Metabolism, life-history, innovation, self-similarity, and social organization
The study of complex systems necessitates understanding the fundamental role of scale and hierarchical levels in governing dynamics and pattern formation. Scaling is a powerful tool used to relate the attributes of a system to changes in dimension. The next two weeks’ readings provide a brief introduction to issues of scale and a more in depth exposition of the recent uses of the scaling approach in human ecology.
Building on allometric and metabolic scaling, the recent metabolic theory of ecology is experiencing great success and controversy because it potentially provides a unifying framework for understanding the flows of energy and materials in ecological systems, as discussed by Brown et al. (2004). How might this theory and approach be extended and adapted to apply to human systems? Moses and Brown find that fertility rate in humans scales with metabolic rate just like in other organisms when total extra-metabolic energy consumption (e.g., electricity and gasoline use) is used as measure of metabolic rate, instead of physiological metabolic rate (Fig.1). But could this similarity be purely coincidental? A rigorous theory is necessary to demonstrate otherwise.
Bettencourt et al. (2007) discuss how cities are similar to and different from biological organisms. They suggest that their social organization, the cooperative interaction between individuals, leads to scaling relations uncommon in organisms, such as the scaling of wealth creation and innovation with city size. Yet how different are scaling relations for cities different from those in sedentary groups of other highly social organisms, such as ant colonies? In any case, an important step in the development of a metabolic theory of ecology will be to include the effects of interactions between agents, whether between individuals in a social group, species in a food web, or nations in a global environment.
Fractals and self-similarity pervade throughout the natural world. They emerge when a process is repeated across a range of a dimension. Due to the simplicity of the processes necessary for their origin and their commonness in nature, in many cases it may even be most appropriate to consider them as null models (e.g., in the spatial distribution of resources). Hamilton et al. (2007) discover an apparent self-similarity in the structure of social networks in hunter-gatherers. They suggest an intimate link between social organization and metabolism in hunter-gatherers (see also Hamilton et al. , 2007, PNAS).
As Brown et al. (2002) write, “Underlying the diversity of life and the complexity of ecology is order that reflects the operation of fundamental physical and biological processes”. Through the use of scaling, these readings investigate the potential existence of such order in human systems.
References
* Bettencourt, L. M. A., J. Lobo, D. Helbing, C. Kuhnert, and G. B. West. 2007. Growth,
innovation, scaling, and the pace of life in cities. Proceedings of the
*Brown, J. H. 2002. The fractal nature of nature: power laws, ecological complexity and biodiversity. Philosophical Transactions: Biological Sciences 357:619-626.
*Brown, J. H., J. F. Gillooly, A. P. Allen, V. M. Savage, and G. B. West. 2004. Toward a Metabolic Theory of Ecology. Ecology 85:1771-1789.
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*Hamilton, M. J., B. T. Milne, R. S. Walker, and J. H. Brown. 2007. Nonlinear scaling of space
*Moses, M. E., and J. H. Brown. 2003. Allometry of human fertility and energy use. Ecology
22 comments:
It seems like a majority of the quarter-power allometries in biology could simply be evolutionary homologues. Is this idea apt?
How can free loading of public goods change the hierarchy, scale, and levels of a government system? What corrective actions can be taken? What lengths should a society go to in excluding free loaders from public goods?
In "The fractal nature of nature" Brown et al point out that underlying the fractal nature of nature may be a "fourth spatial dimension" which causes them to adopt multiples of 1/4. Does this sound a little crazy to anyone else? They also state that Power laws describe emprical scaling relationships that are patterns of structure or dynamics that are fractal-like. So if all Power Laws are Fractal-like then why don't all of them have a exponent of 1/4?
Good question Michael. This idea is very apt and its cool that you touched on something so fundamental so quickly.
So, you are asking if the fact that many organisms share common ancestors and hence traits like body size and the traits that scale with body size that might be heritable drive the scaling relationship? and so we might just be seeing patterns that are driven by the fact that ancestors are likely to be similar to their decedents? - or something like that?
That is a difficult issue and certainly body size is highly heritable. However, notice that many of the allometries span several orders of magnitude from individual cells to the largest animals so its a bit odd that the same proportion between size and the trait in question should be recapitulated at all scales. They also hold when very different taxa are lumped together, especially when we correct for temperature (see figures in Brown et al 2004 - especially figure 2 for biomass production). Also, some studies use phylogenetic analysis, which controls for the common ancestor effect with a method called 'independent contrasts', and they find that the scaling relationships are preserved - for the most part. Lastly, we can take different traits that scale with body size and see if a given species is a little above or a little below the typical allometric relationship (is the data point for the species above or below the regression line) and use that to predict whether or not it should be above or below the line for a bunch of other traits. When we do studies like this we find that the independent traits go together the way they should. - so slow growers have longer lifespans, later ages of maturity, and lower birth rates. Moreover, we have a robust body of theory that bundles almost all of the relationships together rather nicely (the Brown paper again and Charnov 2001, 1991 and many others).
