PROBLEM- The orthodox expectation is for decay rates to be strictly constant for all types of decay (β+, β-, EC, α). However empirical results show strong evidence for nuclides having variable decay rates, typically evident as periodicity. The volume of data available suggests this is a real phenomenon, not merely a spurious outcome of measurement errors. However the problem is complex because the data are conflicted for different decays. Furthermore, there is no coherent theory for why the phenomenon should exist in the first place. The effect is not required or predicted by quantum theory. Consequently it is a significant challenge to explain how the variability might arise, what factors could be involved, and how the underlying mechanisms of causality might operate. This lack of explanation contributes to the phenomenon often being dismissed as erroneous. PURPOSE- This paper develops a theoretical explanation of the variability of nuclide decay rates. APPROACH- The non-local hidden-variable solution provided by the Cordus theory was used, specifically its mechanics for neutrino-species interactions with nucleons. FINDINGS- It is predicted that the β-, β+ and electron capture processes are induced by pre-supply of neutrino-species, and that the effects are asymmetrical for those species. Also predicted is that different input energies are required, i.e. that a threshold effect exists. Four simple non-contentious lemmas are proposed with which it is straightforward to explain why β- and EC would be enhanced and correlate to solar neutrino flux (proximity & activity), and α emission unaffected. It is shown that the concept of a neutrino-species asymmetry makes sense of the broad patterns evident in the empirical data. IMPLICATIONS- The results support the variability of decay rates, on theoretical grounds. The type of decay (β+, β-, EC, α) is found to be a key variable in this theory, as is the type of neutrino species and its energy. Past experiments have generally not recorded the variables sufficiently. Future empirical tests of nuclide decay rates need to be more specific about the identity of the external environmental, neutrino-species, both the energy and flux thereof. It is also necessary to be more specific about the decay path. The different decays have to be considered separately, not lumped together, nor classified primarily by element (e.g. U, Pb, Cl, etc.) but rather by type of decay process (β+, β-, EC, α). A more radical implication is that hidden-variable theories offer profoundly new perspectives on fundamental physics, and can explain complex phenomena that are inconceivable from within the zero-dimensional point framework of quantum theory. ORIGINALITY- The novel contribution is the provision of a theoretical explanation for why decay rates would be variable. A detailed mechanism is presented for neutrino-species induced decay. Also novel is the prediction that the interaction is asymmetrical, and that the energy requirements are different for the various types of decay. The explanation is qualitatively consistent with the empirical evidence.