PRIMARY PRODUCTION 529 



3 also gives the corresponding changes predicted by the model for 

 zooplankton and phosphate. This shows how the variability of the 

 light which is partly smoothed in the plant distribution is even 

 further smoothed out in the nutrients and animals so that changes 

 in light contribute very little to their variability. 



From this point of view, zooplankton variability which is such 

 a marked feature, must be thought of as being imposed by the 

 behavior of the animals themselves. It has been shown by Winsor 

 and Clarke (1940) and Barnes (1952) that in temperate waters, 

 the variable distribution of plankton in net hauls tends to be 

 normalized by a logarithmic transformation. Thus, by using their 

 estimate of the variance, it is possible to imitate the patchiness 

 of the herbivores by transformation from a table of random normal 

 deviates, if it is assumed that on each day the value is taken 

 as a random deviation from the value on the previous day. This 

 produces clumped distributions as shown in the two sequences or 

 runs in Fig. 4. Both of these show how the patchiness produces 

 significant depletion of the plant population if the patches remain 

 in contact with the same plant population for about a week. The 

 phosphate curves in Fig. 4 show again that these changes have 

 little effect on the nutrient concentration, so that the chemical 

 sampling would give an impression of uniformity. These plankton 

 changes could be considered as typical of changes occurring at 

 the same time over an area of sea and, as in the earlier example, 

 pairs of values could correspond to pairs of samples collected over 

 this area. Figure 5 gives the plots of these values and demonstrates 

 again that, with conventional sampling, apparent randomness can 

 result from quite well-defined processes. 



These two factors, light and zooplankton patchiness, tend to 

 produce variability in plant distributions. There is a third factor, 

 the lateral mixing of the water, which tends to decrease this 

 variation. To estimate this effect I have used an expression for 

 lateral eddy diffusion from a center derived by Joseph and Send- 

 ner (1958). By assuming that grazing is zero at the center and 

 increases with distance from it, it can be shown that for a given 

 production rate per unit of plant population there is a gradient in 

 plant concentration for which the net growth of the population 



