Metabolic theory and ecological scaling Geoffrey WestJames Brown Brian Enquist.

Slides:



Advertisements
Similar presentations
Statistical Mechanics and Evolutionary Theory
Advertisements

Correlation and regression
Networks and Scaling.
Data Handling & Analysis Allometry & Log-log Regression Andrew Jackson
By Melissa Jayne and Linda Rocha. Internal heat production through metabolism Examples and Birds Mammals.
Latitudinal gradients Species – latitude relationship of birds across the New World show the typical pattern of increased species diversity towards the.
Experimental design and analysis Multiple linear regression  Gerry Quinn & Mick Keough, 1998 Do not copy or distribute without permission of authors.
Irwin/McGraw-Hill © Andrew F. Siegel, 1997 and l Chapter 12 l Multiple Regression: Predicting One Factor from Several Others.
Community and gradient analysis: Matrix approaches in macroecology The world comes in fragments.
Metabolic scaling in plants Frances Taschuk February 25, 2008 Frances Taschuk February 25, 2008.
FTP Biostatistics II Model parameter estimations: Confronting models with measurements.
Biodiversity of Fishes Death in the Sea Understanding Natural Mortality Rainer Froese GEOMAR
Regression Analysis Module 3. Regression Regression is the attempt to explain the variation in a dependent variable using the variation in independent.
Turning Point At the beginning of the course, we discussed three ways in which mathematics and statistics can be used to facilitate psychological science.
The Structure, Function, and Evolution of Biological Systems Instructor: Van Savage Spring 2010 Quarter Biomath 202.
Patterns in time Population dynamics (1964 to 1983) of the red squirrel in 11 provinces of Finland (Ranta et al. 1997) Lynx fur in Canada Voles in Norway.
How do diversity and stability depend on productivity? The relation between plant species diversity and productivity at a continental scale Australian.
The exponential function is a general description of a random process, where the probability of a certain event is independent of time C 0 /2 C 1 /2 C.
How closely do real biological systems fit these ideal fractal networks of West, Brown, and Enquist? or… great moments in scientific discourse as read.
What if animals were fractals? University of Utah ACCESS 2009.
Topics: Regression Simple Linear Regression: one dependent variable and one independent variable Multiple Regression: one dependent variable and two or.
Scaling Exponent: 2/3 or 3/4? B=aM^b. Scaling Exponents Should it be 2/3 or 3/4? (theoretical controversy) Is it 2/3 or 3/4? (empirical controversy) How.
Allometric exponents support a 3/4 power scaling law Catherine C. Farrell Nicholas J. Gotelli Department of Biology University of Vermont Burlington, VT.
REPRESENTING SIMPLE HARMONIC MOTION 0 not simple simple.
Ch. 14: The Multiple Regression Model building
Biological scaling theory and effects on populations By Van Savage Department of Systems Biology Harvard Medical School Santa Fe CSSS, 2007.
Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. More About Regression Chapter 14.
Lectures 4a,4b: Exponential & Logarithmic Functions 1.(4.1) Exponential & Logarithmic Functions in Biology 2.(4.2) Exponential & Logarithmic Functions:
Metabolism Chapters 5-7.
3. Multiple Regression Analysis: Estimation -Although bivariate linear regressions are sometimes useful, they are often unrealistic -SLR.4, that all factors.
Dynamic Energy Budget Theory - V Tânia Sousa with contributions from :Bas Kooijman with contributions from :Bas Kooijman.
