My impression is therefore that the strong correlations more reflect the fact that we have a small number of datapoints with animals differing dramatically on a wide variety of predictor (or, in principle, outcome) variables which are all highly correlated, rather than indicating that neuron counts are distinctively predictive of any outcomes of interest. See Andrew Gelmanâs similar discussion of our study.
I agree. Moreover, 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 the logarithm of the individual number of neurons explaining well the logarithm of the welfare ranges means this will also be well explained by many other properties. If the welfare range is roughly proportional to âindividual number of neuronsâ^âexponent 1â, and the individual number of neurons is roughly proportional to âproperty (e.g. individual brain mass)â^âexponent 2â, the welfare range will be roughly proportional to âpropertyâ^(âexponent 1â*âexponent 2â). This means the logarithm of the welfare range will be well explained by the logarithm of âpropertyâ. Relatedly, here is an illustration of why I think individual welfare per fully-healthy-animal-year could be proportional to âmetabolic energy consumption per unit time at restâ^âexponentâ.
Given the above, I do not think it matters much whether one estimates welfare per unit time based on the individual number of neurons, or another property which is a power law of it. I believe it matters much more than results are presented for many exponents of the power law determining the welfare per unit time. I did this in the post where I estimated the total welfare of animal populations assuming individual welfare per fully-healthy-animal-year is proportional to âindividual number of neuronsâ^âexponentâ, where I analysed exponents ranging from 0 to 2.
Relatedly, here is an illustration of why I think individual welfare per fully-healthy-animal-year could be proportional to âmetabolic energy consumption per unit time at restâ^âexponentâ.
I have now estimated the total welfare of animal populations, trees, and bacteria and archaea based on the assumption above. 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 welfare per unit time of different organisms and digital systems compares with that of humans.
Thanks for the comment, David!
I agree. Moreover, 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 the logarithm of the individual number of neurons explaining well the logarithm of the welfare ranges means this will also be well explained by many other properties. If the welfare range is roughly proportional to âindividual number of neuronsâ^âexponent 1â, and the individual number of neurons is roughly proportional to âproperty (e.g. individual brain mass)â^âexponent 2â, the welfare range will be roughly proportional to âpropertyâ^(âexponent 1â*âexponent 2â). This means the logarithm of the welfare range will be well explained by the logarithm of âpropertyâ. Relatedly, here is an illustration of why I think individual welfare per fully-healthy-animal-year could be proportional to âmetabolic energy consumption per unit time at restâ^âexponentâ.
Given the above, I do not think it matters much whether one estimates welfare per unit time based on the individual number of neurons, or another property which is a power law of it. I believe it matters much more than results are presented for many exponents of the power law determining the welfare per unit time. I did this in the post where I estimated the total welfare of animal populations assuming individual welfare per fully-healthy-animal-year is proportional to âindividual number of neuronsâ^âexponentâ, where I analysed exponents ranging from 0 to 2.
I have now estimated the total welfare of animal populations, trees, and bacteria and archaea based on the assumption above. 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 welfare per unit time of different organisms and digital systems compares with that of humans.