  The genome-wide recombination rate ($RR$) of a species is often described by
one parameter, the ratio between total genetic map length ($G$) and physical
map length ($P$), measured in centiMorgans per Megabase (cM/Mb). The value of
this parameter varies greatly between species, but the cause for these
differences is not entirely clear. A constraining factor of overall $RR$ in a
species, which may cause increased $RR$ for smaller chromosomes, is the
requirement of at least one chiasma per chromosome (or chromosome-arm) per
meiosis. In the present study, we quantify the relative excess of recombination
events on smaller chromosomes by a linear regression model, which relates the
genetic length of chromosomes to their physical length. We find for several
species that the two-parameter regression, $G= G_0 + k \cdot P$ provides a
better characterization of the relationship between genetic and physical map
length than the one-parameter regression that runs through the origin. A
non-zero intercept ($G_0$) indicates a relative excess of recombination on
smaller chromosomes in a genome. Given $G_0$, the parameter $k$ predicts the
increase of genetic map length over the increase of physical map length. The
observed values of $G_0$ have a similar magnitude for diverse species, whereas
$k$ varies by two orders of magnitude. The implications of this strategy for
the genetic maps of human, mouse, rat, chicken, honeybee, worm and yeast are
discussed.