THE METABOLIC THEORY OF ECOLOGY WITHIN STREAM ECOSYSTEMS This research proposal has been funded by the NSF Bioinformatics Postdoctoral Fellowship. The.
METR and 13 February Introduction What is thermodynamics? Study of energy exchange between a system and its surroundings In meteorology,
1 FORECASTING Regression Analysis Aslı Sencer Graduate Program in Business Information Systems.
Biology I.  Biology offers a framework to pose and answer questions about the natural world.  What do Biologists study?  Questions about how living.
Models and Algorithms for Complex Networks Power laws and generative processes.
Energetic barriers of Ecological Systems
Examining Relationships in Quantitative Research
1 Chapter 12 Simple Linear Regression. 2 Chapter Outline  Simple Linear Regression Model  Least Squares Method  Coefficient of Determination  Model.
Copyright © 2011 Pearson Education, Inc. The Simple Regression Model Chapter 21.
Y X 0 X and Y are not perfectly correlated. However, there is on average a positive relationship between Y and X X1X1 X2X2.
MATHEMATICAL PROCESSES SPI  I can generate ratios to solve problems involving velocity, density, pressure, and population density.
Discussion of time series and panel models
Copyright ©2011 Brooks/Cole, Cengage Learning Inference about Simple Regression Chapter 14 1.
Business Statistics: A Decision-Making Approach, 6e © 2005 Prentice-Hall, Inc. Chap 13-1 Introduction to Regression Analysis Regression analysis is used.
Copyright © 2014, 2011 Pearson Education, Inc. 1 Chapter 21 The Simple Regression Model.
Mortality over Time Population Density Declines through Mortality.
Copyright ©2006 Brooks/Cole, a division of Thomson Learning, Inc. More About Regression Chapter 14.
Ludwid Boltzmann 1844 – 1906 Contributions to Kinetic theory of gases Electromagnetism Thermodynamics Work in kinetic theory led to the branch of.
Introduction to Kinetics Lecture 14. Reading in Chapter 5 Read sections 5.1 through (p.160 to p. 199) and section 5.7 (p ). We will probably.
Regression Analysis1. 2 INTRODUCTION TO EMPIRICAL MODELS LEAST SQUARES ESTIMATION OF THE PARAMETERS PROPERTIES OF THE LEAST SQUARES ESTIMATORS AND ESTIMATION.
Live fast, Die Young? Theory-higher metabolism means a shorter lifespan 1920s proposed aging is a by-product of energy expenditure Hence faster you use.
Simple linear regression. What is simple linear regression? A way of evaluating the relationship between two continuous variables. One variable is regarded.
Chapter 4 More on Two-Variable Data. Four Corners Play a game of four corners, selecting the corner each time by rolling a die Collect the data in a table.
Ch. 12 The Behavior of Gases Ch The Properties of Gases Ch Factors Affecting Gas Pressure Ch The Gas Laws Ch Ideal Gases Ch
Delay-difference models. Readings Ecological Detective, p. 244–246 Hilborn and Walters Chapter 9.
Chapter 11 Linear Regression and Correlation. Explanatory and Response Variables are Numeric Relationship between the mean of the response variable and.
Sustainable Urban Energy Systems A Science of Cities Approach Lorraine Sugar PhD Candidate, University of Toronto ONSEP 2016.
Review/Theory on Kinetics and Reactors
Chapter 2: Measurements and Calculations
FW364 Ecological Problem Solving Class 6: Population Growth
Olivier Maury, Olivier Aumont, Jean-Christophe Poggiale
OFF THE SHOULDERS OF GIANTS:
Biodiversity of Fishes Death in the Sea Understanding Natural Mortality Rainer Froese GEOMAR
Regression Analysis Week 4.
SIMPLE LINEAR REGRESSION
Linear Regression and Correlation
Linear Regression and Correlation
Regression Part II.
MGS 3100 Business Analysis Regression Feb 18, 2016
Presentation transcript:

