Three kinds of equivalence for levels of selection: an information-based approach

The question of equivalence between levels of selection has been one of the most debated topics in evolutionary biology and philosophy of biology. Here I provide an analysis in terms of information. I argue that two hierarchical levels are equivalent only if their informational content overlaps perfectly; conversely, a level of description is indispensable only if it contains unique information not captured by alternative descriptions. I operationalize equivalence in terms of inter-translatability between descriptions and distinguish three relevant forms: state-space, kinematic, and dynamic equivalence. Using a minimal setup, I construct four descriptions by varying informational content—in particular, informational richness (coarse vs. fine)—and level of description (particle vs. collective). I examine the conditions under which descriptions at different levels can be equivalent. I show that some forms of equivalence can occur under a limited set of conditions. This information-based framework clarifies when claims of indispensability are warranted and offers a principled way to adjudicate the realist–conventionalist debate on levels of selection.