386 



POPLJLATIONS 



populations of the knapweed gallfly (Urop- 

 hora jaceana), identified density-independ- 

 ent and density-dependent sources of 

 mortality, and demonstrated that, in gen- 

 eral, his findings gave good agreement with 

 predictions expected from application of the 

 Nicholson-Bailey equations. This paper is 

 particularly useful in that it presents a fresh 

 approach by which populations in the field 

 can be studied. 



Frequently throughout this section we 

 have mentioned the findings of students 

 whose interest, in part at least, lay in the 

 relation of mathematical models to the ob- 

 served facts of population ecology. It 

 seems appropriate to include here a state- 

 ment about such theoretical approaches. 

 This logically falls at the end of a section 

 devoted to host-parasite interactions be- 

 cause much of the work has been done in 

 this field. 



It is only fair to remark that not all 

 workers concerned with population prob- 

 lems of ecological character are convinced 

 of the value of such models as aids in the 

 interpretation of population phenomena. 

 The diversity of opinion on this topic ap- 

 pears to range from those who think this 

 approach almost omniscient to those who 

 feel that it contributes practically nothing. 

 Since this issue is both interesting in its 

 own right and since it is not possible to 

 predict future trends at this time, it is de- 

 sirable to summarize in quotation form 

 certain considered viewpoints expressed by 

 various specialists. 



Thus Thompson (1939), a recognized 

 theoretician, states: "This is not to say 

 that the mathematical theories of popu- 

 lations are useless. They enable us to see 

 clearly how one quantity varies in func- 

 tion of others, under certain definite con- 

 ditions. They may suggest and have 

 already suggested experimental investiga- 

 tions and field studies from which very 

 valuable information is derived. But they 

 do not, and cannot, provide rules for prac- 

 tical operations, and they are not in any 

 degree a substitute for the investigation of 

 nature." 



Salt (1936), in a concluding sentence 

 to the experimental study discussed earlier 

 (p. 384), expresses himself in a skeptical 

 way: "To this extent the group of numeri- 

 cally important and quantitatively unpre- 

 dictable results exhibited in these experi- 

 ments should give pause to those who still 



think to solve the problems of parasite and 

 host relations on paper by mathematical 

 speculation." 



A pleasingly optimistic view is expressed 

 by Elton (1936) in these words: "At the 

 moment ingenious mathematical speculation 

 as to what ought to happen in animal pop- 

 ulations has somewhat outrun the supply 

 of facts about what actually does happen; 

 but when every allowance has been made 

 for this discrepancy between fact and 

 theory, we already know enough to say 

 that the future of this branch of animal 

 ecology will be quite as lustrous as the past 

 of astronomy." 



Gause (1934) adopts with "complete 

 accord" the balanced judgment of Allee 

 (1934a), whom he quotes as follows: 



"Mathematical treatment of population prob- 

 lems is necessary and helpful, particularly in 

 that it permits the logical arrangement of facts 

 and abbreviates their expression by the use 

 of a sort of universal shorthand, but the 

 arrangement and statement may lead to error, 

 since for the sake of brevity and to avoid 

 cumbersome expressions, variables are omitted 

 and assumptions made in the mathematical 

 analyses which are not justified by the bio- 

 logical data. Certainly there is room for the 

 mathematical attack on population problems, 

 but there is also continued need for attack 

 along the lines of experimental physiology, 

 even though the results obtained cannot yet 

 be adequately expressed in mathematical 

 terminology." 



The opinion expressed in this quota- 

 tion epitomizes that held by the authors 

 of this book. It is our opinion, how- 

 ever, that since population ecology does 

 lend itself to rational, mathematical treat- 

 ment, it may be possible at some future 

 date to construct, as Hutchinson (1948) 

 calls it, a "biodemography" that serves a 

 useful function of integration in terms of the 

 field as a whole. In dealing with problems of 

 evolution, population genetics has certainly 

 profited from such an approach. 



A GENERAL CASE 



It is helpful to conclude this discussion 

 with a review of a paper by Barber (1926) 

 which identifies a number of climatic and 

 biotic agents that affect, both singly and 

 in combination, populations of the Euro- 

 pean corn borer (Pyrausta nuhilalis) in all 

 stages of its fife cycle. This is helpful in 

 two ways: as an extension of certain points 



