5 



curves. Given such a form, it is possible to make a more exact "Schmarda's Rule", taking the peak 

 as the "optimum value". In the territory of the USSR, the greatest numbers of mammal, bird, and 

 reptile species are found in quadrats with long-term mean July temperatures around 20-26 C. It 

 is interesting to note that there is no difference in the optimum for amphibian:,, either. 



mathematical dependence of th 



An extension of this method 



Theoretically, with such e 



one includes a sufficient 



proximation but is not dev 



the curves, can give nega 



of species appears sensel 



meaning of a different fu 



specify the limits of sig 



, the parabolas of Figures 



d 80° latitude. Presentl 



ule of the optimum ( ''Schma 



rve mustpossess are (l) that 



lues, and (2) that the asympt 



the curve. The necessary equ 



e qual i ta t i ve nc 



es the parabo 



qua t i on s it is po 



mber of terms. S 



of bas ic shortco 



e ord i nates and m 



but the charact 



on . T here fore , 



cance of the arg 



nd 2 take on the 



ere i s no de t erm i 



's Rule"). The i 



it must not allow 



otes must approac 



a t i ons must take 



The second formula is the preferred one, which even with only a second degree tern-, 'n the 

 denominator of the parabola, still shows the asymmetry so peculiar to the curved reaction In 

 ecological factors. In practice, 't is recommended to compute the ratios x-, , xp , x~ , . . . 



*1 Y 2 Yo 



from the empirical data, and then to smooth these with a parabola of suitable degree (first, 

 second, th i rd, etc. . . . ) . 



What do we obtar , ; n any given case, from such equations ot regression? First of all, they 

 make our theoretical ideas more precise, and secondly, theyallow us to predict the vaiue of data 

 concerning the number of spec es, found : n any given place. In making use of such standards, it 

 is taken for granted that inevitably there will be scatter of empirical points about the 

 predicted line of regression. It makes sense to look for causes only for those factors nb i ch 

 show significant correlations. For example, the long-term mean air temperature in leninarad 

 about 1 7. 5°C (Syelyan mov, 1937). From th.s, it follows that we should expect about 211 species 

 of birds in the Leningrad region. V. Bianki (l°/07) counted 237 bird species in this region, but 

 noted that of these 237 species, 16 were rare, and another 24 were rather uncommon. This is ver\ 

 good agreement between the number of species predicted and the actual number occurrinq in the 

 Leningrad region. On the other hand, if we try our prediction in the Crimea, we estimate that 

 there will be from 39 *° ^6 species o f reptiles. In fact, there are, according to old data, 15 

 species (hikolski, 19^ 5 ) » and according to the latest investigations of N. N. Scherbak, only 14 

 reptile species in th.s region. Clearl/, this particular fauna appears to be impoverished, whict 

 is precisely what N. N. Scherbok considers to be the case for the Crimea. 



Tne amount of impoverishment carries with it a guiding character. On such areas it is 

 desirable to check and to make our estimates more precise, with more detailed Investigations in 

 the separate regions of the USSR; arid on the other hand, it is desirable to make further, more 

 vast studies, taking in even other countries. 



Sun 



nary_ 



A number of species may be named "Qualitative 

 number of individuals, termed the "Quantitative Ri 



ichness of Fauna 

 less of Fauna". 



1 n oppos i t i 



The USSR territory was divided Into 66 rectangles (l0° latitude by 10° longitude). For each 

 rectangle separately the number of Mammal species ( M) was determined, the same for Birds (a), 

 for Reptiles (R), and for Batrachians (Am). Oeviances, estimates, variance-ratios (tables i, 

 3» 5> 7> 9) and regressions (Tables 2, 4, 6, 8) were calculated. Equations are given for the 

 dependence of mammal and bird species numbers on geographical latitude, and for the dependence of 

 mammal, bird, and reptile species numbers on the local mean July temperature. Dependence on 

 geographical longitude and mean rainfall is insignificant. The number of species of amphibans 

 Is determined more strongly by micro-, rather than macrocl i ma t i c conditions. 



