University of Chicago Journals has recently published the first issue of the new journal - Human Capital . This journal is based on a series of theoretical developments in economics beginning about 40 years ago leading to what today is called human capital theory. While it dates back to some classic theorists it is probably most closely associated with economists Gary Becker and Theodore Schultz. Students of human evolution should be familiar with the concept from its role in embodied capital theory, which has been used by Hilly Kaplan and colleagues to explain the coevolution of intelligence, long lifespan, dependent offspring, and complex foraging niche that has characterized primate diversification in general and especially the evolution of the human life course and adaptive niche (a pdf of one of the papers on this can be found here).
All of the articles in this inaugural issue look really interesting and blog worthy, so I'm just going to post titles and abstracts so that they are on your radar. It looks like it should be a really interesting journal to watch and I look forward to taking in some of these papers during vacation.
The first paper is by Isaac Ehrlich and Kevin M. Murphy and explains why a seperate journal of human capital is necessary. It gives a nice explanation for the rationale of human capital theory and its historical development.
The rest of the papers in the journal are as follows:
Education and Consumption: The Effects of Education in the Household Compared to the Marketplace
Gary S. Becker and
Kevin M. Murphy
University of Chicago and Hoover Institution
This article considers various differences between the effects of education in the marketplace and households. It shows that the household sector rewards skills that are useful at the many tasks that household members must execute, whereas the marketplace rewards skill at specialized tasks. In addition, increased supplies of more educated persons reduce returns to education in the marketplace, whereas if anything, increased supplies raise household returns to education. The greater demand over 40 years for household and market skills may have raised returns to education in households compared to those in the market sector.
***
The Changing Role of Family Income and Ability in Determining Educational Achievement
Philippe Belley
University of Western Ontario
Lance Lochner
University of Western Ontario and National Bureau of Economic Research
We use the National Longitudinal Survey of Youth 1979 and 1997 cohorts to estimate the effects of ability and family income on educational attainment in the early 1980s and early 2000s. The effects of family income on college attendance increase substantially over this period. Cognitive ability strongly affects schooling outcomes in both periods. We develop an educational choice model that incorporates both borrowing constraints and a “consumption value” of schooling. The model cannot explain the rising effects of family income on college attendance in response to rising costs and returns to college without appealing to borrowing constraints.
***
The Production of Cognitive Achievement in Children: Home, School, and Racial Test Score Gaps
Petra E. Todd and
Kenneth I. Wolpin
University of Pennsylvania
This paper studies the determinants of children’s scores on tests of cognitive achievement in math and reading. Using rich longitudinal data on test scores, home environments, and schools, we implement alternative specifications for the cognitive achievement production function that allow achievement to depend on the entire history of lagged home and school inputs as well as on parents’ ability and unobserved endowments. We use cross‐validation methods to select among competing specifications and find support for a variant of a value‐added model of the production function augmented to include information on lagged inputs. Using this specification, we study the sources of test score gaps between black, white, and Hispanic children. The estimated model captures key patterns in the data, such as the widening of minority‐white test score gaps with age and differences in the gap pattern between Hispanics and blacks. We find that differences in mother’s “ability,” as measured by AFQT, account for about half of the test score gap. Home inputs also account for a significant proportion. Equalizing home inputs at the average levels of white children would close the black‐white and the Hispanic‐white test score gaps in math and reading by about 10–20 percent.
***
The Evolution of Income and Fertility Inequalities over the Course of Economic Development: A Human Capital Perspective
Isaac Ehrlich
State University of New York at Buffalo and National Bureau of Economic Research
Jinyoung Kim
Korea University
Using an endogenous‐growth, overlapping‐generations framework in which human capital is the engine of growth, we trace the dynamic evolution of income and fertility distributions and their interdependencies over three endogenous phases of economic development. In our model, heterogeneous families determine fertility and children’s human capital, and generations are linked via parental altruism and social interactions. We derive and test discriminating propositions concerning the dynamic behavior of inequalities in fertility, educational attainments, and three endogenous income inequality measures—family‐income inequality, income‐group inequality, and the Gini coefficient. In this context, we also reexamine the “Kuznets hypothesis” concerning the relation between income growth and inequality.
***
Enjoy!
best wishes,
Oskar
Friday, December 21, 2007
Monday, December 17, 2007
Sociobiology revisited: a new paper by Wilson and Wilson
An interesting review paper about multi-level selection was just made available (forthcomming) in the Quarterly Review of Biology by D S Wilson and E O Wilson. It's an interesting read. Here's the citation info and abstract:
"sociobiology is the study of social behavior from a biological perspective, group selection is the evolution of traits based on the differential survival and reproduction of groups..."
