An empirical law describing heterogeneity in the yields of agricultural crops

Abstract

Using data from a blank experiment with wheat it was found that the regression of the logarithms of the variances for plots of different areas on the logarithms of their areas was approximately linear. A graphical review of variances, etc., reported in the literature for thirty-nine other blank experiments indicates that the results of most such experiments conform to the same law.It is shown that the above law can be generalized (so as to be applicable to any size of field) by applying a certain adjustment to the regression coefficient b', so as to give a modified coefficient b applicable to an “infinite” field.From this generalized relationship there has been deduced an expression ((4), p. 16) to indicate average relative efficiencies to be expected for randomized block experiments with varying numbers of plots per block in a field for which the coefficient b is known.A formulae (5), which may be used to estimate the most efficient size of plot for any given experiment, has also been deduced. The cost of using plots of other than the most efficient size is indicated graphically in Fig. 7.

Plot size variation to quantify yield of potato clones

“…Roraima s/n o , Bairro Camobi, 97105-900 Santa Maria-RS; E-mail: dilsonb@smail.ufsm.br; lindolfo@smail.ufsm.br Oliveira, 2005). Yield variation among plots depend upon genetic diversity (Brown, 1987), environmental conditions, inter and intra-plot competition and sampling technique (Smith, 1938;Gomez & Gomez, 1984;Steel et al, 1997).…”

“…The parameters V 1 and b of the empirical relationship VU(x)= V 1 /X b (Smith, 1938) were estimated based upon logarithmic transformation and weighted according to degrees of freedom for each plot size (Steel et al, 1997). V 1 was the variance of one basic unit plots and b the soil heterogeneity index.…”

“…The level of soil heterogeneity affects both plot size and replication number, because of yield variation (Smith, 1938;Hatheway, 1961;Lin & Binns, 1986;Martin et al, 2004; BISOGNIN DA; STORCK L; COSTA LC; BANDINELLI MG. 2006. Plot size variation to quantify yield of potato clones.…”

Towards soil geostatistics

“…However, it is reasonable for the soil scientist to argue that the variables we study are often complex, and cannot be accounted for by the relatively simple models that lie behind the gravimetric form of the Cauchy model, or the models proposed by Whittle [38,39] for diffusion processes. In fact, reflection on the comment by Whittle [39] that the good fit of the diffusion model in three dimensions to the yield data of Fairfield Smith [42] could be explained by the dependence of yield on the concentrations of nutrients that diffuse in the 3-D volume of soil illustrates this. Most soil scientists would not expect diffusion to be a major factor determining their spatial variation at the scales at which we observe variations in crop yield.…”

Optimum plot size and number of replications related to selective precision

“…On the other hand, methodologies and applications to estimate the optimum plot size (SMITH, 1938, MEIER & LESSMAN, 1971LOPES et al, 2005;OLIVEIRA et al, 2006;BRUM et al, 2008) are based on the non-linear relation CV(x)=A/X B , where CV(x) are the variation coefficients for plots planned at different sizes (X), expressed as a number of basic units. The point of maximum curvature (Xo) of the function CV(x)=A/X B is considered to be the optimum plot size (MEIER & LESSMAN, 1971).…”