  Evolution algebras are non-associative algebras that describe non-Mendelian
hereditary processes and have connections with many other areas. In this paper
we obtain necessary and sufficient conditions for a given algebra $A$ to be an
evolution algebra. We prove that the problem is equivalent to the so-called
$SDC$ $problem$, that is, the $simultaneous$ $diagonalisation$ $via$
$congruence$ of a given set of matrices. More precisely we show that an
$n$-dimensional algebra $A$ is an evolution algebra if, and only if, a certain
set of $n$ symmetric $n\times n$ matrices $\{M_{1}, \ldots, M_{n}\}$ describing
the product of $A$ are $SDC$. We apply this characterisation to show that while
certain classical genetic algebras (representing Mendelian and auto-tetraploid
inheritance) are not themselves evolution algebras, arbitrarily small
perturbations of these are evolution algebras. This is intriguing as evolution
algebras model asexual reproduction unlike the classical ones.
