Reducing the Double-Monod Model to Absurdity

Suppose that we have a medium that has several potentially growth-limiting factors such as P, S, N, C, Mg, etc. They may be needed as PO4, NH4, and the like. If each were at 80 % of the concentration that would give the maximum growth rate, extension of the Double Monod model would predict that the specific growth rate coefficient would be 0.8 multiplied by itself as many times as there were limiting nutirients. This gives a ridiculous result. You can experiment yourself or skip to the table below.

Enter how many nutrients : Enter decimal for fraction of maximum growth rate :

Calculated specific growth rate coefficient =

This table shows how small a number gets when you continue to multiply it by itself. The numbers across the top are for the number of potentially growth-limiting nutrients. The first column is the specific growth rate coefficient for one nutrient.

  
  1    2     3        4           5            6            7              8              9

 .1  .01  .001  .0001  .00001  .000001  .0000001  .000000001 .000000001 
 .2  .04  .008  .0016  .00032  .000064  .0000128  .0000025   .00000051 
 .3  .09  .027  .0081  .00243  .000729  .0002187  .0000656   .00001968 
 .4  .16  .064  .0256  .01024  .004096  .0016384  .0006553   .00026214 
 .5  .25  .125  .0625  .03125  .015625  .0078125  .0039062   .00195312 
 .6  .36  .216  .1296  .07776  .04665   .027993   .016796    .0100777 
 .7  .49  .343  .2401  .16807  .117649  .0823543  .057648    .0403536 
 .8  .64  .512  .4096  .32768  .262144  .2097152  .167772    .1342177 
 .9  .81  .729  .6561  .59049  .531441  .478297   .430467    .3874206
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