The effect of sample size and data range on the values of the normalization constant.

<p>The normalization constant <i>b</i> was estimated by nonlinear regression for sets of allometric data generated with the function <i>Y = 2r_c^1.5X^0.75</i> , where <i>2r_c^1.5</i> = <i>b</i> and where random variation was added to both <i>Y</i> and <i>X</i>. Nonlinear regression was then used to estimate the value of <i>b</i> from the data generated either by assuming a constant exponent <i>a</i> = 0.75 (<i>b</i>_{a = 0.75}) or by allowing the value of <i>a</i> to be estimated by regression (producing <i>b</i>_{a = estimated}). For each value of <i>r_c</i>, the graphs show 600 instances of normalization constants estimated using data with either N = 20 or N = 120, and with a range approaching 3-fold, 10-fold or 25-fold differences in the values of <i>X</i>. Each instance is shown as a ‘+’ sign.