  We present results from a numerical study of particle dispersion in the
weakly nonlinear regime of Rayleigh-B\'enard convection of a fluid with Prandtl
number around unity, where bi-stability between ideal straight convection rolls
and weak turbulence in the form of Spiral Defect Chaos exists. While Lagrangian
pair statistics has become a common tool for studying fully developed turbulent
flows at high Reynolds numbers, we show that key characteristics of mass
transport can also be found in convection systems that show no or weak
turbulence. Specifically, for short times, we find Richardson-like $t^3$
scaling of pair dispersion. We explain our findings quantitatively with a model
that captures the interplay of advection and diffusion. For long times we
observe diffusion-like dispersion of particles that becomes independent of the
individual particles' stochastic movements. The spreading rate is found to
depend on the degree of spatio-temporal chaos.
