266 



POPULATIONS 



closely interacting system* wliich can be 

 studied and expressed with some quantita- 

 tive rigor (p. 368). 



Populations can be thought of both in 

 the absolute and the relative sense. An ab- 

 solute population is merely a count of indi- 

 viduals stated in integers. Relative state- 

 ments of population are more meaningful 

 in that they include information not pres- 

 ent in an absolute statement. Under rela- 

 tive statements we recognize space-relative 

 and time-relative statements. 



1. Space-Relative Population. This is the 

 number of organisms per unit of space they 

 occupy. It is necessarily a positive number, 

 but it may be a fraction. This is commonly 

 called "density of population" and will be 

 so designated hereafter. The spatial unit 

 may be any suitable measure. It varies both 

 with the organism studied and the judgment 

 of the investigator. Thus, in human popula- 

 tions one meets such units as square miles, 

 acres, cubic feet, beds, and so on, all of 

 which are meaningful when judiciously 

 used. In studies with tlie flour beetle. Tribo- 

 lium, the favored unit is a gram of flour, 

 i.e., beetles per gram. In protozoan studies 

 the cubic centimeter of culture fluid is a 

 standard of reference. The generalized def- 

 inition of a space-relative population is 



per cent of population." This is defined as 

 follows: 



p 



D = i- or 

 A 



Density = 



CAbsolute number of organisms in an area) 

 (Number of spatial units in that area) 



2. Time -Relative Population. This can be 

 defined in one form as the diflFerence be- 

 tween the numbers of a population at a 

 particular date, T2, and an earlier date, Ti, 

 relative to the absolute number at the ear- 

 lier date, Ti, and averaged to some appro- 

 priate figure of time.f In human popula- 

 tions for which such indices are best devel- 

 oped, time-relative populations are some- 

 times denoted in such a form that they 

 may be called "mean annual growth rates 



* Examples of such interactions on a mixed 

 species level are predator-prey relationships; 

 host-parasite relationships; several species com- 

 peting for a common food supply, and so on. 



-j- There are, of course, other ways to state 

 this, but this definition seems simple and 

 eirithmetically effective. One of us heard the 

 definition in an impublished lectiu'e given by 

 the late Raymond Pearl. We are also indebted 

 to this lecture for several other ideas expressed 

 in this chapter. 



M.A.G.R. % = 



100(P2 - Pi) 

 Pi(T2 - Ti)' 



where Pi is the population size at date Ti; 

 and P2 the population size at the later date, 

 T2. M.A.G.R. may be either a positive or a 

 negative number. It measures the annual 

 (or other) average rate of change in size 

 of a population within a defined time inter- 

 val, relative to the initial magnitude of the 

 changing population. For this rate to have 

 precise meaning the duration of the time 

 interval must be stated. For example, sup- 

 pose a specified population of 576,872 

 individuals in 1920 increased to 834,964 

 individuals in 1930; what is M.A.G.R.? 

 Substituting in the formula 



100(834,964 - 576,872) 

 (576,872) (10) 



= 4.47% 



This means that on the average the popu- 

 ladon increased 4.47 per cent over its initial 

 size each year for ten years. This is purely 

 an arithmetical, empirical description of the 

 growth process. But it does have some use- 

 fulness as an index. 



Methods 



The Determination of Population SIt^.' 

 It is immediately apparent that, since the 

 population problem revolves around the 

 question of enumeration, the techniques 

 employed in this enumeration are of vital 

 importance, and require brief mention even 

 in a book devoted to principles, whenever 

 the understanding of a technique is relevant 

 to the evaluation of a principle. In this sec- 

 tion we review many of the various ways 

 that population size is determined without 

 any detailed description of the methods 

 themselves. There seem to be seven major 

 methods in common use. These are: 



" Animal abundance is usually assayed and 

 reported in terms of the number of individual 

 organisms per unit area or volume. Sometimes 

 it is only possible and in fact desirable to 

 index abundance in terms of weight. This is 

 typically referred to as "biomass" ( live weight ) 

 and has been used most extensively by stu- 

 dents of insect, plankton, and fish populations. 

 Various definitions of biomass appear in a 

 paper by Elton (1932), and applications of 

 these definitions to ant populations are dis- 

 cussed by Pickles ( 1938). 



