P^EBRUARY 9, 1922] 



NATURE 



^11 



Plants and 



geographical distriburion. These two phenomena 

 should therefore show similar expressions. 



But the characteristic feature of geographical dis 

 tribution, as indicated in all the work upon Age 

 and Area, is that species, whether of endemic or of 

 non-endemic genera, are arranged, as regards their 

 areas of dispersal, in " holjow curves."' They 

 show {cf. last curve of Fig. i) many on the smallest 

 area (here one island), fewer on the area next larger 

 (here two islands), and a tail of a few on areas 

 larger again. This type of distribution is practi- 

 cally universal ; if one take, for example, a large and 

 widely distributed genus like Cyrtandra, one finds 



•X3 



Some Statistics of Evolution and Geographical Distribution in 

 Animals, and their Significance. 



By Dr. J. C. Willis, F.R.S., and G. Ucinr Yule, C.B.E., F.R.S 

 N a paper read at the Linnean Society under the 

 above title on February 2, the statistical 

 ethods long employed in " Age and Area " were 



ushed to their final conclusion. Age and area 



review in Ann. of Bot., October, 192 1, p. 493) is 

 the name given to a principle gradually discovered 

 in many years of work upon the flora of Ceylon, 

 which, in brief, affirms that if one take groups 

 of not less than ten allied species and compare 

 them with similar groups allied to the first, the 

 lative total areas occupied in a given country, or 

 the world, will be more or less proportional 



whether directly or not we do not yet know) to their 

 lative total ages, within that 



)untry or absolutely, as the case Monospecific Genera at this end of curve 



lay be. The longer a group has 



existed the more area will it 

 occupy. Tens are compared in 

 order to eliminate chance differ- 

 ences as much as possible, and 

 allied groups to avoid as far as 

 may be the complications introduced 

 by different ecological habit, etc. 

 Herbs, for example, probably 

 spread much more rapidly than ^ 

 trees, but both will obey Age and .^ 

 Area. It is of course obvious that « 

 age of itself cannot effeet dispersal, w 

 but inasmuch as predictions as to ^ 

 distribution of species, occurrence ^ 

 of endemics, etc., can be success- ^ 

 fully made upon the basis of age g 

 alone, it is clear that the average c5 

 rate of spreading of a given «^ 

 species, and still more of a group 

 of allied species, is very uniform, 

 and therefore affords a measure of 

 age. The result of the work is to 

 show that in general the species 

 (and genera) of smallest areas are 

 the youngest, and are descended 

 from the more widespread 

 species that usually occur beside 

 them. 



To Age and Area must be 

 added, as will be shown in 

 a forthcoming book, the twin 

 principle of " Size and Space," which affirms that 

 within any circle of affinity the total of areas 

 occupied by any group of ten genera will go 

 with the total number of species, being large 

 when that is large. The monotypic genera, 

 like the species of small area, must in general 

 be young beginners, and descended from larger 

 genera. Putting these two principles together, it is 

 clear that age, area (or space), and size go together, 

 and as age (representing the resultant of the active 

 factors) is the only working factor of the three, 

 whatever phenomena are shown by size should be 

 similar to those shown by space. But size of genera 

 represents evolution, and area or space represents 

 NO. 2728, VOL. 109] 



The lar^c dots represent the Origins. 



Number of species (or size of area.) 



Mixed hollow curves. The numbers (thus 446/1) at the beginning of each are the 

 numbers of monotypes. 



145 species on small areas, twenty on areas of 

 moderate size, and two on very large areas. If 

 one take the Hawaiian Islands alone, one finds that 

 this genus has twenty-four on single islands, two 

 on two, two on three, and one on four. 



Now evolution, as expressed in the sizes of genera, 

 shows exactly similar phenomena, and if one group 

 together genera that are associated in any way, 

 systematically, ecologically, or in a given local flora, 

 one gets just the same type of hollow curve, as 



1 By a hollow curve is meant the curve obtained by plotting graphically 

 a series of numbers of which the first is much the largest, while there is a 

 considerable drop to the second and again to the third, and then a gradual 

 falling ofi to the end. The first two make up about half the totaL For 

 instance, a hollow curve will be obtained by plotting 40/1 (40 of one species), 

 15/2, 8/3, 6/4, 5/5, 3/10, 2/20, 1/30. Many example* are givea in Fig. i. 



