The question of whether gravity influences blood pressure, cardiac work, and heart position in the circulatory systems of vertebrate animals has been controversial (Patterson et al. 1965; Seymour and Lillywhite 1976; Badeer 1986; Hicks and Badeer 1989, 1992; Seymour et al. 1993; Pedley et al. 1996; Badeer 1997; Seymour 2000; Seymour and Blaylock 2000; Seymour and Lillywhite 2000; Gisolf et al. 2005; Hicks and Munis 2005; Mitchell et al. 2006; Gartner et al. 2010; Gartner et al. 2011; Lillywhite and Seymour 2011; Lillywhite et al. 2012). On one hand, the arterial pressure developed by the left ventricle is considered to have two conceptual components—the pressure necessary to perfuse the capillary beds of the body, plus the hydrostatic pressure generated by the vertical distance between the heart and the head (Mitchell et al. 2006). Because the total height of the blood column above the heart increases with animal size, and the hydrostatic pressure at the bottom of a column of fluid is calculated as the product of fluid density (ρ), gravitational acceleration (*g*), and the vertical height of the column (*h*), then central systemic arterial blood pressure should be positively related to body size. Consequently, the hearts of larger animals must work harder against gravity, not only to pump blood to the head, but also to pump against a higher peripheral resistance of the body that is necessary to maintain the elevated blood pressure. If, on the other hand, the siphon principle operates in the continuous, closed loops above the heart, the heart does no work against gravity, because gravity acts equally on the ascending and descending limbs of the circuit (Hicks and Badeer 1992). Assuming that the pressure necessary to perfuse the capillary beds of the body is independent of size, then, in the first case, central arterial systemic blood pressure should be influenced by the vertical distance above the heart, but in the second case, blood pressure should be size-invariant.

The hypothesis that the heart works against gravity can be tested by examining the scaling of arterial blood pressure and determining if the scaling exponent of blood pressure is significantly greater than 0. Because the aspect ratio of most mammals does not vary systematically with body mass (Roberts et al. 2010), they can be considered geometrically similar for the purposes of predicting the scaling of hydrostatic pressure. For geometrically similar objects, linear dimensions are proportional to the cube root of volume, so it can be predicted that the hydrostatic component of blood pressure (ρ*gh*) should be proportional to mass raised to the 0.33 power. However, previous studies report scaling exponents of blood pressure of around 0.03 (Günther 1975) to 0.05 (Seymour and Blaylock 2000). This effect of size on blood pressure is regarded as small (Gartner et al. 2011), and is certainly smaller than the exponent of 0.33 expected based on variation in the vertical distance between the heart and head observed in mammals.

Previous analyses of the scaling of blood pressure have been criticized because they fail to incorporate phylogenetic information (Hicks and Munis 2005; Gartner et al. 2011). Many, but not all, traits show significant phylogenetic signal (Freckleton et al. 2002; Blomberg et al. 2003; Losos 2011), and phylogenetically informed analyses may yield differences in estimates of scaling exponents as compared with nonphylogenetic estimates (Garland et al. 2005). Thus, there is a clear need to reevaluate the scaling of mammalian blood pressure to determine if they conform to the predictions based on size-dependent changes in hydrostatic pressure. A further unidentified problem with previous analyses is that scaling exponents are estimated based on log–log transformed data for pressure (*P*, mmHg) and body mass (*M*, kg) by fitting a linear relationship of the form:

which, when untransformed, is converted to a two-parameter power equation:

A critical assumption of such an approach is that the original data conform with a power function having an intercept of 0 in a plot with arithmetic coordinates (Packard and Boardman 2008). This assumption is rarely checked and is not always met (Packard and Boardman 2009; MacLeod 2010; Packard et al. 2011). Assuming that the heart must work against resistance to perfuse tissues and potentially also against gravity, a more appropriate statistical model of the relationship between blood pressure and body mass is a three-parameter power equation:

This statistical model introduces an intercept term, *c*, and thereby removes the assumption of the two-parameter power equation that the smallest animals must have negligible blood pressure.

In the present study, we test the hypothesis that blood pressure is positively associated with body mass due to increased hydrostatic pressure above the heart in larger mammals. We test for a relationship between systolic, mean, and diastolic arterial blood pressure (*P*_{systolic}, *P*_{mean}, and *P*_{diastolic}, respectively) and body mass using phylogenetic generalized least squares (PGLS; Grafen 1989; Martins and Hansen 1997; Garland and Ives 2000) to fit two-parameter power equations to log–log transformed data from 47 species, virtually doubling the sample size of the previous study that was limited to 24 because of requirements for additional data on heart size and function (Seymour and Blaylock 2000). We also use nonlinear regression to fit three-parameter power equations to untransformed data, and compare the values of the scaling exponent to those predicted on the basis of variation in hydrostatic pressure. We analyze the data with and without inclusion of the long-necked giraffe, and we run a sensitivity analysis to assess experimental errors and variability.