  Consider a dynamical many-body system with a random initial state
subsequently evolving through stochastic dynamics. What is the relative
importance of the initial state ("nature") vs. the realization of the
stochastic dynamics ("nurture") in predicting the final state? We examined this
question for the two-dimensional Ising ferromagnet following an initial deep
quench from $T=\infty$ to $T=0$. We performed Monte Carlo studies on the
overlap between "identical twins" raised in independent dynamical environments,
up to size $L=500$. Our results suggest an overlap decaying with time as
$t^{-\theta_h}$ with $\theta_h = 0.22 \pm 0.02$; the same exponent holds for a
quench to low but nonzero temperature. This "heritability exponent" may equal
the persistence exponent for the 2D Ising ferromagnet, but the two differ more
generally.
