Interesting, Vasco. I wouldn’t have guessed that this has much to do with hedonic capacity at all. Endotherms sacrifice energy efficiency for thermal independence; ectotherms sacrifice thermal independence for energy efficiency. But these traits don’t obviously have much to do with the cognitive capacities of the animals in question. Would you say more about your hunch?
Any production requires energy. So I feel like metabolic energy consumption should be relevant for the production of (positive or negative) welfare. In addition, in allometry, “the study of the relationship of body size to shape,[1]anatomy, physiology and behaviour”, “The relationship between the two measured quantities is often expressed as a power law equation (allometric equation)”. So I would say welfare per fully-healthy-organism-year being proportional to “property of interest”^”exponent” is a reasonable initial speculation.
To elaborate, I think individual welfare per fully-healthy-animal-year could be proportional to “metabolic energy consumption per unit time at rest”^”exponent 1“ because i) individual welfare per fully-healthy-animal-year could be proportional to “individual number of neurons”^”exponent 2”, and ii) metabolic energy consumption per unit time at rest is roughly proportional to “individual number of neurons”^”exponent 3“ (which means the individual number of neurons is roughly proportional to “metabolic energy consumption per unit time at rest”^(1/”exponent 3”)). Under these conditions, “metabolic energy consumption per unit time at rest”^”exponent 1“ would be proportional to “metabolic energy consumption per unit time at rest”^(“exponent 2”/”exponent 3“), and therefore “exponent 1” = “exponent 2”/”exponent 3″.
On i) the possibility of individual welfare per fully-healthy-animal-year being proportional to “number of neurons”^”exponent 2″, as illustrated in the graph below, the estimates for welfare ranges in your book about comparing welfare across species are pretty well explained by “individual number of neurons”^0.188. The welfare range is the difference between the maximum and minimum welfare per unit time, and I would say it is reasonable to assume it is proportional to the welfare per fully-healthy-animal-year, although I would like to see more research on this.
On ii) metabolic energy consumption per unit time at rest being roughly proportional to “individual number of neurons”^”exponent 3“, from Equation [1] of the article (see here), metabolic energy consumption per unit time at rest is proportional to “individual mass of carbon”^0.95 “when viewed over the entire tree of life”. From the Supplementary Information of the article, the ratio between the individual carbon and dry mass is “generally taken to be 0.5 [constant across species]”. So the metabolic energy consumption per unit time at rest is proportional to “individual dry mass”^0.95 “when viewed over the entire tree of life”. I believe individual dry mass is roughly proportional to individual mass. From the Supplementary Information of the article, “the ratio of dry mass to wet mass (DM/WM) used in our database ranges from 0.04 in the medusae of Cnidaria (jellyfish) to 0.40 in insects, with intermediate values of 0.26 in fishes, 0.3 in bacteria, 0.34 in birds and 0.38 in mammals. Makarieva et al. [9] used a conversion factor of DM/WM = 0.3 for all organisms”. So I think metabolic energy consumption per unit time at rest is roughly proportional to “individual mass”^0.95 “when viewed over the entire tree of life”. From Figure 2 of Sargo et al. (2009), which is below, I also suspect individual mass is roughly proportional to “brain mass”^”exponent 4” (A), and that brain mass is roughly proportional to “individual number of neurons”^”exponent 5“ (C). So I conclude metabolic energy consumption per unit time at rest is roughly proportional to “individual number of neurons”^(0.95*”exponent 4”*”exponent 5“), such that ii) holds for “exponent 3” = 0.95*”exponent 4“*”exponent 5”.
You are welcome! I have now estimated the total welfare of animal populations, trees, and bacteria and archaea assuming individual welfare per fully-healthy-organism-year is proportional to “metabolic energy consumption per unit time at rest”^”exponent”. I had recommended research informing how to increase the welfare of soil animals, but I am now more pessimistic about this. I currently think it is better to focus on decreasing the uncertainty about how the individual welfare per unit time of different organisms and digital systems compares with that of humans.
In addition, in allometry, “the study of the relationship of body size to shape,[1]anatomy, physiology and behaviour”, “The relationship between the two measured quantities is often expressed as a power law equation (allometric equation)”.
From the book “Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies” by Geoffrey West:
This scaling law for metabolic rate [this one], known as Kleiber’s law after the biologist who first articulated it, is valid across almost all taxonomic groups, including mammals, birds, fish, crustacea, bacteria, plants, and cells [see this section of my linkpost for further discussion]. Even more impressive, however, is that similar scaling laws hold for essentially all physiological quantities and life-history events, including growth rate, heart rate, evolutionary rate, genome length, mitochondrial density, gray matter in the brain, life span, the height of trees and even the number of their leaves. Furthermore, when plotted logarithmically this dizzying array of scaling laws all look like Figure 1 and therefore have the same mathematical structure. They are all “power laws” and are typically governed by an exponent (the slope of the graph), which is a simple multiple of ¼, the classic example being the ¾ for metabolic rate. So, for example, if the size of a mammal is doubled, its heart rate decreases by about 25 percent. The number 4 therefore plays a fundamental and almost magically universal role in all of life.13
Footnote 13:
There are several excellent texts summarizing the various allometric scaling laws in biology. Among them are: W. A. Calder, Size, Function and Life History (Cambridge, MA: Harvard University Press, 1984); E. L. Charnov, Life History Invariants (Oxford, UK: Oxford University Press, 1993); T. A. McMahon and J. T. Bonner, On Size and Life (New York: Scientific American Library, 1983); R. H. Peters, The Ecological Implications of Body Size (Cambridge, UK: Cambridge University Press, 1986); K. Schmidt-Nielsen, Why Is Animal Size So Important? (Cambridge, UK: Cambridge University Press, 1984).