"From an evolutionary perspective, a behavior can be regarded as social whenever it influences
the fitness of other individuals in addition to the actor."
"Group advantageous traits do increase the fitness of groups, relative to other groups, even if they are selectively neutral or disadvantageous within groups. Total evolutionary change in a
population can be regarded as a final vector made up of two component vectors, within and between-group selection, that often point in different directions."
They make a point that words like 'sociobiology' and 'evolutionary psychology' have become "tainted" due to their negative associations and bad reputations in many fields. This is of course especially true in the social sciences. I have almost never heard an anthropologist use sociobiology in a positive or even neutral context (only very negative - 'oh that stuff - we know better than that') but the vast majority of anthropologists would think of sociology as a field arguing that genes cause every observable trait we might observe - a much more extreme view than that used by its actual practitioners (above in the definitions).
In a similar vein, anything related to 'group selection' carries the connotation of being an automatically naieve argument even in fields where Darwinian analysis is accepted. I am mostly a behavioral ecologist (studying macroecological patterns) and I have been guilty of this. In many cases, arguments about group selection involve people speaking past each other and missing the point, this is why Wilson and Wilson often use the term 'multi-level selection' instead. We can show that altruism is costly to a perfectly self-interested actor but that a group of altruists out-competes a group of selfish social defectors. If we are comparing groups (populations) and focus only on individual-level benefits we may indeed miss part of the picture, but on the other hand the individual does a lot better in the group that doesn't get killed off by the more altruistic group. So the tension between the two views is not always necessary. Wilson and Wilson look at cases like the evolution of eukaryotic cells and argue that group selection must have been present to get the once autonomous entities (prob some form of early bacteria) to cooperate so closely in a tightly knit network of symbiotic mutualisms that they became organelles in the same cell.
So group selection must be common, they argue. Consider this view: "If a trait is locally disadvantageous wherever it occurs, then the only way for it to evolve in the total population is for it to be advantageous at a larger scale." Is altruism really locally disadvantageous though?
Getting back to relationships between groups, if we want to talk about why different populations spread at the expense of others then I think population level fitness measures are necessary and quite uncontroversially logical. George Williams himself proposed measures of population level fitness in his 1966 treatise against the brand of group selection proposed by Wynn-Edwards and others. [One of these measures was population density or size which he thought was not as good as the second measure, the numerical stability of the population through time, but this has much larger data requirements. These discussions are definitely relevant for our discussions of human evolution.] Wilson and Wilson also point out that there is room for multi-level selection in Williams' view, he only underestimated how frequently it could be important.
They are very careful to separate cogent arguments of multilevel selection from those they label naive group selection. The level of selection needs to be appropriate for the analysis being conducted. My feeling is that we can't categorically reject arguments of selection at the level of genes, individuals, families, other groups, maybe even species in some restricted geological cases like the study of mass extinction, and maybe higher levels like ecological network structures. Here's a nice quote they bring to this issue:
"In biological hierarchies that include more than two levels, the general rule is “adaptation at any level requires a process of natural selection at the same level and tends to be undermined by natural selection at lower levels.” All students of evolution need to learn this rule to avoid the errors of naı¨ve group selectionism. Notice that, so far, we are affirming key elements of the consensus that formed in the 1960s."
Humans are used as an example in many cases in the paper.
"The importance of genetic and cultural group selection in human evolution enables our groupish nature to be explained at face value. Of course, within-group selection has only been suppressed,
not entirely eliminated. Thus multilevel selection, not group selection alone, provides a comprehensive framework for understanding human sociality."
There seems little question that understanding how selection may play out at higher levels will be necessary for explaining how anatomically modern humans came to spread and conquer the globe. But we do need to be cautious with how such arguments are invoked.
This paper is extremely well written and thought provoking. I recommend checking it out.
Best,
Oskar
RETHINKING THE THEORETICAL FOUNDATION OF SOCIOBIOLOGY
Departments of Biology and Anthropology, Binghamton University Binghamton, New York 13902 USA dwilson@binghamton.edu
Museum of Comparative Zoology, Harvard University Cambridge, Massachusetts 02138 USA
KEYWORDS
altruism, cooperation, eusociality, group selection, human evolution, inclusive fitness theory, kin selection, major transitions, multilevel selection, pluralism, sociobiology
ABSTRACT
Current sociobiology is in theoretical disarray, with a diversity of frameworks that are poorly related to each other. Part of the problem is a reluctance to revisit the pivotal events that took place during the 1960s, including the rejection of group selection and the development of alternative theoretical frameworks to explain the evolution of cooperative and altruistic behaviors. In this article, we take a “back to basics” approach, explaining what group selection is, why its rejection was regarded as so important, and how it has been revived based on a more careful formulation and subsequent research. Multilevel selection theory (including group selection) provides an elegant theoretical foundation for sociobiology in the future, once its turbulent past is appropriately understood.
