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3 Some Examples of Optimality Models (formal or informal) Applied to Biology:

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Page 1: 1 Lecture 20 Optimality and Symmorphosis. 2 1.Comparisons of Species (or populations) = "The Comparative Method“ Shows what has happened in past evolution

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Lecture 20Optimality andSymmorphosis

Page 2: 1 Lecture 20 Optimality and Symmorphosis. 2 1.Comparisons of Species (or populations) = "The Comparative Method“ Shows what has happened in past evolution

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1. Comparisons of Species (or populations)= "The Comparative Method“

Shows what has happened in past evolution2. Biology of Natural Populations

Shows present evolution in action3. Selection Experiments

Shows, experimentally, what might happen during future evolution

4. Comparison of Real Organisms withPredictions of Theoretical Models

Shows how close selection can get to producing optimal solutions

Four General Approaches to Studying Evolution:

Page 3: 1 Lecture 20 Optimality and Symmorphosis. 2 1.Comparisons of Species (or populations) = "The Comparative Method“ Shows what has happened in past evolution

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Some Examples of Optimality Models (formal or informal) Applied to Biology:

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Bird Wing Shapes:

http://www2.unil.ch/biomapper/opengl/Bird_wing_types.gif

Lots of interest, lots of data (including informal observations), lots of models due to out interest in human flying machines.Nice resource:http://people.eku.edu/ritchisong/554notes3.html

http://i.bnet.com/blogs/bird-plane.jpg

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Bird Wing Shapes:As many as 7 Basic Wing Shapes and Arrangements have

been recognized, and they seem to represent evolutionary adaptations for different flying styles:

short, broad, cupped wings for rapid takeoff and short-distance flight;

shorter and broader wings with slotted primary feathers for soaring flight;

flat moderately long, narrow, triangular wings for high-speed flight;

large, distinctly arched wings for flapping flight; long, narrow, flat pointed wings for gliding flight; pointed, swept-back wings for hovering or motionless flight

http://www.paulnoll.com/Oregon/Birds/flight-shape.html

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Four Common Wing Shapes in Birds

http://www.birds.cornell.edu/education/kids/books/wingshapes

Passive Soaring(Bald Eagle)

High-speed (Forster's Tern)

Active Soaring(Calif. Gull)

Elliptical - good forshort bursts of high speed (Common Raven)

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Optimality Models (formal or informal) can be useful in biology, but in general …

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Organisms are not optimal!

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Why Organisms are not Optimal:1. Organisms are not "designed;"

natural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Although engineers have final goals and purposes, natural selection does not.Moreover, engineers often design for a single purpose, whereas organisms must do many things, not just one.Jared Diamond has used the analogy of elevators to consider what he likes to call "safety factors."

You can show that freight elevatorshave lower safety factors -- smallercables -- than do passenger elevators.

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Safety factors of some engineered structuresCable of fast passenger elevator 11.9Cable of slow passenger elevator 7.6Cable of slow freight elevator 6.7Wooden building 6.0Cable of powered dumbwaiter 4.8Steel building or bridge 2.0

Diamond, J. M. 1993. Evolutionary physiology. Pages 89-111 in C. A. R. Boyd and D. Noble, eds. The logic of life: the challenge of integrative physiology. Oxford University Press, Oxford.

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This analogy is spurious because although elevators may only carry one thing, such as freight, and be designed for that purpose alone, organisms are different.Human "elevators" not only carry freight, they also carry people (including during pregnancy).In addition, they feed themselves, grow, repair themselves, avoid becoming food, mate, and raise offspring.

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What if functional demands on a given structure conflict?Can it be "optimally" designed in any meaningful sense?Think about skin …

Lindstedt, S. L., and J. H. Jones. 1987. Symmorphosis: The concept of optimal design. Pages 289-309 in M. E. Feder, A. F. Bennett,W. W. Burggren, and R. B. Huey, eds. New directions in ecological physiology. Cambridge Univ. Press, New York.

Should skin be designed optimally for gas exchange, temperature regulation, regulation of vitamin D, exteroception, osmoregulation, crypsis, as a barrier to infection, protection from physical assaults, or rapid healing from wounds?

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Think about the lung …

Should the lung be designed optimally foruptake of O2, elimination of CO2, temperature regulation, vocalization, resistance to infection, resistance to particulates, or rapid healing?

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Another way to view excess capacities:

Gans, C. 1979. Momentarily excessive construction as the basis for protoadaptation. Evolution 33:227-233.

