The process of myoglobin/leghemoglobin-facilitated oxygen diffusion is adapted to function in different environments in diverse organisms. We enquire how the functional parameters of the process are optimized in particular organisms. The ligand-binding properties of the proteins, myoglobin and plant symbiotic hemoglobins, we discover, suggest that they have been adapted under genetic selection pressure for optimal performance. Since carrier-mediated oxygen transport has probably evolved independantly many times, adaptation of diverse proteins for a common functionality exemplifies the process of convergent evolution. The progenitor proteins may be built on the myoglobin scaffold or may be very different.