Iterative algorithms are often used for range image matching. In this paper, we treat the iterative process of range image matching as a live biological system: evolving from one generation to another. Whilst different generations of the population are regarded as range images captured at different viewpoints, the iterative process is simulated using time. The well-known replicator equations in theoretical biology are then adapted to estimate the probabilities of possible correspondences established using the traditional closest point criterion. To reduce the effect of image resolutions on the final results for efficient and robust overlapping range image matching, the relative fitness difference (rather than the absolute fitness difference) is employed in the replicator equations in order to model the probability change of possible correspondences being real over successive iterations. The fitness of a possible correspondence is defined as the negative of a power of its squared Euclidean distance. While the replicator dynamics penalize those individuals with low fitness, they are further penalised with a parameter, since distant points are often unlikely to represent their real replicators. While the replicator equations assume that all individuals are equally likely to meet each other and thus treat them equally, we penalise those individuals competing for the same points as their possible replicators. The estimated probabilities of possible correspondences being real are finally embedded into the powerful deterministic annealing scheme for global optimization, resulting in the camera motion parameters being estimated in the weighted least squares sense. A comparative study based on real range images with partial overlap has shown that the proposed algorithm is promising for automatic matching of overlapping range images.