Dear Class,

            This outline is intended to be a guide through our talk.  Please print this out and bring it with you as a reference.  We believe it will help you keep track of the complex ideas we are presenting.  BTW, to be accurate in attribution… much of this text is direct quotation from personal communication with Jamie Gillooly.

Outline:
I. Scale: what it is and why it is important
A. Facts about scale
       - Life operates over vast scales of mass, time, and space

- Biological processes: ~40 orders of magnitude molecules and biochemical reactions global carbon cycle

        - Sizes of organisms: >1022 Mycoplasma ~10-13 g blue whale ~108 g, Sequoia ~109 g

        - Times/rates of biological activities: >1015 ATP cycling, nerve impulses: milliseconds        “lifetimes” of species: millions of years

 

How does variance scale?
At what scale do we need to examine ecological trends to formulate a unifying theory?      
       
II. The history of studying scale.
    A. 1920s: Julian Huxley and D’Arcy Thompson used allometric equations to describe growth            and form

            Y = Y0 Mb
            Y = independent variable: metabolic rate or lifespan
            Y0 = normalization constant

            M = body mass

            b = allometric exponent

      B. 1930s: Max Kleiber and Samuel Brody showed that whole-organism metabolic rate scales          as M (3/4) so differs from:

             isometric or linear: M1

             Euclidean or geometric: M2/3 (e.g., as surface area)

    C. 1980s:

       1. synthetic books by Peters, Calder, Schmidt-Nielsen, McMahon & Bonner showed        pervasiveness of quarter-power scaling:

                b is a simple multiple of 1/4

                M (3/4) - whole organism metabolic rate

                M (1/4) - most rates (e.g., mass-specific metabolic heart rate, population growth rate)

                M (1/4) - biological times (cell cycle time, lifespan)

        2. Fractal breakthrough:

-Self-similar:  means fractal-like over a wide span/range of temporal and spatial scales.  Extrapolation between this wide range can take place if structures and processes are found to be self similar.   

-self-similar large scale examples: globe, region, ecosystem or habitat where relationships are found to be complex 

-self-similar small scale examples: fields studies and/or laboratory settings 

 

-studying systems through the use of scaling can be a very powerful way of simplifying ecological complexity and can in turn infer principles that regulate biodiversity.   

                        Scaling for organisms= M3/4 (for the whole metabolic rate) 

Scaling for developmental time= M1/4 (for biological times i.e. Resource distribution) 

                        Scaling for max population growth= M-1/4         

 

E. 1990s: West, Enquist & Brown (1997, 1999): complete whole-system models for structure    and function of mammalian and plant vascular system.

            -Quarter powers reflect design of fractal-like resource distribution networks

“Because metabolism reflects both resource uptake from the environment and resource allocation to maintenance, growth and reproduction, it is possible to extend these models to account for the scaling of such ecological phenomena as population densities and growth rates of trees in forest stands (Equist et al. 1998,1999)."

        
What are some other examples of fractal geometry you have seen in your life or your science?

IV. The theory behind metabolic theory including predictions
    A. Theory
         -Metabolic rate is the most fundamental biological rate; it sets the pace of life

          - Rate of processing of energy and materials within an organism
           - Known for decades that metabolic rate is governed by two primary variables:

                1) body size: power law with quarter-power exponent due to fractal-like networks

                 2) temperature: exponential relationship due to kinetics of biochemical reactions

           -P = whole-organism metabolic rate
                  P = P0 M (3/4) exp (-E/kt)                   
                  B = mass-specific metabolic rate
                  B = B0 M -1/4) exp (-E/kt)
                  P0 and B0 = normalization constants
                  M = body mass
                  E = activation energy ≈ 0.65 eV
                  k = Boltzmann’s constant
                  T = temperature (in K)

-          Variation in ecosystems depends on the metabolic characteristics of the organisms that are present.

-          Variation among organisms, including life history and ecological roles is constrained by body size (allometry), operating temperature (biochemical kinetics), and chemical composition (stoichiometry). 

-          Variation in metabolism due to other factors (resource shortage, hibernation etc.) occur within the overarching constraints determined by body size, temperature and stoichiometry.

 

B. Basic Equations:

-          Whole-organism metabolic rate (I) = Constant (I0) * Body Mass (M)3/4

-          Or: Y = Y0Mb where Y is some dependent variable like population growth rate, rate of molecular evolution, M is mass and b is an allometric exponent.

-          Van’t Hoff-Arrhenius relation between temperature and chemical reaction rates:

            e-E/kt where E is activation energy, k is Boltzmann’s constant and T is temperature.

-          Combining the two equations you get the joint effects of body size and temperature on metabolic rate: Metabolic Rate (I) = Constant (I0) * Body Mass (M)3/4 e-E/kt

-          Can also solve this equation to get mass specific metabolism by dividing by M

-          Individual generation times and metabolic turnover times are the reciprocal of the individual rates, so that process per unit time becomes time per process.

 B. Predictions
        Temperature dependence
               1) plots of ln(P M^(-3/4)) and ln(P M^(1/4)) versus 1/kT will be linear
               2) slope will be –E, where E ≈ 0.65 eV
        Mass dependence
               1) plots of ln(B exp (E/kt)) versus ln(M) will be linear
               2) slope will be 3/4 for whole-organism and -1/4 for mass-specific rates
     
VI. Applications for the theory
    A. Organism:
      - embryonic development rate
       explaining residual variation

-       Development rates (time to hatching)

-       Explains mortality rates (ex in marine fish), possible hypotheses for why this is the case include cumulative effects of metabolism over time, or the fact that interactions that lead to death are governed by metabolic theory as well.



