208 THE EVOLUTION THEORY 



would become a symmetrical curve, highest in the middle and falling 

 equally at either side. 



Ammon has worked out the hypotheses on which the curve of 

 frequency would become asymmetrical. Firstly, when the fertility 

 is greater towards the upper or lower limit of the area of exemption : 

 secondly, when germinal selection forces the variation in a particular 

 direction, upwards or downwards ; and thirdly, ' when natural selection 

 intervenes diversely at the upper or lower limit.' Of these three 

 possibilities the first two must be acknowledged as quite probable, 

 but the third, it seems to me, could only cause a temporary asym- 

 metry of the curve, lasting, that is, only until a state of equilibrium 

 has again been reached ; but that may in certain conditions take 

 a long time. 



Asymmetrical curves of frequency (Fig. 120, B) therefore arise, 

 for instance, when the intra-germinal conditions (the 'constitution 

 of the species ') more easily and therefore more frequently produce 

 extreme variations. In this case the area of exemption can only 

 extend on one side, and must remain in this state. In Galtha palustris, 

 the marsh marigold, we may find, according to De Vries, among 

 a hundred flowers, those with five, six, seven, and eight petals, in 

 the following proportions : — 



Petals 5 678 



Number of flowers 72 21 6 1 



and thus there is an asymmetrical curve of frequency. But if we 

 take the whole area of variation as the area of exemption, that is, 

 if we assume that it is indiflferent for the species whether the flowers 

 have five, six, seven, or eight petals, the preponderance of the five- 

 petalled flowers may have its reason in the fact that it is much easier 

 for five than six or more petals to be produced because of the internal 

 structure of the whole plant. 



In this case the maximum of frequency lies at the lower limit 

 of variation, but it may also lie at the upper. Thus, according to 

 De Vries, the blossoms of Weigelia vary, in regard to the number of 

 their petal-tips, in the following manner. Six-tipped corollas were not 

 found, and among 1,145 flowers there were the following proportions : — 



Tips of the corolla .345 

 Number of flowers . 61 196 888 



It is thus clear that amphimixis is an essential factor in the 

 fixing of forms, but that it certainly does not of itself determine these, 

 and that it is not always the average of the variations that is the 

 most frequent, but that the form of the curve of frequency is 



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