Tables 1, 2, and 3 of chapter 4 have lots of predicted and observed allometric equations.
Interesting, Vasco. I wouldn’t have guessed that this has much to do with hedonic capacity at all. Endotherms sacrifice energy efficiency for thermal independence; ectotherms sacrifice thermal independence for energy efficiency. But these traits don’t obviously have much to do with the cognitive capacities of the animals in question. Would you say more about your hunch?
Thanks for the relevant question, Bob!
Any production requires energy. So I feel like metabolic energy consumption should be relevant for the production of (positive or negative) welfare. In addition, in allometry, “the study of the relationship of body size to shape,[1] anatomy, physiology and behaviour”, “The relationship between the two measured quantities is often expressed as a power law equation (allometric equation)”. So I would say welfare per fully-healthy-organism-year being proportional to “property of interest”^”exponent” is a reasonable initial speculation.
To elaborate, I think individual welfare per fully-healthy-animal-year could be proportional to “metabolic energy consumption per unit time at rest”^”exponent 1“ because i) individual welfare per fully-healthy-animal-year could be proportional to “individual number of neurons”^”exponent 2”, and ii) metabolic energy consumption per unit time at rest is roughly proportional to “individual number of neurons”^”exponent 3“ (which means the individual number of neurons is roughly proportional to “metabolic energy consumption per unit time at rest”^(1/”exponent 3”)). Under these conditions, “metabolic energy consumption per unit time at rest”^”exponent 1“ would be proportional to “metabolic energy consumption per unit time at rest”^(“exponent 2”/”exponent 3“), and therefore “exponent 1” = “exponent 2”/”exponent 3″.
On i) the possibility of individual welfare per fully-healthy-animal-year being proportional to “number of neurons”^”exponent 2″, as illustrated in the graph below, the estimates for welfare ranges in your book about comparing welfare across species are pretty well explained by “individual number of neurons”^0.188. The welfare range is the difference between the maximum and minimum welfare per unit time, and I would say it is reasonable to assume it is proportional to the welfare per fully-healthy-animal-year, although I would like to see more research on this.
On ii) metabolic energy consumption per unit time at rest being roughly proportional to “individual number of neurons”^”exponent 3“, from Equation [1] of the article (see here), metabolic energy consumption per unit time at rest is proportional to “individual mass of carbon”^0.95 “when viewed over the entire tree of life”. From the Supplementary Information of the article, the ratio between the individual carbon and dry mass is “generally taken to be 0.5 [constant across species]”. So the metabolic energy consumption per unit time at rest is proportional to “individual dry mass”^0.95 “when viewed over the entire tree of life”. I believe individual dry mass is roughly proportional to individual mass. From the Supplementary Information of the article, “the ratio of dry mass to wet mass (DM/WM) used in our database ranges from 0.04 in the medusae of Cnidaria (jellyfish) to 0.40 in insects, with intermediate values of 0.26 in fishes, 0.3 in bacteria, 0.34 in birds and 0.38 in mammals. Makarieva et al. [9] used a conversion factor of DM/WM = 0.3 for all organisms”. So I think metabolic energy consumption per unit time at rest is roughly proportional to “individual mass”^0.95 “when viewed over the entire tree of life”. From Figure 2 of Sargo et al. (2009), which is below, I also suspect individual mass is roughly proportional to “brain mass”^”exponent 4” (A), and that brain mass is roughly proportional to “individual number of neurons”^”exponent 5“ (C). So I conclude metabolic energy consumption per unit time at rest is roughly proportional to “individual number of neurons”^(0.95*”exponent 4”*”exponent 5“), such that ii) holds for “exponent 3” = 0.95*”exponent 4“*”exponent 5”.
Thanks for explaining!
You are welcome! I have now estimated the total welfare of animal populations, trees, and bacteria and archaea assuming individual welfare per fully-healthy-organism-year is proportional to “metabolic energy consumption per unit time at rest”^”exponent”. I had recommended research informing how to increase the welfare of soil animals, but I am now more pessimistic about this. I currently think it is better to focus on decreasing the uncertainty about how the individual welfare per unit time of different organisms and digital systems compares with that of humans.
From the book “Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies” by Geoffrey West:
Footnote 13:
Tables 1, 2, and 3 of chapter 4 have lots of predicted and observed allometric equations.