What is the reason that musk deer have the smallest red blood cells and amphibians have the largest? Should they not be proportionate to the size of the organism?
In the abstract of (Duke, 1963) we see that mouse deer (Tragulus) have the smallest erythrocytes, not musk deer (Moschus). The paper also explains the origin of the confusion. Mouse deer have 1.5 µm erythrocytes but those of musk deer are 3.6 µm (p. 240). In fact musk deer erythrocytes are the same size as goat erythrocytes at (2.5-3.9) µm (Weiss, D. (2010). Schalm's Veterinary Hematology. 6th ed. pp. 836–842). Whether smaller erythrocytes have since been found, I can't say.
I don't have a definite answer why mouse deer erythrocytes are the size they are but I'd posit a few factors. The size of the erythrocyte needs to approximately match the size of the capillaries so they can press tightly to the epithelium and increase the efficiency of gas exchange. Another factor affecting erythrocyte size is cell number. If you have smaller cells, you need a larger number of them to keep the same sum total volume (as in the figure below). So then factors affecting blood vessel size and the rate of erythrocyte production could possibly affect erythrocyte size.
Size also changes surface area to volume ratio (sa/vol) by the square-cube law and this changes characteristics of diffusion over the cell membrane. A larger erythrocyte may have more plasma membrane, which would allow more diffusion and transporter activity but this may also increase the erythrocyte's volume, which would limit the rate of gas exchange due to solutes needing to work their way out of the middle of the cell. Having a high sa/vol is dependent on morphology (hence, our erythrocytes are biconcave) but Duke claims that mouse deer erythrocytes are actually spherical. So, in theory, the cells' small size could be a compensation to keep their sa/vol high, despite not being biconcave.
Interestingly the size of the cells might not affect the sum total intracellular volume of the cells. In fact, sphere packing density is independent of the size of the spheres. If the cells were made larger, this would increase the size of the gaps between them by the same amount. This could indicate that the the total amount of solutes in the blood is independent of the size of the cells, which could explain the great variation in the size of erythrocytes.