Metabolic theory and ecological scaling Geoffrey WestJames Brown Brian Enquist

The grand idea of scaling theory is that animal and plant branching systems and tissues are self similar. They are assumed to have a fractal structure. Kleiber’s rule In the Euclidean case A  V 2/3 Metabolic rate is proportional to tissue surface area Animal or plant body weight is proportional to body volume

A textbook example for Kleiber’s rule Hemmingson classic plot of metabolic rate against body size. Each regression line has a slope of 3/4

How to derive Kleiber’s rule? The second grand idea of Brown, West and Eberhard is that life during evolution optimized the relation between tissue surface and volumen to get maximum energetic efficiency at a given body volume (size). WBE proposition The optimization argument is still heavility disputed. Recent analysis rather point to rather complex relationships between tissue surface and volume. The ¾ power function is then only a rough approximation.

Metabolism and temperature E a = Activation energy k = Jmol -1 K -1 T = absolute temperature A = Proportionality factor The Arrhenius equation holds approximatily for most enzymatic processes. E a is often not a constant but related to the square root of T Temperature [K] k

The basic equation of metabolic theory M: metabolic rate M 0 : basal metabolic rate W: body weigth E a : Mean activation energy for biochemical reactions k: Boltzmann factor: Jmol -1 K -1 = eVK -1 Andrew Allen Adding the concentration of an assumed limiting resource gives The activation energy can be estimated from plots of M against W (at constant temperature) or from plots of M against 1/T for species of similar body size E a takes values from 0.6 to 0.7 eV with a mean of 0.65 eV = 62693Jmol -1 -E a /k = 0.65/ = 7541K James Gillooly

The basic assumption of metabolic theory Living organsims are composed of fractal networks Evolution operated as to optimize energetic efficiency Limiting constraints operate in a multiplicative manner Parameter values are whole organism means are fairly constant Body weight is independent of temperature Parameters are not functions of the amounts of resources available. The theory cannot explain why animals of the same size can have strikingly different metabolic rates and lifespan. Kleiber’s law holds even for organisms without fractal networks.

Empirical support The temperature corrected metabolism – weight relation From Brown et al. (2004), Ecology 85:

It is now easy to derive other relationships that involve basic ecological variables: Abundance: Take the the expression MN as the total metabolism of of a population of size N. At equilibrium (dN/dt = 0) the product NM must be constant (NM = c) that is total resource use remains stable. Hence Hence at stable temperature metabolic theory predicts that abundance scales to body weight to a power of -3/4. From Brown et al. (2004), Ecology

The energy equivalence rule The product NM is the total amount of energy use of the whole population of size N. In poikilothermes and plants NM is a proxi to population biomass. The equal biomass hypothesis

Ontogenetic growth Assume multicellular animals (or plants) where energy is transported through a network of branches. The total energy can be expressed as the sum of the energy need to maintain the existing cells plus the energy needed to create new cells. N is the total number of cells at time t, M is energy demand. M total is the total energy needed w is the ontogenetic mass and w cell the mean cell mass.

Body weight corrected developmental times should exponentially decrease with increasing environmental or body temperature Temperature corrected developmental times should scale to body weight to a power of ¼.

Biological times should scale to body weight to the quarter power Examples: Generation time, lifespan, age of maturation, average lifetime of a species The inverse of time are rates. Examples: Growth rates, mutation rates, species turnover rates, migration rates Hence biological rates should scale to body weight and temperature by The slope –E/k is predicted to be about For a slope –E/k of about E should take a value of 0.95eV.

Criticisms Living organims are not or at least not in total fractals. The derivation of the ¾ scaling rule is mathematically flawed. The ¾ scaling rule has no empirical justification. The Arrhenius temperature term is much too simplified and the parameters are poorly defined. More important than universal scaling is the variability in metabolism. The theory predicts average scaling rates but does not account for the oberserved variance in scaling relationships. The variablility of living organisms prohibits any useful predictions from the theory. In other words, even if the thory is correct it does not tell much about the functioning of real world ecological systems.

Slopes of metabolic rate – body weight relationships of different taxonomic groups scatter around There is no single slope for all taxa. Data from Peters 1983.

Cell size theory (Kozłowski et al. 2003) Total body weight is the product of mean cell size W cell and its number n Cell metabolic rate scales allometrically to cell size Upper boundary: If body size increases solely due to the increase in the number of cells we get Lower boundary: If body size increases due to the increase in cell size we get z < 1 The theory predicts Metabolic rate should scale allomtrically to body weight The scaling exponent should be less than 1 If cell metabolic rate is proportional to cell surface then z = 2/3 2/3 < z < 1

Major criticism The theory uses species as as major driver in evolution. Cells have a fractal nature. Hence the lower slope boundary should be The theory applies only to taxa with large differences in cell size like mammals. The theory does not explain scaling intercepts. The theory does not explain scaling in plants and invertebrates.

Brown, J. H., Gillooly J. H., Allen A. P., Savage V. M., West G. B., 2004, Towards a metabolic theory of ecology. Ecology 85: Ecology’s big, hot idea: Today’s reading