The Quarterly Review of Biology, December 2007, vol. 82, no. 4
They are careful about defining their terms. Here are some useful definitions:
"From an evolutionary perspective, a behavior can be regarded as social whenever it influences
the fitness of other individuals in addition to the actor."
"Group advantageous traits do increase the fitness of groups, relative to other groups, even if they are selectively neutral or disadvantageous within groups. Total evolutionary change in a
population can be regarded as a final vector made up of two component vectors, within and between-group selection, that often point in different directions."
They make a point that words like 'sociobiology' and 'evolutionary psychology' have become "tainted" due to their negative associations and bad reputations in many fields. This is of course especially true in the social sciences. I have almost never heard an anthropologist use sociobiology in a positive or even neutral context (only very negative - 'oh that stuff - we know better than that') but the vast majority of anthropologists would think of sociology as a field arguing that genes cause every observable trait we might observe - a much more extreme view than that used by its actual practitioners (above in the definitions).
In a similar vein, anything related to 'group selection' carries the connotation of being an automatically naieve argument even in fields where Darwinian analysis is accepted. I am mostly a behavioral ecologist (studying macroecological patterns) and I have been guilty of this. In many cases, arguments about group selection involve people speaking past each other and missing the point, this is why Wilson and Wilson often use the term 'multi-level selection' instead. We can show that altruism is costly to a perfectly self-interested actor but that a group of altruists out-competes a group of selfish social defectors. If we are comparing groups (populations) and focus only on individual-level benefits we may indeed miss part of the picture, but on the other hand the individual does a lot better in the group that doesn't get killed off by the more altruistic group. So the tension between the two views is not always necessary. Wilson and Wilson look at cases like the evolution of eukaryotic cells and argue that group selection must have been present to get the once autonomous entities (prob some form of early bacteria) to cooperate so closely in a tightly knit network of symbiotic mutualisms that they became organelles in the same cell.
So group selection must be common, they argue. Consider this view: "If a trait is locally disadvantageous wherever it occurs, then the only way for it to evolve in the total population is for it to be advantageous at a larger scale." Is altruism really locally disadvantageous though?
Getting back to relationships between groups, if we want to talk about why different populations spread at the expense of others then I think population level fitness measures are necessary and quite uncontroversially logical. George Williams himself proposed measures of population level fitness in his 1966 treatise against the brand of group selection proposed by Wynn-Edwards and others. [One of these measures was population density or size which he thought was not as good as the second measure, the numerical stability of the population through time, but this has much larger data requirements. These discussions are definitely relevant for our discussions of human evolution.] Wilson and Wilson also point out that there is room for multi-level selection in Williams' view, he only underestimated how frequently it could be important.
They are very careful to separate cogent arguments of multilevel selection from those they label naive group selection. The level of selection needs to be appropriate for the analysis being conducted. My feeling is that we can't categorically reject arguments of selection at the level of genes, individuals, families, other groups, maybe even species in some restricted geological cases like the study of mass extinction, and maybe higher levels like ecological network structures. Here's a nice quote they bring to this issue:
"In biological hierarchies that include more than two levels, the general rule is “adaptation at any level requires a process of natural selection at the same level and tends to be undermined by natural selection at lower levels.” All students of evolution need to learn this rule to avoid the errors of naı¨ve group selectionism. Notice that, so far, we are affirming key elements of the consensus that formed in the 1960s."
Humans are used as an example in many cases in the paper.
"The importance of genetic and cultural group selection in human evolution enables our groupish nature to be explained at face value. Of course, within-group selection has only been suppressed,
not entirely eliminated. Thus multilevel selection, not group selection alone, provides a comprehensive framework for understanding human sociality."
There seems little question that understanding how selection may play out at higher levels will be necessary for explaining how anatomically modern humans came to spread and conquer the globe. But we do need to be cautious with how such arguments are invoked.
This paper is extremely well written and thought provoking. I recommend checking it out.