    B. Ecology:
       - structure and dynamics of forests
       - seeing the forests for the trees

-  Population growth rates of all kinds of organisms (because reproduction is fueled by metabolism).  Has implications for r and k selected species.

-       Population density:  Add a linear variable R to account for limiting resources. 

-       Interspecific Interactions: (no empirical examples) metabolic theory predicts the speed of competitive exclusion, parasitism rates, and predator attack rates.  This is explained because population growth is determined by metabolic rates.

-       Species diversity: varies inversely with body size.  Species richness also seems to related to environmental temperature via the Boltzmann constant (Allen et al 2002).  Hypothesis this is the case because diversity is a consequence of evolutionary processes (small/warm animals have faster dynamics than large/cool ones).

-       Potential problems with diversity relationship: a) inextricable from higher productivity with increasing temperature, and b) Why does faster rate of interspecific interaction result in more species?

-       Energy Flux and biomass production rates

-       Trophic dynamics

 

Thought Question: Is it valid to extend the metabolic theory to explain patterns in population and community dynamics?  Does it exclude too many relevant factors to be feasible/useful?

Evolution:
         rates of DNA nucleotide substitution reconciling the molecular clock with the

fossil record

Utility of the theory

-       Particularly good example of a true theory because it allows us to generate numerous predictions, and involves a low number of assumptions and parameters. 

-       Quite useful as a “null theory” that is capable of unifying/connecting questions that were previously thought to be independent. 

-       By exploring areas where the null theory fails we can gain insight into the true mechanisms that are at work. 

-       Cross-scale integration because temperature acts at molecular scale, body size at the organismal scale, and stoichiometry at the environmental scale. 

-       Depicts emergent properties of global aggregation of ecosystems, does not hold up as well at smaller scales of variation.  The fit is strong because tendencies are being averaged over broad-scale patterns, and idiosyncracies are blended out.  The utility in the theory comes from determining what causes the scatter 

-       Theory may be most useful for ecosystem ecology which is driven more by energy and nutrients and chemistry than community/population ecology. 

May be severely handicapped by the assumption that field metabolic rates are proportional to basal metabolic rates – need more empirical evidence of this according to

VII. Assumptions of the theory
            -network branches hierarchically to supply a three-dimensional body invariant terminal   units (e.g., capillaries, leaves) minimize energy expended
            -mass- and temperature-dependence follow our
            model:
            M^b exp (-E/kt)
            residual variation due to nutrient limitation

    - Because field metabolic rate is difficult to measure, it is typically assumed that it is about    2-3 times the basal metabolic rate 


VIII.  Problems with the theory

        "It seems an open question whether such widespread patterns reflect the operation of an interesting class of common mechanistic processes or just a large class of stochastic phenomena (Brown et al.2002)."

-        Won’t be a true metabolic theory of ecology because it can’t hope to account for many aspects of ecology such as behavior, stochastic variability, disturbance impacts, and food webs.  Specifically it tends to perform poorly in areas of interspecific interaction, and nonstable ecosystem dynamics/fluxes. Dynamics of natural populations are also driven by external factors. 

-       Theory needs to be tested on communities of organisms that actually live in the same environment since global allmoetric relationships include too many other sources of variability. 

-       Tilman: Strength of correlation between ecology process and body size diminishes as the range in body size decreases (see Fig. 1 in Tilman).  Thus “the variation that seems small when comparing bacteria to elevphants looms large when comparing beech trees to oaks”  Therefore, it is a scale issue, body size may be driving patterns on a very broad scale, but at smaller scale other factors are much more important in driving patterns.  “Perhaps when comparisons are made across larger body size ranges, the constraints of body size and its correlates increasingly predominate over the interspecific trade-offs in resource use, dispersal, and disease resistance that are more proximate determinants of species interactions and abundance. 

-       Ecological theory of everything not even possible because of dependence of all of ecology on the scale of the question being asked. 

-       Theory as phenomological (based on correlated patterns resulting from unknown causation) rather than truly mechanistic: 

a) Marquet argues that the equation is “statistical mechanical” meaning that it describes the properties of the molecules within the organism, (I think he means as opposed to the properties of the organism itself?)  Specifically the theoretical justification for using the Boltzmann constant to describe metabolism is weak due to the vast number of biochemical reactions involved. It is a statistical approximation rather than a mechanistic certainty. 

b) Cottingham: The derivation of the equation is not fleshed out satisfactorily.  She makes a few main points about this in her article. Specifically, the behavior of a chain of reactions is not usually best described by the sum, but rather the limiting reaction.  Also, different reactions have different mass-dependencies. 

- Kaspari: The theory ignores seasonal fluctuations that might matter when predicting densities.  (high latitude could have same productivity squeezed into a few months as an environment at lower latitutde that has that productivity spread over the whole year.) If respiration slows in winter, then area with winter with same NPP should be able to support more species because net respiration is lower. 

 -Pleiotropy can constrain optimization of physiological systems. 

 - Other problems described by Cottingham include: sexual dimorphism (how is average  body size determined, not to mention temperature and metabolic rate?)   Additionally the data suffer from lack of phylogenetic independence. 

- Cottingham also brings up again that they are focusing on steady-state averages and ignoring the temporal dynamics within organisms and ecosystems (not applicable to real world). 

-Kaspari (2004) points out that much of the data supporting MTE is taken from plant

data and he wonders about the lack of data concerning consumer abundance across global gradients. He also suggests that this is exclusively a bottom up threory. He also wonders if MTE can be applied to the seasonal variability related to the movement from equatorial to polar regions.

-Hawkins et al. (2007) note the number of abiotic limitations (eg. water deficit regions,  regions with limited temperature variability)

-Log transformation of orders of magnitude that can create large variances.