The nature of the chiasma as a cytological parameter for analysing cross-over was reexamined quantitatively by an improved chiasma graph method. It was reconfirmed in Mus platythrix (n =13) that interstitial chiasmata at diakinesis are distributed randomly and almost uniformly along bivalents except for the centromere and telomere regions. The size of these chiasma blank regions was consistently 0.8% of the total length of haploid autosomes in all chromosomes. There was a minimum value of chiasma interference distance between two adjacent chiasmata, which was constantly 1.8% in all chromosomes. The chiasma frequency at diakinesis was 20.1+/-2. 0 by the conventional method including terminal chiasmata. However, the primed in situ labeling technique revealed that terminal chiasmata were mostly telomere-telomere associations. From these data and also from recent molecular data we concluded that the terminal chiasma is cytologically functional for ensuring the normal disjunction of bivalents at anaphase I, but genetically non-functional for shuffling genes. The chiasma frequency excluding terminal chiasmata was 14.6+/-1.8. Reexamination of the chiasma frequency of 106 animal species revealed that the chiasma frequency increased linearly in proportion to the haploid chromosome number in spite of remarkable difference in their genome size. The increase in chiasma frequency would be evolution-adaptive, because gene shuffling is expected to be accelerated in species with high chromosome numbers. Copyright 1999 Academic Press.