora (Ramat.) Kitamura `Bright Golden Anne'] plants grown under 2 to 22 mol·day-1·m-2 photosynthetic photon flux and 10 to 20C was modeled using Richards function. Parameters for the function were determined by first transforming data of shoot length and time from pinch (start of short photoperiods) to flower to a relative scale of 0.0 to 1.0 by dividing all intermediate shoot lengths and measurement dates by final shoot length and number of days to flower, respectively. Data used for parameter estimation originated with plants grown at a daily average of ≤20C, since those grown at a daily average above 20C exhibited delayed morphological flower induction and reached 50% of the final shoot length earlier in development. Relative shoot elongation was described by Richards function in the following form: Relative shoot length = SF × {1 + [(SF/SO)N-1] e-SF Kt}-1/N where t (relative time) = 0.0 to 1.0, SF (maximum relative shoot length) = 1.018, SO (relative shoot length at t = o) = 0.0131, N (model parameter related to the shape of the curve) =0.3923, and K (model parameter related to mean relative growth rate) = 5.8138.

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William Terry Kelley

Statistical analysis of agricultural research has traditionally been via the use of fixed model methods. However, recent advances in statistical software have made analysts through random or mixed model methods more practical. Errant or inappropriate use of statistical programs to analyze data has been a recurring problem in the reporting of agricultural research findings. Often variables are all considered to be fixed in order to facilitate analysis, when in reality some variables in field research are nearly always random. Proper selection of error terms and calculation of standard errors are also frequently done incorrectly when statistical analysts packages are not used correctly. Unbalanced data is also quite normal in field research due to unforseen circumstances that result in lost information. Most of these situations can be more early handled with a mixed model approach. In this work, a broccoli field trial involving tillage and planting dates was analyzed using the General Smear Models procedure in SAS and the General Elmer Mixed Models Procedure in GLMM. Comparison of the analyses revealed that conclusions would differ somewhat with balanced data and even more with unbalanced data. Since variance components from all random effects are used to calculate standard errors in GLMM, standard errors in the mixed model were larger, but likely more accurate Inference space was also broader and allowed prediction space to include the entire population of experimental units which were sampled in the experiment. The mixed model procedure was more efficient and thus more sensitive to differences in treatments.

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James E. Faust and Royal D. Heins

The effects of temperature and irradiance on flower initiation and development were quantified to provide a basis for an inflorescence development model. The percentage of leaf axils forming an inflorescence increased as the daily integrated PPF increased from 1 to 4 mol m-2 d-1, while the rate of inflorescence development was a linear function of temperature from 18 to 26C. The appearance of a visible flower bud in the leaf axil was correlated with leaf blade length of the subtending leaf. Mathematical functions were used to describe leaf blade length at the time of visible flower bud as a function of temperature and irradiance, and also to describe the influence of temperature on the rate of leaf extension. The time of visible flower bud in the leaf axil was then predicted by measuring the current length of the subtending leaf blade and estimating the time required for the leaf blade to extend to the length required for visible flower bud appearance. A phasic development scale was used to describe the developmental status of an inflorescence from visible flower bud to anthesis. A model was then created which predicted time to anthesis based upon temperature and the current stage of inflorescence development.

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Alan N. Lakso and Michael D. White

Several models of apple tree carbon balance have been developed, including a simplified model by our lab. Tree photosynthesis and total dry matter production is the best characterized except for root growth and root respiration. Once dry matter is produced and partitioned to the different organs (another key problem for modeling), the effects of carbon availability to the fruits on their growth and abscission needs to be modeled. Our approach is based on an observed relationship between increased abscission with decreased fruit growth rate of populations of fruit. From several empirical studies of fruit growth and abscission during chemical thinning or imposed stress early in the season, a relationship was found between % abscission and classes of fruit growth rates. It appears to be best if the fruit growth rate is expressed as a percent of the growth rate of the fastest growing group of fruits in each study. Thus in the model the fruit growth allowed by the available carbon each day is compared to a pre-determined maximum growth rate for the cultivar. The percent-of-maximum growth rate then determines how much abscission will occur. Then the growth rate of the remaining fruit is calculated. Additional parameters of the model allowed for a multiple-day buffer of carbon availability, an imposed fruit number reduction (i.e. equivalent to hand thinning), and temperature effects. Although there are more improvements planned, the initial tests have been promising with the simulations showing realistic patterns of fruit abscission and fruit growth.

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Dewayne L. Ingram, Charles R. Hall, and Joshua Knight

Euphorbia pulcherrima (poinsettia) annually ( USDA-NASS, 2016 ). This model enterprise grew ≈32,000 pots in 2015; they were sold at an average price of $4.94 if grown in pots 12.7-cm or larger ($2.14 for those grown in pots smaller than 5 inches). Profit

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Paul R. Fisher, William R. Argo, and John A. Biernbaum

the WSF effect on substrate pH could be modeled based on the concentration of different N forms (NH 4 + , NO 3 – , or urea) despite a wide range in concentration of other ions. By analyzing the observed pH change for impatiens, petunia, and pelargonium

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Fan-Hsuan Yang, David R. Bryla, and R. Troy Peters

plants and fruit ( Cellier et al., 1993 ; Monteith and Unsworth, 2013 ; Saudreau et al., 2009 ). To estimate blueberry temperatures more effectively according to local environmental conditions, mathematical models based on energy balance are an option

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K.J. Boote and N.B. Pickering

. Goudriaan for their excellent suggestions for adapting the sunlit leaf area index approach for hedgerow canopies. We thank J. Norman for his advice on the model and E.B. Blazey and G. Bourgeois for their assistance with photosynthesis measurements. The cost