"Why should phenotypes be overdesigned?Statements that such overdesign represents a 'factor of safety' (cf. Kummer, 1959) hardly explain its origin.In any case they implytechnological planningor prescience and shouldprobably be discouraged."(Gans, 1979, p. 227)

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"... for most individual organisms the structural and physiological capacities are likely to be excessive for the needs of any particular moment.Obviously, natural selection does not 'look' just at an organism's momentary utilization of each aspect of the phenotype,but at the requirements imposed on all phenotypic aspects of an individual throughout its life span."

(Gans, 1979, p. 227)

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Although engineers can start from scratch, natural selection cannot.Selection works with pre-existing materials, whatever a species happened to inherit from its ancestors.And these may not be the best possible materials for a particular function.Thus, relatively severe "constraints" are placed on living systems.If an engineer wants to build a shell out of titanium, to maximize strength while minimizing mass, they can.

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But selection cannot do that with, say, tortoises, because a mutation conferring the ability to produce titanium apparently has never occurred during the course of life on this planet.Similarly, as compared with natural materials, engineers can make artificial joints and heart valves that last far longer than tissues and are not susceptible to disease.

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what

selection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Often for simplicity, most optimality models are phrased in terms of energy as the common currency, and the "goal" of selection is seen as minimizing energy costs, maximizing energy gain or maximizing energetic efficiency (gain/cost).But we have little empirical evidence that this is what selection actually tends to do.

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Moreover, what matters in evolutionary models is relative fitness -- how good one individual is as compared with others in its population -- not absolute fitness measured against some external scale.

To escape from a predator,you only have to run faster thanthe guy next to you …

Thus, selection generally leads to adequacy or sufficiency, not necessarily optimality.

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"In spite of occasional statements to the contrary, there can be little argument that natural selection is unlikely to be a mechanism for generating perfection in individual animals. ... that the structure of an animal allows [it] to perform particular actions, highly advantageous under a particular set of circumstances, does not require perfect matching, but only adequacy ..."

(Gans, 1983, pp. 101-102)Gans, C. 1983. On the fallacy of perfection. Pages 101-112 in R. R. Fay and G. Gourevitch, eds. Perspectives on modern auditory research. Amphora Press, Groton, Connecticut.

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Selection cannot change organisms very rapidly, for 3 reasons:1. if selection is too strong, then population size will be reduced such that extinction by demographic stochasticity is likely;2. the narrow-sense heritability of traits is usually far less than 1.00;3. genetic correlations with other traits, e.g., caused by pleiotropy, will "constrain" the organismal response to selection.Quantitative genetics clearly indicates that evolution often will fail to keep pace with the rate of environmental change.

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Even if selection could generally track typical rates of environmental change,it cannot anticipate major environmental changes, such as asteroids hitting the earth, severe droughts, "100-year floods"or even the invasion of a population by some new pathogenic organism, such as HIV (which causes AIDS) in the human population.Thus, what is "optimal" now may soon not be.Today's adaptation is tomorrow's constraint:

specialization is often an evolutionarydead end.

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Random genetic drift operates in all populations that are of less than infinite size -- which means all populations.Both theoretical and empirical studies suggest that random drift is often strong enough to counter selection.Thus, drift alone should ensure that average values for populations or species are rarely if ever at the optimum dictated by selection.

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You can think of the interplay between selection and drift with the following analogy.Imagine the population's mean phenotype as a billiard ball on a pool table with a lumpy surface.Selection is a pool cue that aims the population's mean phenotype at a particular pocket, but drift is the lumpy surface which makes it go off course.But, if the cue hits the ball with enough force, it may get there anyway.

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Another analogy is an unbalanced bowling ball.The bowler may throw it straight down the alley towards the pins, but the unbalance, as genetic drift, will often make it not go straight to the center pin.

Genetic drift is a key element of Sewall Wright's shifting balance theory of evolution, in which drift is argued to often push populations temporarily in the direction of lower fitness.

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32http://evolutionarysystemsbiology.org/intro/index.html

Under the action of natural selection alone, populations often might get stuck on local optima (never make it to the highest peak).

Drift can allow them to "explore" valleys on the adaptive landscape.

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http://www.sdbonline.org/fly/lewheldquirk/1.2.jpg

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly8. Sexual selection counters natural selection8. Sexual selection counters natural selection

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Natural& Sexual Selection

BehaviorAct On

Organismal Performance

Abilities

Constrain

Morphology,Physiology,Biochemistry

Deter- mine

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Figure 3 (page 257) from D. J. Futuyma. 1986. Evolutionary biology. 2nd. Ed. Sinauer Associates, Sunderland, Massachusetts.

