From what I can glean, testosterone increases coloration, but is also immunosuppressant, and it seems like extra carotenoids are first diverted to immune function, then to coloration thus providing an honest signal.
Testosterone increases bioavailability of carotenoids: Insights into the honesty of sexual signaling
J. Blas, L. Pérez-Rodríguez, G. R. Bortolotti, J. Viñuela , and T. A. Marchant
PNAS Published online before print November 22, 2006
Abstract: Androgens and carotenoids play a fundamental role in the expression of secondary sex traits in animals that communicate information on individual quality. In birds, androgens regulate song, aggression, and a variety of sexual ornaments and displays, whereas carotenoids are responsible for the red, yellow, and orange colors of the integument. Parallel, but independent, research lines suggest that the evolutionary stability of each signaling system stems from tradeoffs with immune function: androgens can be immunosuppressive, and carotenoids diverted to coloration prevent their use as immunostimulants. Despite strong similarities in the patterns of sex, age and seasonal variation, social function, and proximate control, there has been little success at integrating potential links between the two signaling systems. These parallel patterns led us to hypothesize that testosterone increases the bioavailability of circulating carotenoids. To test this hypothesis, we manipulated testosterone levels of red-legged partridges Alectoris rufa while monitoring carotenoids, color, and immune function. Testosterone treatment increased the concentration of carotenoids in plasma and liver by >20%. Plasma carotenoids were in turn responsible for individual differences in coloration and immune response. Our results provide experimental evidence for a link between testosterone levels and immunoenhancing carotenoids that (i) reconciles conflicting evidence for the immunosuppressive nature of androgens, (ii) provides physiological grounds for a connection between two of the main signaling systems in animals, (iii) explains how these signaling systems can be evolutionary stable and honest, and (iv) may explain the high prevalence of sexual dimorphism in carotenoid-based coloration in animals.