Best,
Oskar
Saturday, December 15, 2007
Complex Systems Summer School 2008
The Santa Fe Institute is now looking for applications for next year's complex systems summer school. I attended the international school in Beijing 2005 and loved it (went back the next year as staff). I recommend it for folks interested in complex systems research from any perspective.
Here's the basic information on the school and how to apply (this is just the text of the email they send to alumni to help circulate the announcement):
_____
Here's the basic information on the school and how to apply (this is just the text of the email they send to alumni to help circulate the announcement):
_____
Complex Systems Summer Schools
Summer 2008
The annual Complex Systems Summer Schools provide an intensive introduction to complex behavior in mathematical, physical, living, and social systems for graduate students and postdoctoral fellows. Schools will be held in Santa Fe, New Mexico and Beijing, China. Applications are now available at http://www.santafe.edu/csss08.html.
Program Details
Santa Fe: June 1-28, 2008 at St John’s College in Santa Fe, New Mexico, USA. Directed by Dan Rockmore, Dartmouth College and Santa Fe Institute (SFI); administered by the Santa Fe Institute (SFI).
Beijing: June 30-July 25, 2008. Sponsored by SFI in cooperation with The Institute of Theoretical Physics, the Chinese Academy of Sciences (CAS). Co-directors: Dr. David P. Feldman, College of the Atlantic and SFI, and Dr. Chen Xiao-song, Institute for Theoretical Physics, CAS.
General Description
The Complex Systems Summer School offers an intensive four-week introduction to complex behavior in mathematical, physical, living, and social systems for graduate students and postdoctoral fellows in the sciences and social sciences. The schools are for participants who want background and hands-on experience to help prepare them to do interdisciplinary research in areas related to complex systems.
Each school consists of an intensive series of lectures, laboratories, and discussion sessions focusing on foundational ideas, tools, and current topics in complex systems research. These include nonlinear dynamics and pattern formation, scaling theory, information theory and computation theory, adaptation and evolution, network structure and dynamics, adaptive computation techniques, computer modeling tools, and specific applications of these core topics to various disciplines. In addition, participants will formulate and carry out team projects related to topics covered in the school.
Further details about topics and faculty at each school will be posted
as they become available.
Eligibility
Applications are welcome from all countries. Participants are expected to attend one school for the full four weeks. All activities will be conducted in English at both schools. No tuition is charged, and some support for housing and travel expenses is available. Enrollment is limited.
Applications are solicited from graduate students and postdoctoral fellows in any discipline. Some background in science and mathematics (including multi-variate calculus and linear algebra) is required. Proficiency in English is also required.
Students should indicate school location preference when applying. Placements may be influenced by restrictions in U.S. foreign visitor policies.
Application Requirements
1. Current resume or CV. Include a clear description of your current educational or professional status, and a list of publications, if any.
2. A statement of your current research interests and comments about why you want to attend the school (suggested length: one to two pages).
3. Two letters of recommendation from scholars who know your work.
How to Apply
Online: Our online application form allows you to submit all of your materials electronically (including a feature which allows your recommenders to upload letters of recommendation directly to your file). We strongly encourage you to apply online to expedite your application.
Postal Mail/Courier: Applications sent via postal mail will also be accepted. Include a cover letter providing your e-mail address and fax number, and specifying whether you wish to be considered for a travel scholarship. (This will not influence the review of your application.) Do not bind your application materials in any manner. Send application materials to:
Summer Schools
Santa Fe Institute
1399 Hyde Park Road
Santa Fe, NM 87501 USA
If applying via post, letters of recommendation may be sent separately to the address above, or included in your application package in sealed envelopes.
DEADLINE
All application materials, including letters of recommendation, must be received at SFI or electronically submitted no later than January 7, 2008.
Women, minorities, and students from developing countries are especially encouraged to apply.
If you have further questions about the Complex Systems Summer Schools, please e-mail goodwin@santafe.edu
Thursday, December 13, 2007
Human Macroecology on Facebook
I've created the "Human Macroecology" group on Facebook to help us keep in contact. Join if you dare.
