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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 <i>A</i> 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 <i>n</i>-dimensional algebra <i>A</i> is an evolution algebra if and only if a certain set of <i>n</i> symmetric <inline-formula><math display="inline"><semantics><mrow><mi>n</mi><mo>×</mo><mi>n</mi></mrow></semantics></math></inline-formula> matrices <inline-formula><math display="inline"><semantics><mrow><mo>{</mo><msub><mi>M</mi><mn>1</mn></msub><mo>,</mo><mo>…</mo><mo>,</mo><msub><mi>M</mi><mi>n</mi></msub><mo>}</mo></mrow></semantics></math></inline-formula> describing the product of <i>A</i> 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 intringuing, as evolution algebras model asexual reproduction, unlike the classical ones.