Our results are generally consistent with the MST, where the timing of pathogenesis is controlled by host cellular metabolic rate. That is, the progression of disease to symptoms and to death slows as a function of M1/4. Variation in tS and tD for each disease appears to scale with host body size with exponents consistent with the scaling of host metabolism. Observed relationships all scale with exponents very close and often indistinguishable from the predicted value of 1/4 ().
As indexed by the fitted allometric intercepts, each disease differs in the relative timing of tS
(i.e. host-pathogen interactions differ in their value of c2
and possibly c1
). A plot of tS
across the diverse diseases studied reveals that the timing of pathogenesis for each disease, remarkably, falls on the same function that is approximately isometric (slope of 1) (). Such invariance indicates that the allometric value of the ratio
(see Eq. 3) is the same invariant quantity for each of the diseases studied here. We also provide a histogram of
to show this ratio typically has a mean value of 1.6 (standard deviation 0.80) () and does not change systematically with M
. This implies a relationship, general among these diseases, whereby the time to the first sign of infection is a constant proportion of the time to death–a constant that is conserved across each of the diseases studied here. The histogram of
shows a long tail (); perhaps these outliers are influenced by host immune response, medial care in humans, or specific host-pathogen interactions. Further investigation of pathogenesis in these mammals (cat, human, camelid, and elephant) may shed more light on mechanisms of allometric pathogenesis. It would also be interesting to understand how variation in evolutionary forces on these organisms affects host-pathogen interactions.
The scaling for PRV appears to not follow the predicted pattern of timing of pathogenesis as strongly as the other four diseases. PRV has a positive trend in the scaling relationship with significant slopes but they are more-shallow than predicted. It is unclear why PRV differs from the other diseases. Nevertheless, our model provides a baseline to begin to explore why PRV may deviate from the exact predictions of the MST. Explaining the causes of variation around the regression lines in is a natural, and we believe, fruitful next step to this analysis.
Our results also indicate that disease allometry across diverse populations may be characterized by invariant dimensionless quantities. Because mammalian life-span and population doubling time scale as tLS
, respectively 
, where c3
are allometric constants with units of time, and if tD
, then the values for both
are equal to:
Note, both X1
are dimensionless ratios invariant of mammalian body size. Thus, remarkably, across all mammals the fraction of adult lifespan or population cycle influenced by a given disease is an approximately constant value independent of mammalian body size.
We have shown that the scaling of times associated with pathogenesis is consistent with the scaling of host metabolic rate, supporting the MST. We have suggested that such scaling could result if pathogen growth and replication are directly limited by the cellular metabolic rates of the hosts. We are not aware of any other model(s) that would lead to functional relationships of tS and tD that are power-functions of body mass with exponents near 1/4. However, it is possible that the observed scaling could be an indirect result of metabolic rate. For example, host immune and other physiological responses to pathogens may cause the observed scaling, rather than the rate at which pathogens replicate, or the scaling may represent some combination of factors. It is also possible that pathogens may evolve latency periods in order to maximize their fitness given the population dynamics of the host. Evidence of this is seen in the evolution of tS in TSE. When laboratory mice are infected with TSE from larger animals (sheep or cows), tS is initially several times longer than after the infection has persisted in mouse populations for several generations. This effect is known as the ‘species barrier’ (Gardash'yan 1976, Nonno and Trevitt 2006; in supplementary material). Thus, when TSE is transmitted to a new, smaller, species, it evolves a faster tS after just a few generations.
We would like to note that an extensive survey of the veterinary and disease literature (see Supplementary Information) revealed only five diseases that allowed for sufficient body size variation and with enough reported values of pathogenesis times, and only three of those gave both time to symptoms and time to death. In future pathogenesis studies, we urge researchers to carefully report associated pathogenesis times as this will greatly increase the range of studies available for disease allometry, and greatly improve the ability to discriminate between MST and other hypotheses, such as the geometric hypothesis (scaling exponent of 1/3). While data were available for a large range of mammal body sizes (see ), data were unavailable for animals at either extreme of the spectrum of body masses, such as shrews and whales. MST makes theoretical predictions for these animals. For example, in whales, experimental infection with disease would be very difficult. Our model, however, indicates that we would expect pathogenesis times for a blue whale to be about 1.5 orders of magnitude longer than for a 1 kg mammal.
Our results suggest that a comparative approach to pathogenesis is valuable, and that MST gives novel theoretical predictions for understanding the pace and progression of disease. While there is variation in the scaling relationships we show, there are clearly systematic and allometric (slopes less than 1) relationships between times of pathogenesis and body size. Our initial survey indicates that the observed scaling exponents are consistent with the scaling of host metabolic rate (MST). These results support the notion that the scaling of metabolism fundamentally constrains rates of pathogenesis. Furthermore, our results have important implications for epidemic models that often assume that the timing of and dynamics of pathogenesis is independent of host body size, metabolism, or pathogen transport times 
. Our findings also suggest that a focus on the fundamental role of how the scaling of host metabolism influences the pace of pathogenesis could contribute to a mechanistic understanding of pathogenesis, and in turn, a foundation for predictive diagnostics, effective vaccination and therapy.