Final answer:
The correct order of evolutionary energy metabolism breakthroughs is III, II, I, IV, beginning with anaerobic metabolism and culminating in oxygen-dependent ATP synthesis.
Step-by-step explanation:
Initially, living organisms evolved in an oxygen-lacking atmosphere about 3.8 billion years ago, leading to the development of anaerobic metabolism, which includes pathways such as glycolysis to break down organic compounds without oxygen. This would correspond with the consumption of fermentable organic acids (III). Subsequently, cells developed anoxygenic photosynthesis, which involves the light-dependent transfer of electrons from H2S to NADPH without producing free oxygen (II).
In the evolution of energy metabolism, the next significant breakthrough was the emergence of the H₂O-splitting enzyme activity that led to oxygenic photosynthesis, whereby water was used as the electron source, producing free oxygen as a byproduct (I). Lastly, with rising atmospheric oxygen, cells adapted to use oxygen in the electron transport chain for oxygen-dependent ATP synthesis through the process of oxidative phosphorylation (IV).