The Dipper:example of an organism in which a behavior, diving to forage, seems to have evolved more rapidly than underlying morphological and physological traits that might enhance the ability to dive.

Cinclus mexicanus

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"In the case of the water ouzel, the acutest observer by examining its dead body would never have suspected its subaquatic habits. ... In such cases, and many others could be given, habits have changed without a corresponding change of structure."

Charles Darwin, in The Origin of Species, Ch. 6

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Maybe a penguin is close to optimally adapted for underwater foraging (at the cost of greatly reduced abilities for terrestrial locomotion), but even penguins still reproduce and lays eggs on land, and have not reevolved gills.

… hard to argue that the dipper is optimally designed for its current behavior.

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Quotes about behavior as an evolutionary pacemaker:

Ernst Mayr & others (1904-2005)

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"A shift into a new adaptive zone is, almost without exception, initiated by a change in behavior …other adaptations to the new niche, par ticularly the structural ones, are acquired secondarily (Mayr 1958, 1960).With habitat and food selection - behavioral phenomena - playing a major role in the shift into new adaptive zones,

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the importance of behavior ... is self- evident. ...Most shifts into new ecological niches are, at first, unaccompanied by structural modifications (Robson and Richards 1936)."(Mayr, 1963, p. 604)

Ernst Mayr in 1994, after receiving an honorary degree at the University of Konstanz.

Mayr, E. 1963. Animal species and evolution. The Belknap Press of Harvard Univ. Press, Cambridge, Mass. 797 pp.

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"Many if not most acquisitions of new structures in the course of evolution can be ascribed to selection forces exerted by newly acquired behaviors (Mayr, 1960).Behavior, thus, plays an important role as the pacemaker of evolutionary change.Most adaptive radiations were apparently caused by behavioral shifts." (Mayr, 1982, p. 612)

Mayr, E. 1982. Systematics and the origin of species. Columbia Univ. Press, New York. 334 pp. Columbia Classics in Evolution Series.

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"... when a major environmental shift occurs, natural selection should initially favor compensatory changes in behavior ..." (Huey and Bennett, 1987, p. 1098)"These results indicate that rather striking differences in ecology and behavior may be accompanied by modest differences in physiology." (Taigen and Pough, 1985, p. 991)"Indeed, behavior is in the vanguard of evolution."(Plomin, 1990, p. 183)"It has often been said that behavior is one of the most labile traits in animal evolution. Whether this is so remains to be demonstrated..." (Bush, 1986, p. 1)

Bush, G. L. 1986. Evolutionary behavior genetics. Pages 1-5 in M. D. Huettel, ed. Evolutionary genetics of invertebrate behavior, progress and prospects. Plenum Press, New York. 335 pages.

Huey, R. B., and A. F. Bennett. 1987. Phylogenetic studies of coadaptation: preferred temperatures versus optimal performance temperatures of lizards. Evolution 41:1098-1115.

Plomin, R. 1990. The role of inheritance in behavior. Science 248:183-188.

Taigen, T. L., and F. H. Pough. 1985. Metabolic correlates of anuran behavior. American Zoologist 25:987-997.

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Why Organisms are not Optimal:1. Organisms are not "designed;"1. Organisms are not "designed;"

natural selection is not engineeringnatural selection is not engineering2. Biological materials have limitations2. Biological materials have limitations3. Energetic efficiency is not necessarily what3. Energetic efficiency is not necessarily what

selection maximizesselection maximizes4. Environments often change too rapidly4. Environments often change too rapidly5. Selection cannot anticipate5. Selection cannot anticipate6. Genetic drift operates in all populations6. Genetic drift operates in all populations7. Behavior evolves too rapidly7. Behavior evolves too rapidly8. Sexual selection counters natural selection

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Sexual selection by male-male competition for access to females, or by female choice of particular males, can cause the evolution of bizarre structures and behaviors.

Extinct"IrishElk"

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Among these species of tragopan's, males vary, but females are similar and presumably adapted for crypsis, etc. The females may be relatively close to the "optimum" dictated by natural selection.However, the males of these closely related species are thought to have diverged and speciated non-adaptively by sexual selection. Some of their external traits may even be disadvantageous from the standpoint of natural selection. Note the amazing colors on the next slide, which may be relatively easy for a potential predator to see!

