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, âthe study of the relationship of body size to shape,[1]anatomy, physiology and behaviourâ, âThe relationship between the two measured quantities is often expressed as a power law equation (allometric equation)â. So I would say welfare per fully-healthy-organism-year being proportional to âproperty of interestâ^âexponentâ is a reasonable initial speculation.
To elaborate, I think individual welfare per fully-healthy-animal-year could be proportional to âmetabolic energy consumption per unit time at restâ^âexponent 1â because i) individual welfare per fully-healthy-animal-year could be proportional to âindividual number of neuronsâ^âexponent 2â, and ii) metabolic energy consumption per unit time at rest is roughly proportional to âindividual number of neuronsâ^âexponent 3â (which means the individual number of neurons is roughly proportional to âmetabolic energy consumption per unit time at restâ^(1/ââexponent 3â)). Under these conditions, âmetabolic energy consumption per unit time at restâ^âexponent 1â would be proportional to âmetabolic energy consumption per unit time at restâ^(âexponent 2â/ââexponent 3â), and therefore âexponent 1â = âexponent 2â/ââexponent 3âł.
On i) the possibility of individual welfare per fully-healthy-animal-year being proportional to ânumber of neuronsâ^âexponent 2âł, as illustrated in the graph below, the estimates for welfare ranges in your book about comparing welfare across species are pretty well explained by âindividual number of neuronsâ^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 âindividual number of neuronsâ^âexponent 3â, from Equation [1] of the article (see here), metabolic energy consumption per unit time at rest is proportional to âindividual mass of carbonâ^0.95 âwhen viewed over the entire tree of lifeâ. From the Supplementary Information of the article, the ratio between the individual carbon and dry mass is âgenerally taken to be 0.5 [constant across species]â. So the metabolic energy consumption per unit time at rest is proportional to âindividual dry massâ^0.95 âwhen viewed over the entire tree of lifeâ. I believe individual dry mass is roughly proportional to individual mass. From the Supplementary Information of the article, âthe ratio of dry mass to wet mass (DM/âWM) 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/âWM = 0.3 for all organismsâ. So I think metabolic energy consumption per unit time at rest is roughly proportional to âindividual massâ^0.95 âwhen viewed over the entire tree of lifeâ. From Figure 2 of Sargo et al. (2009), which is below, I also suspect individual mass is roughly proportional to âbrain massâ^âexponent 4â (A), and that brain mass is roughly proportional to âindividual number of neuronsâ^âexponent 5â (C). So I conclude metabolic energy consumption per unit time at rest is roughly proportional to âindividual number of neuronsâ^(0.95*âexponent 4â*âexponent 5â), such that ii) holds for âexponent 3â = 0.95*âexponent 4â*âexponent 5â.
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 âmetabolic energy consumption per unit time at restâ^âexponentâ. 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, âthe study of the relationship of body size to shape,[1]anatomy, physiology and behaviourâ, âThe relationship between the two measured quantities is often expressed as a power law equation (allometric equation)â.
From the book âScale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companiesâ by Geoffrey West:
This scaling law for metabolic rate [this one], known as Kleiberâs 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 âpower lawsâ and are typically governed by an exponent (the slope of the graph), which is a simple multiple of Âź, the classic example being the ž 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.
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, âthe study of the relationship of body size to shape,[1] anatomy, physiology and behaviourâ, âThe relationship between the two measured quantities is often expressed as a power law equation (allometric equation)â. So I would say welfare per fully-healthy-organism-year being proportional to âproperty of interestâ^âexponentâ is a reasonable initial speculation.
To elaborate, I think individual welfare per fully-healthy-animal-year could be proportional to âmetabolic energy consumption per unit time at restâ^âexponent 1â because i) individual welfare per fully-healthy-animal-year could be proportional to âindividual number of neuronsâ^âexponent 2â, and ii) metabolic energy consumption per unit time at rest is roughly proportional to âindividual number of neuronsâ^âexponent 3â (which means the individual number of neurons is roughly proportional to âmetabolic energy consumption per unit time at restâ^(1/ââexponent 3â)). Under these conditions, âmetabolic energy consumption per unit time at restâ^âexponent 1â would be proportional to âmetabolic energy consumption per unit time at restâ^(âexponent 2â/ââexponent 3â), and therefore âexponent 1â = âexponent 2â/ââexponent 3âł.
On i) the possibility of individual welfare per fully-healthy-animal-year being proportional to ânumber of neuronsâ^âexponent 2âł, as illustrated in the graph below, the estimates for welfare ranges in your book about comparing welfare across species are pretty well explained by âindividual number of neuronsâ^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 âindividual number of neuronsâ^âexponent 3â, from Equation [1] of the article (see here), metabolic energy consumption per unit time at rest is proportional to âindividual mass of carbonâ^0.95 âwhen viewed over the entire tree of lifeâ. From the Supplementary Information of the article, the ratio between the individual carbon and dry mass is âgenerally taken to be 0.5 [constant across species]â. So the metabolic energy consumption per unit time at rest is proportional to âindividual dry massâ^0.95 âwhen viewed over the entire tree of lifeâ. I believe individual dry mass is roughly proportional to individual mass. From the Supplementary Information of the article, âthe ratio of dry mass to wet mass (DM/âWM) 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/âWM = 0.3 for all organismsâ. So I think metabolic energy consumption per unit time at rest is roughly proportional to âindividual massâ^0.95 âwhen viewed over the entire tree of lifeâ. From Figure 2 of Sargo et al. (2009), which is below, I also suspect individual mass is roughly proportional to âbrain massâ^âexponent 4â (A), and that brain mass is roughly proportional to âindividual number of neuronsâ^âexponent 5â (C). So I conclude metabolic energy consumption per unit time at rest is roughly proportional to âindividual number of neuronsâ^(0.95*âexponent 4â*âexponent 5â), such that ii) holds for âexponent 3â = 0.95*âexponent 4â*âexponent 5â.
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 âmetabolic energy consumption per unit time at restâ^âexponentâ. 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 âScale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companiesâ by Geoffrey West:
Footnote 13:
Tables 1, 2, and 3 of chapter 4 have lots of predicted and observed allometric equations.