Minimalist models of proteins, in which amino acid chains are represented by a necklace of beads that reconfigure the native fold on the sites of a cubic lattice, have been an important tool to infer early events in folding and to typify the energy landscapes of small globular proteins. In this paper, we try to determine in what sense these models are viable to describe protein evolution. An important first step toward this goal is to establish whether there are any limitations on the lattice model, such as on heterogeneity of the interactions and the size and topology of the native folds, that are necessary before cooperative (2-statelike) folding behavior typical of small proteins evolves robustly from the sequence selection process. The model we construct to test this feature selects sequences that fold reliably to a fixed topology on relevant timescales near their folding transition temperatures. The cross-chain (nonbonded) interactions are defined by empirical amino acid contact potentials, and the sequences evolve by random drift subject to the selection criteria. We investigate the folding profiles of these evolutionarily selected sequences in terms of the free energy, F(Q), and the participation of native contacts, Q(j)(Q), along a folding reaction coordinate Q (the percentage of native contacts formed). Both size and topology effects are evident in the results, and weakly heterogeneous, 2-statelike folding behavior emerges most consistently from larger folds that are specially selected to suppress the effect of heterogeneity in native interactions. (C) 2003 American Institute of Physics.