392 



POPULATIONS 



has a certain potential, maximal value. 

 When a mortality component is subtracted 

 hom this highest possible rate of reproduc- 

 tion, the difference represents the actual 

 size of the population at that moment. 

 Such a mortality component is under the 

 control of "environmental resistance" 

 (Chapman, 1928), which induces the mor- 

 tality and can be factored into density- 

 independent and density-dependent in- 

 fluences. 



This situation can be restated somewhat 

 as follows: 



Population growth = potential reproduction — 

 environmental resistance. 



This is a highly useful representation, par- 

 ticularly for the mathematician, since it 

 helps him keep a situation already highly 

 complex as simple as possible. H. S. Smith 

 states the case well when, in discussing the 

 reproductive potential concept, he says:** 

 "It seems to me that this is a useful concept 

 even though largely theoretical. If we wish 

 to measure the effect of the environment 

 on populations, is it not easier to work with 

 the interaction of one constant and one 

 variable, than with two variables? I do not 

 see that the concept of a maximum repro- 

 ductive capacity does any great violence 

 to sound biological reasoning even though 

 it is diflBcult to measure." 



To return to Figure 138. Here it can be 

 seen that reproduction is not viewed as a 

 constant of maximal value, and mortality is 

 not treated as a factor that is always in- 

 creased by environmental influence. Rather, 

 it is suggested that both natality and mor- 

 taUty can fluctuate from a high to a low 

 value and that certain environmental and 

 genetic influences affect these rates in 

 either a positive or a negative direction. 

 Population shifts still are explained as a 

 function of birth rate minus death rate. But 

 the focus is placed as much on the varia- 

 bility in reproductive performance as on 

 mortality. While we have no quarrel with 

 the more simplified point of view as a 

 pragmatic device, we do believe that the 

 interplay schematized in the diagram is 

 more in accordance with the evidence and 

 therefore more descriptive of actual popu- 

 lation workings. 



Earlier in this chapter examples were 

 presented that deal with the following as- 

 pects stylized in the diagram. These are: 



** Personal communication. 



1. Density-independent factors favoring 

 population decrease; the contribution of 

 E' to C 



2. Density-independent factors favoring 

 population increase; the contribution ol 

 E to C 



3. Density-dependent factors favoring popu- 

 lation decrease; the contribution of D' 

 to C 



4. Density-dependent factors favoring popu- 

 lation increase; the contribution of D to C 



These require no finrther discussion here. 



What, then, is integration at this infra- 

 social level? Obviously it is the interaction 

 of pressures caused by categories of factors 

 of the type represented in the figure with- 

 out indicating whether they are additive or 

 multiplicative. These pressures are statis- 

 tical in the sense that they arise from 

 group phenomena. A particular pressure 

 grows out of a particular operation. It 

 merges with another that is closely re- 

 lated. These in turn join with others 

 and finally emerge as a pressure such 

 as A or A' that is the product of many 

 factors and performs some major function 

 in the population. These pressures are inte- 

 grated in the sense that, as in an organism, 

 change in one affects another and always 

 results in some compensatory regulation in 

 the system. There is nothing inherently 

 mystical in this statement. If more com- 

 plete data were available about a certain 

 population, it should be possible to express 

 the integration in arithmetical terms. To a 

 great extent we have been able to treat 

 here a problem that is basically quantita- 

 tive in quaUtative terms only. Our inade- 

 quacies probably are related largely to in- 

 complete information rather than to any 

 lack of validity of the population as a bio- 

 logical unit. Perhaps when more data exist 

 we can apply to them a statistical method 

 that takes account of the correlations be- 

 tween factors and evaluates the contribu- 

 tion one factor makes toward a particular 

 response. This is a multiple regression prob- 

 lem and possibly can be analyzed by 

 Wright's (1921) path coeflBcient solution. 

 Even now we might assign arbitrary values 

 to our diagram and obtain a stylized, nu- 

 merical illustration of integration. 



Despite the fact that the population has 

 been discussed in statistical terms, it does 

 not follow that populations are statistical 

 rather than biological units. The fact is that 

 they are both. It is not our purpose to sug- 