Friday, December 7, 2007
Island Rule Paper
Ok, I am admittedly way behind on this, as the paper I'm now blogging about came out over a week ago but given that we've posted about the Island Rule in here before, I'd feel remiss if we didn't cover a paper arguing that this well known rule from biogeography is a statistical artifact. If you are wondering why human ecologists should care about the Island Rule, that is also addressed in the previous post. So, this paper was published in the Proceedings of the Royal Society:
title: The island rule: made to be broken?
authors: Shai Meiri, Natalie Cooper, and Andy Purvis
abstract: The island rule is a hypothesis whereby small mammals evolve larger size on islands while large insular mammals dwarf. The rule is believed to emanate from small mammals growing larger to control more resources and enhance metabolic efficiency, while large mammals evolve smaller size to reduce resource requirements and increase reproductive output. We show that there is no evidence for the existence of the island rule when phylogenetic comparative methods are applied to a large, high-quality dataset. Rather, there are just a few clade-specific patterns: carnivores; heteromyid rodents; and artiodactyls typically evolve smaller size on islands whereas murid rodents usually grow larger. The island rule is probably an artefact of comparing distantly related groups showing clade-specific responses to insularity. Instead of a
rule, size evolution on islands is likely to be governed by the biotic and abiotic characteristics of different islands, the biology of the species in question and contingency.
So the issue in this and lots of studies that look at body size related trends is whether or not species can be treated as independent data points or whether adjustments have to be made for the phylogenetic relatedness of the species. That is, a bunch of species could exhibit a similar trend in something simply because they are closely related and if this is not adjusted for then we run the risk of identifying trends that we think are related to body size but are really just due to genetics/ancestry. Let's pretend that there are 3 camps on this issue - those that think you always have to adjust for phylogeny, those that think you have to sometimes, and those that think you never do. The authors of this paper would be in the first group, I would be in the second. Issues of statistical independence may indeed be under-appreicated in cross-species analysis of the sort common in biogeography and in studies of allometry. But as Jim Brown has pointed out (in informal lab-meeting type settings) it is not always clear exactly what things need to be controlled for in any given analysis. So, sure, for some things phylogeny might be the most important but in others it could be something like biome or some attribute of the niche that is occupied - or some general feature of ecology. There could potentially be a lot of uncontrolled confounds out there... How do we know which ones are most important, especially when we rarely have data on all of the potential variables we might want to examine?
So, this paper specifically argues that the trends that we think are behind the Island Rule are due to lineage specific responses to island colonization. That due to some issue of shared ancestry different but related species consistently respond similarly to island environments with respect to body mass change simply because they are related and not because of any general relationship between the mass of a colonizing organism and the island environment. The authors point out that none of the papers that have previously looked at the Island Rule have considered the role of phylogeny. After using methods that control for phylogeny, they state that:
"We did not find convincing evidence that larger size leads to insular size reduction within mammals in general (using independent contrasts) or within clades. Neither do we find that, as a rule, large mammals dwarf on islands nor that small mammals grow large..."
I'll also include a quote from their methods:
"We used only those studies that reported body size of mainland populations geographically closest to the island in question (Lawlor 1982). Some insular populations have their nearest
sister taxon on a mainland areawhich is a considerable distance away (e.g. Hafner et al. 2001). The paucity of good intraspecific phylogenetic data, however, precludes us from identifying the
closest relatives for most insular populations and we therefore use geographical distance to approximate phylogenetic affinity."
The issue of when we can and when we can't use species as data points won't be fully resolved any time soon. I'm sure that this paper will lead to some careful attention to this issue in the biogeographic community.
Cheers,
O
title: The island rule: made to be broken?
authors: Shai Meiri, Natalie Cooper, and Andy Purvis
abstract: The island rule is a hypothesis whereby small mammals evolve larger size on islands while large insular mammals dwarf. The rule is believed to emanate from small mammals growing larger to control more resources and enhance metabolic efficiency, while large mammals evolve smaller size to reduce resource requirements and increase reproductive output. We show that there is no evidence for the existence of the island rule when phylogenetic comparative methods are applied to a large, high-quality dataset. Rather, there are just a few clade-specific patterns: carnivores; heteromyid rodents; and artiodactyls typically evolve smaller size on islands whereas murid rodents usually grow larger. The island rule is probably an artefact of comparing distantly related groups showing clade-specific responses to insularity. Instead of a
rule, size evolution on islands is likely to be governed by the biotic and abiotic characteristics of different islands, the biology of the species in question and contingency.
So the issue in this and lots of studies that look at body size related trends is whether or not species can be treated as independent data points or whether adjustments have to be made for the phylogenetic relatedness of the species. That is, a bunch of species could exhibit a similar trend in something simply because they are closely related and if this is not adjusted for then we run the risk of identifying trends that we think are related to body size but are really just due to genetics/ancestry. Let's pretend that there are 3 camps on this issue - those that think you always have to adjust for phylogeny, those that think you have to sometimes, and those that think you never do. The authors of this paper would be in the first group, I would be in the second. Issues of statistical independence may indeed be under-appreicated in cross-species analysis of the sort common in biogeography and in studies of allometry. But as Jim Brown has pointed out (in informal lab-meeting type settings) it is not always clear exactly what things need to be controlled for in any given analysis. So, sure, for some things phylogeny might be the most important but in others it could be something like biome or some attribute of the niche that is occupied - or some general feature of ecology. There could potentially be a lot of uncontrolled confounds out there... How do we know which ones are most important, especially when we rarely have data on all of the potential variables we might want to examine?
