A quantitative study of command elements for abdominal positioning behavior in the crayfish Procambarus clarkii

We develop a statistical method to estimate the total number of command elements devoted to abdominal positioning behavior in crayfish. We assumed that all command elements can be identified, that each identified cell is equivalent to a tagged individual in a population, and that the cells were sampled randomly. Samples of 29, 30, 20, and 35 cells from abdominal ganglia A3, A4, A5, and A6, respectively, were taken from our catalog. We characterized each cell using several morphological and physiological criteria, determined how many times each identified cell was present in the sample, and estimated the total number of command elements using both a maximum likelihood method and a modification of the Lincoln index. The larger the proportion of identified cells seen only once in the sample, the more identified cells there were that were unrepresented in the sample. We estimate there are approximately 34, 60, 86, and 98 command elements in ganglia A3, A4, A5, and A6, respectively. Using a slightly different data set we show that the motor output of unipolar cells is more often stronger in the direction of the cell's axonal projection. In bipolar command elements, the output strength was uncorrelated with the relative sizes of the two projecting axons. No two cells in our sample were completely identical, and this morphological variability sometimes made it difficult to determine whether or not two cells obtained from different individuals were the same identified cell. We discuss why caution should be exercised in studies requiring precision in cell identification.