A key paper in this area is Purvis and Harvey 1995 in the Journal of Zoology. See also the Introduction to Charnov's 1993 book "Life History Invariants" for a discussion of the assumptions of regression, its application in allometry, and why species can be used as data points.
I'm going to such length here because lots of people wonder about this sort of thing and its an ongoing discussion amongst scholars of various sorts that use allometry in their work.
see you tomorrow,
O
PS - I should add that of course not everything in my previous comment is directly aimed at a question about homology but diverges into some more general points for typical issues raised when looking at allometric relationships...
:)
gibson et al state:
social scientists are increasingly
drawing upon ecological ways of thinking.
Would the social scientists in the group agree with that?
I haven't read very many critiques of the MTE, but one that I found interesting was in the August issue of Ecology: Hawkins et al. 2007. A global evaluation of metabolic theory as an explanation for terrestrial species richness gradients. This article specifically tests predictions of the MTE and finds it lacking. The article is followed by a response and counterresponse, and it's definitely worth checking out.
Brown et al.: “Because of these [upper and lower] limits to self-similarity, it is preferable to refer to these [biological] systems as fractal-like.” But doesn’t the self-similarity of true fractals have to break down at the atomic or quantum level? I think by the definition of quanta, you can’t get any smaller. Which is like capillaries in mammals, leaves of plants, etc., right?
But maybe even self-similar physical systems can only be fractal-like, and that only imagined things can be truly self-similar.
Are the metabolic theory of ecology and the "general theory of biological allometry" (Brown et al 2002) the same body of theory, or just related?
How are human systems fractal-like/self-similar?
Thank you for the clarification Oskar,
Similarly, a common theme in these papers seems to be a ¼ scaling relationship, contrary to 1/3 as predicted by Euclidean geometry. How does Euclidean geometry predict the 1/3 ratio? (If the answer is an obvious identification/nomenclature issue, I apologize)
It makes sense that body size can be fractal like in organisms. At the cellular level the cell has a certain surface area it reaches and a maximum proportion of energy it can metabolize at one time. It does not surprise me that there are constraints at this microlevel, which in theory of its constraints and maximum proportion, should translate into more complex organisms such as humans.
Assuming that the metabolic rate is an organism's physiological response to his environment, and that as Brown insists, this can be scaled - how would we go about scaling Behavior, as an organism's phenotypic reaction to his environment?
Is the change in metabolic rate based on temperature due to changes within the individual itself, or due to the fact that warmer areas have greater species diversity, and organisms can choose more energy-rich resources? Or is this a chicken-egg type of question?
I can see where scaling is important for helping provide a level playing field to study metabolism in an effort to attempt verification of the 1/4 allometric scaling relationship. This was an interesting reading.
In the Brown et al. paper, they use the example of the fractal nature of the Linnean taxonomic system. Can a system that was created by man to make distinctions within the continual variance of flora and fauna really be used to support the fractal patterns of nature?
I don't feel that I have a good grasp on fractels and look forward to your help with my comprehension so I can ask an appropriate question.
Hey all,
Good job today. We are suddenly in a sea of new terms that everyone has different levels of familiarity with. Try and roll with us but don't at all feel bad if its a bit overwhelming. Things like 'fractals' and what is really meant by 'Euclidean' geometry are not at all immediately intuitive even after repeated exposure. If you want to cover these or scaling or anything else more thoroughly - or just quickly for review - don't hesitate to let us know. While they can be non-intuitive, in understanding these topics a lot of folks just all of a sudden 'get it' with no apparent reason and wonder why they ever saw them as difficult. Its odd. Anyway, if this stuff is not clear you are not alone and don't worry. but let us know if we can help.
As always, we appreciate your efforts. Lets finish strong - the semester's almost over!
Oskar
The structure which organisms have today would be an optimizated or nearly optimizated structure. West gave a lecture in last year's PIBBS class. He gave a clear proof that the three quarter thing maybe relate to the dimension organism has. If the organism is 'n' dimension, then the exponent of the scaling should be n/(n+1). Does anyone in the class remeber the detail of the proof?
Most organisms change because of pressure, but humans can change before those pressures make them. How could that impact algorithms based on social aspects?
I'm currently reading Brown and Maurer 1989 for another class, and noticed that in that paper, the equation for energy use scaling with body mass was given as E=kM^2/3, rather than to the 3/4 power. What gives?
In continuing the discussion on fractals, are there patterns that are non-fractal? Do organisms who follow the 1/4 power laws for body mass have other physiological characteristics that follow the Euclidean 1/3 laws? Or are these patterns mutually exclusive? Also, we have only talked about Euclidean and 1/4 power laws, but are there other non-Euclidean laws that have been found, such as 1/5 power laws?
Along lines with Paul's comment and the discussion on Tuesday, if indeed Pual is right and physical systems can only be fractal-like what might be the slight divergences from fractals? Is there the possibility of patterns in change in the systems from one level to another?
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