So, this paper specifically argues that the trends that we think are behind the Island Rule are due to lineage specific responses to island colonization. That due to some issue of shared ancestry different but related species consistently respond similarly to island environments with respect to body mass change simply because they are related and not because of any general relationship between the mass of a colonizing organism and the island environment. The authors point out that none of the papers that have previously looked at the Island Rule have considered the role of phylogeny. After using methods that control for phylogeny, they state that:
"We did not find convincing evidence that larger size leads to insular size reduction within mammals in general (using independent contrasts) or within clades. Neither do we find that, as a rule, large mammals dwarf on islands nor that small mammals grow large..."
I'll also include a quote from their methods:
"We used only those studies that reported body size of mainland populations geographically closest to the island in question (Lawlor 1982). Some insular populations have their nearest
sister taxon on a mainland areawhich is a considerable distance away (e.g. Hafner et al. 2001). The paucity of good intraspecific phylogenetic data, however, precludes us from identifying the
closest relatives for most insular populations and we therefore use geographical distance to approximate phylogenetic affinity."
The issue of when we can and when we can't use species as data points won't be fully resolved any time soon. I'm sure that this paper will lead to some careful attention to this issue in the biogeographic community.
Cheers,
O
Wednesday, December 5, 2007
Next year's human ecology conference
The call for participation in next year's human ecology conference has just recently been announced. The theme for this meeting seems quite relevant for a lot of the things we've discussed this semester (and is also on something we didn't spend much time on) and I encourage interested parties to think about attending or even presenting. The conference proposes to focus on "Integrative thinking for complex futures: creating resilience in human-nature systems." The conference is the official meeting of the Society for Human Ecology. Information about the call for papers and the theme of the conference are posted in .pdf format.
cheers,
O
cheers,
O
Tuesday, December 4, 2007
New scaling paper: Organisms as 4 dimensional objects
A new paper has just been released as forthcoming in American Naturalist that takes a novel and curious approach to scaling in ecology and evolution. I'll elaborate on the paper below but first a bit of context:
We've talked some about scaling relationships and why they emerge but haven't gotten too much into the details of the theories attempting to explain why certain scaling properties exist. These fall into two camps, life history models that usually take certain extrinsic properties as givens and more complicated physical models that attempt to explain why metabolic rate is body mass to the 3/4 power from first principles of energetics and geometry. Examples of life history models predicting the allometries for traits like birth rate, mortality rate, age at first reproduction, and life span are those of Charnov (1991, 1993, 2001). These tend to take factors like the production function (growth rate is some constant a*mass^(3/4)) as a given and predict the other allometries, which tend to be +1/4 powers for times (life span, generation length, etc) or -1/4 powers for rates (birth rate, mortality rate, intrinsic rate of increase r, etc.). These models often have mortality rate as an external environmental parameter, but not always, and often take size at independence as a given (which is a linear function of adult mass and this predicts the -1/4 power scaling of fertility rate). One very successful geometric model is presented in West et al. (1997, 1999) and demonstrates that the 3/4 scaling of metabolic rate results from an optimal solution to the problem of efficiently constructing biological resource distribution networks that must deliver resources to all the cells in an organism while satisfying certain design characteristics. That is, the network should efficiently fill space and deliver resources to cells as effectively as possible. This problem generates a fractal distribution network that optimally fills space and generates a predicted 3/4 power of metabolic rate with mass. The 'networks' we are referring to in this context are vascular systems in plants and circulatory systems in animals. (This treatment is shockingly rudimentary but hopefully good enough for present purposes).
This paper by Lev Ginzburg and John Damuth takes a different view on scaling relationships in ecology by looking at the dimensionality of organisms. First, here's the citation info and abstract. I'll continue to comnent below.
