Prospective models are developed for analysing sperm competition data so as to predict the underlying mechanisms determining paternity in multiply mated females. The models require: 1) estimations of proportion of offspring sired by the last male to mate (P2), 2) knowledge of the number of sperm transferred by each male, and 3) knowledge of the sperm storage capacity of the female, should this be limited. They will distinguish between "raffles" (sperm mixing without displacement) and sperm displacement mechanisms. The sensitivity of the techniques can be increased by manipulating the number of sperm transferred by each male. Typically, this can be done by manipulating copula duration or number of ejaculations, given a knowledge of the rate of sperm transfer. Data from two contrasting insect species are fitted to the models to demonstrate the techniques. These models are prospective only, and their limitations are discussed. The principal limitation is that we assume that sperm used for fertilization mix randomly in a "fertilization set" immediately prior to fertilization; in reality this may be difficult to identify. When sperm mixing is very rapid, the fertilization set will often be equivalent to the sperm stores, but with slow mixing, the fertilization set may be equivalent to a much more restricted zone and may change with time.

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Fruit pH, inflection point pH, % acid content at inflection point pH, and % acid content at pH 8.1 were unpredictable based on days from full bloom and were not useful as maturity indices for 3 red strains of ‘Delicious’ or ‘Law Rome’ apple (Malus domestica Borkh.). Soluble solids content of the red strains of ‘Delicious’ could not be predicted consistently. Soluble solids/% acid (SS/A) at pH 8.1 values were the most predictable for all red strains of ‘Delicious’ with apparent optimum fruit quality within the 40 to 50 range index. None of these parameters were reliable for ‘Law Rome’ fruits.

A rearrangement of the Harris et al. equation was used to determine a precise and economical field plan for conducting a randomized complete block muscadine grape cv. and selection trial. An increase in the number of replications decreased the magnitude of the yield differences that are detectable as being significant to a greater extent than did an increase in plot size or number of clones being tested. Relatively little precision was gained by increasing the plot size from 1 to 2 vines and almost nothing was gained by increasing the plot size further to 3 or 4 vines. Muscadine grape yield trials can be conducted most efficiently by using 1-vine plots and 5 or more replications.

Experimental results from horticultural field trials are obscured by the effect of systematic variation. This variation is directly related to the position of the plot in the field and is referred to as a fertility gradient(s). Trend analysis eliminates the effect of fertility gradients by fitting a polynomial regression equation (response surface model) to the systematic variability in the experimental units. Two cultivar trials of potato (Solanum tuberosum L.) conducted to compare results from trend analysis with that using the standard design analysis indicated that fertility gradients existed in the fields and were of a form that could be adequately fitted by a response surface model. A 3-dimensional plot of the response surface model indicated that the fertility gradients formed a very complex surface which could not be eliminated by experimental design. Of the 3 experimental designs used, the Latin square was the most efficient while the completely random was the least efficient. Trend analysis resulted in a large gain in relative efficiency over the standard analyses of completely random and randomized block designs. It also resulted in a substantial gain over that of a Latin square design. Adjusting the means using a response surface model in trend analysis also improved treatment estimates. Tests of significance using adjusted means were more precise and easier to interpret. Trend analysis proved to be the most efficient way to analyze the data, regardless of the experimental design used.