27The underlying genetic changes that regulate the appearance and disappearance of 28 repeated traits, or serial homologs, remain poorly understood. One hypothesis is 29 that variation in genomic regions flanking master regulatory genes, also known as 30 input-output genes, controls variation in trait number, making the locus of 31 evolution almost predictable. Other hypotheses implicate genetic variation in up-32 stream or downstream loci of master control genes. Here, we use the butterfly 33Bicyclus anynana, a species which exhibits natural variation in eyespot number 34 on the dorsal hindwing, to test these two hypotheses. We first estimated the 35 heritability of dorsal hindwing eyespot number by breeding multiple butterfly 36 families differing in eyespot number, and regressing eyespot number of offspring 37 on mid-parent values. We then estimated the number and identity of independent 38 genetic loci contributing to eyespot number variation by performing a genome-39 wide association study with restriction site-associated DNA Sequencing (RAD-seq) 40 from multiple individuals varying in number of eyespots sampled across a freely 41 breeding lab population. We found that dorsal hindwing eyespot number has a 42 moderately high heritability of approximately 0.50. In addition, multiple loci near 43 previously identified genes involved in eyespot development display high 44 association with dorsal hindwing eyespot number, suggesting that homolog 45 number variation is likely determined by regulatory changes at multiple loci that 46 build the trait and not by variation at single master regulators or input-output 47 49 Body plans often evolve through changes in the number of repeated parts or serial 50 homologs by either addition or subtraction. For instance, the pelvic fins of 51 vertebrates are inferred to have originated by addition to a body plan displaying 52 only pectoral fins, perhaps via co-option of the pectoral or caudal fin 53 developmental programs to a novel location in the body (Ruvinsky and Gibson-54 Brown 2000; Larouche et al. 2017). In insects, the absence of limbs and wings in 55 the abdomen is inferred to be due to a process of subtraction, i.e. via the repression 56 or modification of limbs and wings in these segments by hox genes (Galant and 57 Carroll 2002; Ronshaugen et al. 2002; Tomoyasu et al. 2005; Ohde et al. 2013). 58 Regulatory targets of abdominal hox genes are likely to underlie loss of limb/wing 59 number in these body segments (Tomoyasu et al. 2005; Ohde et al. 2013), 60 although these mutations have not yet been identified. Thus, while serial homolog 61 number variation is a common feature in the evolution of organisms' body plans, 62 the underlying genetic changes that regulate the appearance and disappearance of 63 these repeated traits remain poorly understood. 64 65 Studies in Drosophila have contributed most to the identification of the genetic 66 basis underlying the evolution of serial homolog number. Larvae of different 67 species have different numbers of small hairs, or tr...