Do yeast multiply in the initial aerobic phase or do they continue to multiply all the way through the entire anaerobic phase?
During the aerobic phase there is a presence of oxygen in the brew, during this phase there is a rapid increase in yeast and an almost exponential growth of yeast. During the anaerobic phase there is an absence oxygen, this causes the yeast growth to slow down and almost come to a halt. This since yeast does not grow well 'anaerobically' but needs the presence of oxygen to grow.
You might be interested to look up Krebs cycle and the electron transport chain which yeast follow when in its aerobic respiration phase. This is when the yeast can create a ton of energy and that surplus of energy is used to replicate.
After the oxygen runs out, it goes into anaerobic processes where the yeast produce CO2, ethanol, and sometimes lactate depending on the yeast or bacteria.