  A \emph{numerical semigroup} is a subset $\Lambda$ of the nonnegative
integers that is closed under addition, contains $0$, and omits only finitely
many nonnegative integers (called the \emph{gaps} of $\Lambda$). The collection
of all numerical semigroups may be visually represented by a tree of element
removals, in which the children of a semigroup $\Lambda$ are formed by removing
one element of $\Lambda$ that exceeds all existing gaps of $\Lambda$. In
general, a semigroup may have many children or none at all, making it difficult
to understand the number of semigroups at a given depth on the tree. We
investigate the problem of estimating the number of semigroups at depth $g$
(i.e.\ of genus $g$) with $h$ children, showing that as $g$ becomes large, it
tends to a proportion $\phi^{-h-2}$ of all numerical semigroups, where $\phi$
is the golden ratio.
