THE ORIGIN AND THE EXTINCTION OF SPECIES 351 



Let us assume that it takes place along a certain line — in this case 

 from south to north — and that the numerical strength of the species 

 remains constant, each pair of hares yielding a pair of surviving 

 offspring, which will attain to reproduction. Let us suppose that one 

 of these hares moves his home northwards to the extent of his range, 

 that is, as far as a hare is accustomed to range from his head 

 quarters, and that he pairs with one of the descendants on the next 

 stretch. 



Let us further suppose that this stretch is ten kilometres in 

 extent, and that the change of quarters take place once in each 

 year, then the blood of a South Scandinavian hare would have 

 extended ten kilometres further north in ten years, and in a 

 hundred years lOo kilometres; it would not, however, be quite 

 pure, but mixed and thinned by crossing with a hundred mates 

 of different individual bloods, that is, thinned to the extent of 

 <l to the ICO*'' power, that is, to less than a millionth part. Thus 

 even with these much too favourable assumptions the influence of 

 a region of hares ico kilometres distant would be actually nil upon the 

 inhabitants of a region which was in process of new adaptation. That 

 the assumptions are too favourable is quite obvious, since every 

 surviving hare would not be likely to move his home, and probably 

 the majority would remain in the old quarters and find mates there. 

 The blood-mingling would therefore take place much more rarely, 

 perhaps only once in ten years, and the wandering descendants of the 

 second generation might move southward, and so neutralize the pre- 

 vious blood-mingling, and so on. But let us keep to our favourable 

 assumptions, and attempt to determine how strong the assimilating 

 influence of the blood-mingling from south to north would be upon 

 a point A. The blood of the nearest stretch diluted to a half would 

 affect the inhabitants of A once in each year ; the second stretch would 

 only contribute blood of \ strength, the third of \, the fourth of -^q, 

 and the blood of the tenth would be diluted to xo^24- ^ region B, 

 extending over twenty such stretches, or 200 kilometres, would thus 

 shelter within it a hare population of which the centre would only 

 be influenced from the periphery in vanishing proportions. If the 

 winter were of equal length over the whole area of B, all the inhabi- 

 tants would be tending to vary the period for which the winter dress 

 was worn in correspondence with the length of the winter, and the 

 centre of the region would be the less impeded in this process because 

 the more peripheral areas would also be approximating to the same 

 adaptation. But since even the admixture of 3^2 o^' strange blood 

 could have no hindering influence upon a variation, there would 



