284 The Ruffed Grouse 



Hill) totaling 777 acres were subjected to artificial control of the 

 grouse population beginning the winter of 1933-34. All but four 

 grouse were collected after the public hunting season. With this 

 beginning, the population was deliberately reduced each successive 

 winter to about half normal survival in order to maintain a breed- 

 ing population well below carrying capacity. 



The productivity rates for 1935, 1936, and 1937, from moderately 

 sparse breeding populations were one hundred per cent, one hun- 

 dred sixteen per cent and one hundred sixty-one per cent compared 

 vdth nineteen per cent, eighty-four per cent and one hundred 

 twenty-five per cent, respectively, on the uncontrolled portion of 

 the survey area in the same periods. Thus, additional evidence sup- 

 ports the contention that as populations approach the range-carry- 

 ing capacity, their productivity declines, and that productivity is 

 higher in breeding populations well below carrying capacity. 



LIFE EQUATION 



In terms of populations, rather than the individual, the life story 

 of tlie grouse tends toward an equation— the population at any given 

 period of the year resulting from a balance of the losses on the one 

 side of the scale and the gains on the other during the preceding 

 year. Actually this yearly circle of events on any given unit of range 

 almost invariably leads to an inequation— with the gains sometimes 

 exceeding the losses and other times the reverse. This equation 

 might be expressed as: BP + MY — AL = BT' where BP — breed- 

 ing population, MY = maturing young, AL = adult losses and BT' 

 = breeding population of the succeeding year. If the yearly changes 

 actually result in a stable population, the equation may be sim- 

 plified to BP = BT' in which case MY = AL. When the population 

 increases from one year to the next, B'P' exceeds BP and hence MY 

 exceeds AL. This condition may be expressed graphically as fol- 

 lows (Fig. 13) for eighteen grouse breeders (nine pairs) producing 

 one hundred eggs. 



Such an inequation cannot long continue. The trend must be 

 toward an actual equation, but oscillating first to one side and 

 then to the other of a true balance. From 1932 through 1941 in 

 New York, the balance has been nearly true. This theoretically true 

 equation is illustrated in Fig. 14, again for nine pairs of breederb 

 producing one hundred eggs. 