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Note the amazing colors of the males (but not the female), which may be relatively easy for a potential predator to see!

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Sexual selection can even work in direct opposition to natural selection, because it is a largely independent process.

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In summary, we may not generally expect organisms to be optimal.Nevertheless, optimality models can be useful tools for understanding the "design"* of biological systems, as they provide a sort of measuring stick or frame of reference.

* Note that use of the word "design" here does NOT imply any sort of "intelligent design," which is a form of creationism. "Design" in the present context is simply a common and convenient shorthand for "how organisms work." Biologists understand that organisms came to be they way they are, and work the way they do, by a number of evolutionary processes, including natural selection, sexual selection, and random genetic drift. As noted above, they were not "designed" by anything. Scientists attempt to formulate testable hypotheses about how organisms work and how they have evolved. Intelligent design and creationism are not scientific theories and do not attempt to formulate testable hypotheses. They are based on faith and are generally outside the scope of scientific discourse or the scientific method.

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Optimality models can indicate the best that organisms could be, given some explicit assumption of a design criterion and specified constraints; in other words, one end of a continuum (a frame of reference)Even if we don't believe organisms are likely to be optimal, it is useful to know what an optimal organism would be like.

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Establishing the hypothetical best possible can facilitate quantitative tests of the degree of departure from perfect design. Symmorphosis is an informal optimality model, so it may be useful for understanding how and why organisms work the way they do.

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Weibel, E. R., and C. R. Taylor, eds. 1981. Design of the mammalian respiratory system. Respiration Physiology 44:1-164.

Symmorphosis

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Taylor, C. R., and E. R. Weibel. 1981. Design of the mammalian respiratory system. I. Problem and strategy. Respiration Physiology 44:1-10.Passage from page 3:

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Weibel, E. R., and C. R. Taylor, eds. 1981. Design of the mammalian respiratory system. Respiration Physiology 44:1-164.Passage from pages 151-152:

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Weibel, E. R., C. R. Taylor, and L. Bolis, eds. 1998. Principles of animal design: the optimization and symmorphosis debate. Cambridge University Press, Cambridge, U.K. xx + 314 pp.

Weibel, E. R. 2000. Symmorphosis: on form and function in shaping life. Harvard Univ. Press, Cambridge, Mass. xiii + 263 pp.

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Symmorphosis is based on an old idea in biology:"The principle of symmorphosis assumes that animals incur a selective penalty for maintaining structures in 'excess' of the immediate demand.This idea, implied by Aristotle and Cuvier, was explicitly stated by Darwin in The Origin of Species (1959):'... natural selection will tend in the long run to reduce any part of the organism, as soon as, through changed habits, it becomes superfluous."

(Lindstedt and Jones, 1987, p. 290)Lindstedt, S. L., and J. H. Jones. 1987. Symmorphosis: The concept of optimal design. Pages 289-309 in M. E. Feder, A. F. Bennett,W. W. Burggren, and R. B. Huey, eds. New directions in ecological physiology. Cambridge Univ. Press, New York.

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This idea was also mentioned by Bennett and Ruben (1979, p. 651) in their original paper on the aerobic capacity model for the evolution of endothermy:

"It is reasonable to assume, however, that these coevolved transport and utilization systems will not differ greatly from each other within an individual animal in their capacity for oxygen processing."

Bennett, A. F., and J. A. Ruben. 1979. Endothermy and activity in vertebrates. Science 206:649-654.

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How might we test the general validity of symmorphosis?Pick a physiological system.Determine how much excess capacity (if any) is present.Compare lots of species

(or individual with species).Does symmorphosis apply always, most of the time, rarely or never?

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59Garland, T., Jr. 1998. Testing the predictions of symmorphosis: conceptual and methodological issues. Pages 40-47 in E. R. Weibel, L. Bolis, and C. R. Taylor, eds. Principles of animal design: the optimization and symmorphosis debate. Cambridge University Press, New York.

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60Garland, T., Jr. 1998. Testing the predictions of symmorphosis: conceptual and methodological issues. Pages 40-47 in E. R. Weibel, L. Bolis, and C. R. Taylor, eds. Principles of animal design: the optimization and symmorphosis debate. Cambridge University Press, New York.

Note that symmorphosis does not suggest the throughout capacity of a given physiological system should always be high, only that, whatever the throughput capacity, no excess capacity should be present at any step. Hence, the system on the right can be considered highly symmorphotic, even though it has low capacity.