The authors argue that organisms can literally be viewed as four dimensional objects, three spatial and one temporal. While many traits scale with body size, they specifically focus on the well-known finding that metabolic rate scales as the +3/4 power of body mass whereas lifespan goes as the +1/4 power. This makes the product of the two an isometric relationship (m3/4 x m1/4 = m1), such that a doubling in an organism’s size predicts a doubling in the energy it metabolizes in a lifetime. While many researchers take this as a consequence of other scaling relationships, it plays a fundamental role in the 4D view. As they state it, “these observations suggest instead that the scaling of lifetimes may reflect a fundamental manner in which organisms of all body masses are ecologically and evolutionarily functionally similar.” Thus the organism’s four dimensions, three spatial (length, area, volume) and one temporal (generation time) together give m1. If these four dimensions are evenly divided into the isometric scaling of lifetime metabolic rate then each will be m1/4. This predicts that metabolic rate should be m3/4 because energy is taken in through a 3D surface and then allocated to processes that take place in 4D (the dimension of time and within the 3 dimensional space of the organism). And if metabolic rate is m3/4, the remaining dimension, generation time (or lifespan), should be m1/4 to preserve the isometric scaling lifetime metabolic rate.
The role of generation time in ecology and evolution itself is another key component of the 4D argument: “Constructing one viable and reproductively capable daughter requires a certain duration (a “generation time”) that is conveniently viewed as an organism’s fourth dimension. So, on average, it takes a generation time of metabolism for a mother to guarantee the existence of her replacement.” This establishes the reasoning for why generation time is fundamentally an organism’s fourth dimension.
Where this argument becomes even less conventional is in the stated lack of a mechanism. In fact, my reading of the paper is that they intend the argument to predict the set of criteria to which any proposed mechanistic explanation of ¾ power scaling in biology must conform. For instance, they can predict that progressive reductions in dimensionality, by holding constant generation time, length, etc. should lead to predictable reductions in the exponent. So if generation time is held constant then they predict that metabolic rate should be a 2/3 power of mass, rather than ¾, and cite examples where within species metabolic rates have been shown to go as the 2/3 power of mass (if length and generation time are held constant, as with species of same size and lifetime, the scaling should be ½, etc.). They do this with multiple regressions. For instance, they predict that if height and generation length are controlled for, then metabolic rate should scale as the 1/2 power of mass and their data seem to conform to this prediction.
Because they do not suggest a mechanism, they are not necessarily at odds with any particular theory of metabolic scaling, such as that of the space-filling fractal geometry of supply networks in the circulatory and vascular systems of mammals and plants (e.g., West et al. 1999 - mentioned above). The explicitly non-mechanistic argument in the paper adds to its uniqueness but is also where some people may have the greatest trouble with the paper, as we are taught to focus on mechanisms and this nature of dimensional thinking is much more foreign to us (and maybe difficult to interpret at first). The theory makes simple and elegant predictions that should lead readily to either coherence or conflict with some of the existing takes on the topic (note that I'm saying the predictions are simple and elegant but am not saying anything about whether the empirical results are broadly accurate. Its of course too soon to see if how these predictions will weather the tests of time. They do give some good empirical support in the paper). Either way, dimensional thinking is a novel approach in this area that, when combined with the argument for the importance of generation time, makes a fundamental contribution to the literature and will certainly alter future approaches to the subject of scaling in ecology.
We've talked some about scaling relationships and why they emerge but haven't gotten too much into the details of the theories attempting to explain why certain scaling properties exist. These fall into two camps, life history models that usually take certain extrinsic properties as givens and more complicated physical models that attempt to explain why metabolic rate is body mass to the 3/4 power from first principles of energetics and geometry. Examples of life history models predicting the allometries for traits like birth rate, mortality rate, age at first reproduction, and life span are those of Charnov (1991, 1993, 2001). These tend to take factors like the production function (growth rate is some constant a*mass^(3/4)) as a given and predict the other allometries, which tend to be +1/4 powers for times (life span, generation length, etc) or -1/4 powers for rates (birth rate, mortality rate, intrinsic rate of increase r, etc.). These models often have mortality rate as an external environmental parameter, but not always, and often take size at independence as a given (which is a linear function of adult mass and this predicts the -1/4 power scaling of fertility rate). One very successful geometric model is presented in West et al. (1997, 1999) and demonstrates that the 3/4 scaling of metabolic rate results from an optimal solution to the problem of efficiently constructing biological resource distribution networks that must deliver resources to all the cells in an organism while satisfying certain design characteristics. That is, the network should efficiently fill space and deliver resources to cells as effectively as possible. This problem generates a fractal distribution network that optimally fills space and generates a predicted 3/4 power of metabolic rate with mass. The 'networks' we are referring to in this context are vascular systems in plants and circulatory systems in animals. (This treatment is shockingly rudimentary but hopefully good enough for present purposes).
