Continuous, quantized and modal variation

In traspecific varia tio n m ay be continuous, or it m ay be quantized , if th e num ber of s truc tu res p resen t is alw ays an integer. I f there is some m odal num ber of struc tu res p resen t in alm ost all individuals, varia tio n is said to be m odal. A developm ental process is defined as one o f 6 simple q u an tiz a tio n ’ if, first, i t gives rise to an in teg ra l num ber of struc tu res, and secondly, if th e num ber of stru c tu res form ed depends on th e ra tio betw een tw o continuous variables, for exam ple the field size and th e chem ical w avelength in th e m odel suggested by T uring (1952). W hether v a ria tion is quantized or m odal will th en depend on th e accuracy w ith w hich these continuous variables are regulated . The larger the m odal num ber, the m ore accura te m u st th is regu lation be. D a ta on the range of continuous varia tion w ith in anim al populations sug­ gest th a t sim ple quan tiza tion canno t give rise to m odal num bers g rea ter th a n ab o u t 5 to 7. Y e t m odal num bers of 30 or m ore occur. Three processes w hich m ight account for th is d is­ crepancy are suggested, and evidence is p resen ted to show th a t tw o of them occur. These are ‘m u ltip lica tiv e ’ processes, involving successive processes of simple quan tiza tion , and ‘chem ical co u n tin g ’ processes, depending on qualita tive differences betw een successively form ed structu res. The relevance of processes of quan tiza tion to the genesis of tw o-dim ensional p a tte rn s is discussed.