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If we did the foregoing analysis for lots of species, then we might find most of them are nearly optimal.

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Or not.

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This sort of an extensive survey has not been done, so we do not know how well symmorphosis (or any other optimality model) describes biological diversity.

Following is a reanalysis of the original data that were presented to test symmorphosis:Garland, T., Jr., and R. B. Huey. 1987. Testing symmorphosis:

does structure match functional requirements?Evolution 41:1404-1409.

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Using the original data of Taylor, Weibel, and collaborators, Garland and Huey (1987) found no matching at the level of: 1. scaling slopes (A & B) 2. family deviations (A vs B) 3. residual (species) correlations (C).

Symmorphosis is not supported.

Slope = 1.025

ANCOVASlope = 0.833

Slope = 0.787

Residuals(from ANCOVA lines in A)r = 0.061

P = 0.821

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Symmorphosis would predict that all of these traits (residuals from log-log regressions on body mass) should be positively correlated, but they are not.

Garland, T., Jr., and R. B. Huey. 1987. Testing symmorphosis: does structure match functional requirements? Evolution 41:1404-1409.

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Extra Slides Extra Slides FollowFollow

Garland, T., Jr., and P. A. Carter. 1994. Evolutionary physiology. Annu. Rev. Physiol. 56:579-621.Garland, T., Jr. 1998. Testing the predictions of symmorphosis: conceptual and methodological issues. Pages 40-47 in E. R. Weibel, L. Bolis, and C. R. Taylor, eds. Principles of animal design: the optimization and symmorphosis debate. Cambridge University Press, New York.Garland, T., Jr., and R. B. Huey. 1987. Testing symmorphosis: does structure match functional requirements? Evolution 41:1404-1409.Dudley, R., and C. Gans. 1991. A critique of symmorphosis and optimality models in physiology. Physiol. Zool. 64:627-637.Lindstedt, S. L., and J. H. Jones. 1987. Symmorphosis: The concept of optimal design. Pages 289-309 in M. E. Feder, A. F. Bennett, W. W. Burggren, and R. B. Huey, eds. New directions in ecological physiology. Cambridge Univ. Press, New York.Rosen, R. 1967. Optimality principles in biology. Butterworths, London. 198 pp.Weibel, E. R., C. R. Taylor, and H. Hoppeler. 1991. The concept of symmorphosis: A testable hypothesis of structure-function relationship. Proc. Natl. Acad. Sci. USA 88:10357-10361.

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Slide 42: Stopped here 10 Feb. 2009, but gave entire lecture in one period in 2011

Slide 43: Start here 12 Feb. 2009

In Spring 2012, this lecture was about 20 minutes short.

In Winter 2014, this lecture was about 15 minutes short.

Add examples of other optimality models at the start:

optimal HCT see mouse paper related to Kolb

I added bird wing shapes in 2015, but need formal models, Norberg, etc. Migration V formations? Was still 15 min short in 2015.

optimal foraging theory

Ask Altshuler, Higham?

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Suggestions for Next time:

Fix animations.

This needs to be strunked, cut out some verbiage, get to the point.

Reduce some quotes.

Check Robson book … is this what I meant?

Robson, G. C., and O. W. Richards. 1936. The variation of animals in nature. Longmans, Green and Co., London. 425 pp.Or this? Rosen, R. 1967. Optimality principles in biology. Butterworths, London. 198 pp.Optimal hemoglobin?Add examples of biological safety factors from Diamond book chapter? Or maybe in 1987 symmorphosis book.

Add Brown and West stuff ... Larry Li

Note that the Garland 1988 paper introduces the Lande-Arnold multivariate equation ...

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For Winter 2008, the readings were:

11. 12 Feb. 2008 - Optimality Models and Symmorphosis

Gans, C. 1979. Momentarily excessive construction as the basis for protoadaptation. Evolution 33:227-233.

Weibel, E. R., C. R. Taylor, and H. Hoppeler. 1991. The concept of symmorphosis: A testable hypothesis of structure-function relationship. Proc. Natl. Acad. Sci. USA 88:10357-10361.

13 Feb. 2008 Discussion Reading:

Metabolic theory of ecology from Wikipedia 21 Dec. 2007.

Allen, A. P., and J. F. Gillooly. 2007. The mechanistic basis of the metabolic theory of ecology. Oikos 116:1073-1077.

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Sexual selection and Cnemidophorus tigris high VO2max

See Oufiero and Garland 2007 Functional Ecology