This paper by Lev Ginzburg and John Damuth takes a different view on scaling relationships in ecology by looking at the dimensionality of organisms. First, here's the citation info and abstract. I'll continue to comnent below.
The Space‐Lifetime Hypothesis: Viewing Organisms in Four Dimensions, Literally
1. Department of Ecology and Evolution, Stony Brook University, Stony Brook, New York 11794;
2. Department of Ecology, Evolution and Marine Biology, University of California, Santa Barbara, California 93106
Abstract:
Much of the debate about alternative scaling exponents may result from unawareness of the dimensionality appropriate for different data and questions; in some cases, analysis has to include a fourth temporal dimension, and in others, it does not. Proportional scaling simultaneously applied to an organism and its generation time, treating the latter as a natural fourth dimension, produces a simple explanation for the 3/4 power in large‐scale interspecies comparisons. Analysis of data sets of reduced dimensionality (e.g., data sets constructed such that one or more of the four dimensions are fixed), results in predictably lower metabolic exponents of 2/3 and 1/2 under one and two constraints, respectively. Our space‐lifetime view offers a predictive framework that may be useful in developing a more complete mechanistic theory of metabolic scaling.
The authors argue that organisms can literally be viewed as four dimensional objects, three spatial and one temporal. While many traits scale with body size, they specifically focus on the well-known finding that metabolic rate scales as the +3/4 power of body mass whereas lifespan goes as the +1/4 power. This makes the product of the two an isometric relationship (m3/4 x m1/4 = m1), such that a doubling in an organism’s size predicts a doubling in the energy it metabolizes in a lifetime. While many researchers take this as a consequence of other scaling relationships, it plays a fundamental role in the 4D view. As they state it, “these observations suggest instead that the scaling of lifetimes may reflect a fundamental manner in which organisms of all body masses are ecologically and evolutionarily functionally similar.” Thus the organism’s four dimensions, three spatial (length, area, volume) and one temporal (generation time) together give m1. If these four dimensions are evenly divided into the isometric scaling of lifetime metabolic rate then each will be m1/4. This predicts that metabolic rate should be m3/4 because energy is taken in through a 3D surface and then allocated to processes that take place in 4D (the dimension of time and within the 3 dimensional space of the organism). And if metabolic rate is m3/4, the remaining dimension, generation time (or lifespan), should be m1/4 to preserve the isometric scaling lifetime metabolic rate.
The role of generation time in ecology and evolution itself is another key component of the 4D argument: “Constructing one viable and reproductively capable daughter requires a certain duration (a “generation time”) that is conveniently viewed as an organism’s fourth dimension. So, on average, it takes a generation time of metabolism for a mother to guarantee the existence of her replacement.” This establishes the reasoning for why generation time is fundamentally an organism’s fourth dimension.
Where this argument becomes even less conventional is in the stated lack of a mechanism. In fact, my reading of the paper is that they intend the argument to predict the set of criteria to which any proposed mechanistic explanation of ¾ power scaling in biology must conform. For instance, they can predict that progressive reductions in dimensionality, by holding constant generation time, length, etc. should lead to predictable reductions in the exponent. So if generation time is held constant then they predict that metabolic rate should be a 2/3 power of mass, rather than ¾, and cite examples where within species metabolic rates have been shown to go as the 2/3 power of mass (if length and generation time are held constant, as with species of same size and lifetime, the scaling should be ½, etc.). They do this with multiple regressions. For instance, they predict that if height and generation length are controlled for, then metabolic rate should scale as the 1/2 power of mass and their data seem to conform to this prediction.
Because they do not suggest a mechanism, they are not necessarily at odds with any particular theory of metabolic scaling, such as that of the space-filling fractal geometry of supply networks in the circulatory and vascular systems of mammals and plants (e.g., West et al. 1999 - mentioned above). The explicitly non-mechanistic argument in the paper adds to its uniqueness but is also where some people may have the greatest trouble with the paper, as we are taught to focus on mechanisms and this nature of dimensional thinking is much more foreign to us (and maybe difficult to interpret at first). The theory makes simple and elegant predictions that should lead readily to either coherence or conflict with some of the existing takes on the topic (note that I'm saying the predictions are simple and elegant but am not saying anything about whether the empirical results are broadly accurate. Its of course too soon to see if how these predictions will weather the tests of time. They do give some good empirical support in the paper). Either way, dimensional thinking is a novel approach in this area that, when combined with the argument for the importance of generation time, makes a fundamental contribution to the literature and will certainly alter future approaches to the subject of scaling in ecology.
Well, something to think about anyway.
Oskar
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