Research has shown plants growing in even-aged pure stands of a single species are subject to a maximum size-density relationship. The relationship between average plant size and stand density is bounded asymptotically by the -3/2 power rule:

s = a r ^-3/2

where s = plant size, a = a constant and r = stand density. This can also be written as:

ln s = ln a - 3/2 ln r .

The second equation can be solved by least squares regression analysis.

Another way of stating the relationship is that plants grow until they reach a certain size for a given density before mortality begins to occur; provided mortality occurs remaining plants can continue to increase in size. Without mortality the plants can not grow larger than a certain size for a given density. Thus all plants show a maximum size-density relationship.

Experiment. Tomato plants were grown in a greenhouse at original densities of 1, 3, 10, 30 and 100 per pot. After 10 weeks the plants were harvested to determine the final density and average plant size. They were measured for oven dry weight after 48 h at 70 ° C. Plant size was plotted against plant density and the slope of the maximum size-density relationship determined.

Report. Prepare a report that shows the graph of the data and the line representing the maximum size-density relationship for tomato. The graph should be done with log-transformed data on arithmetic graph paper. Show all the data points from the class. In addition show a line with the slope of –1.5.

1. What appears to be the slope of the maximum size-density line? Why is the slope different from –1.5? How large would a tomato plant at the lowest density have to grow to achieve this slope?
2. Why does mortality occur?
3. What is an appropriate density at which to grow a stand of tomatoes or trees, the line of imminent mortality or lower? Explain your answer.
4. How can the size density relationship be used to manage stands of trees or other vegetation?