1. Netherlands Graduate School of Linguistics LOT Summer School 2006 Issues in the biology and evolution of language Massimo Piattelli-Palmarini University of Arizona Session 4 (June 15) The return of the laws of form (The third factor in language design)

2. LOT Summer 2006The return of the laws of form2 My line of argument today n The Minimalist Program can be on the right track or can be on a wrong track n (I think it’s on the right track) n However n The central importance of general principles of optimal design would not be the only instance we find in biology (pace Pinker and Jackendoff)

3. LOT Summer 2006The return of the laws of form3 A basic datum: n About 30,000 genes in the human genome n Which, among other things, have to build: n Millions of specific varieties of antibodies n And n 10 11 “situated” neurons n 10 13 to 10 14 synapses (some excitatory, some inhibitory) n The crazy neuro-anatomist: Identifies a different synapse every minute, nonstop n It will take him 10 million years to complete the job

4. LOT Summer 2006The return of the laws of form4 Possible solutions: n A combinatorial process of gene assortments (the immune system) n Only the basic “guidelines” are genetically specified (Monod’s and Changeux’s notion of a genetic “envelope”) n Massive auto-organization (mass laws, diffusion phenomena, morphogenes, internal gradients, spontaneous inter-coordination via nearest neighbor contacts, cell-adhesion molecules etc.) n Physico-chemical laws acting from “above” and “below” n Natural maximization processes (densest packing, minimal distance, minimal computation, minimal memory, surface-to-volume ratio, etc.) n Other kinds of combinatorics (birdsongs, parameters, syntactic derivations - the infinite use of finite means)

5. LOT Summer 2006The return of the laws of form5 A caveat: n Diehard neo-Darwinians would be OK with optimization as an outcome of random trials n But, has there been enough time? Enough generations? Is the search-space too vast? n Sometime it seems to be (Cherniak et al. optimization up to “best-in-a-billion”) n What about optimization without a “search”? n (Antonio Coutinho’s joke about the stones) n Can evolution (adaptation and selection) be “riding” the narrow channels of what is possible? n Steepest descent, narrow canalization n Necessity from “below” and from “above”

6. LOT Summer 2006The return of the laws of form6 Natural selection n Can only select what can be selected n Stability and reproducibility are basic constraints n The Evo-Devo revolution n Resistance to (small) perturbations is another (Waddington’s chreods and homeorhesis) n A very important concept: nudging n Genes as “nudgers” towards one or another pre-fixed pathway of development, among the very few that are at all possible (given physical laws and the boundary conditions) n Natural selection as the fixation of just such nudges

7. LOT Summer 2006The return of the laws of form7 A logical priority: “The primary task of the biologist is to discover the set of forms that are likely to appear [for] only then is it worth asking which of them will be selected.” ( P. T. Saunders, (ed.). (1992). Collected Works of A. M. Turing: Morphogenesis. London: North Holland:xii).

8. LOT Summer 2006The return of the laws of form8 The grand unification: n “Unless we adopt a vitalistic and teleological conception of living organisms, or make extensive use of the plea that there are important physical laws as yet undiscovered relating to the activities of organic molecules, we must envisage a living organism as a special kind of system to which the general laws of physics and chemistry apply. And because of the prevalence of homologies of organization, we may well suppose, as D’Arcy Thompson has done, that certain physical processes are of very general occurrence... What is novel in [this diffusion reaction] theory is the demonstration that, under suitable conditions, many diffusion reaction systems will eventually give rise to stationary waves; in fact to a patterned distribution of metabolites”. (Turing and Wardlaw 1953/1992: 45)

9. LOT Summer 2006The return of the laws of form9 A traditional debate: n The extremely low probability of every biological trait (Monod, Dawkins, Pinker, among others) n What is the probability baseline? n Of the aggregation of molecules whirling freely in a broth? n Or of complex spontaneous morphogenetic processes to start with? (Ilya Prigogine versus Monod; Hilary Putnam versus Daniel Dennett) n Is there a theory-free (absolute) metric of probabilities? n Probably not!

10. LOT Summer 2006The return of the laws of form10 Order from chaos: The Belhusov- Zhabotinsky reaction http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm Boris P. Belousov, director of the Institute of Biophysics in the Soviet Union, submitted a paper to a scientific journal purporting to have discovered an oscillating chemical reaction in 1951, it was roundly rejected with a critical note from the editor that it was clearly impossible. His confidence in its impossibility was such that even though the paper was accompanied by the relatively simple procedure for performing the reaction, he could not be troubled. If citric acid, acidified bromate and a ceric salt were mixed together the resulting solution oscillated periodically between yellow and clear. He had discovered a chemical oscillator.

11. LOT Summer 2006The return of the laws of form11 Order from chaos: The Belhusov- Zhabotinsky reaction Another Russian biophysicist, Anatol M. Zhabotinsky, refined the reaction, replacing citric acid with malonic acid and discovering that when a thin, homogenous layer of the solution is left undisturbed, fascinating geometric patterns such as concentric circles and Archimedian spirals propagate across the medium. Therefore, the reaction oscillates both in space and time, a so-called spatio-temporal oscillator.

12. LOT Summer 2006The return of the laws of form12 The Belouzov-Zhabotinsky patterns in a Petri dish

13. LOT Summer 2006The return of the laws of form13 Oscillations in time and space (spontaneous morphogenesis) Bautiful animations are to be found in: http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm

14. LOT Summer 2006The return of the laws of form14 Oscillations in time and space (spontaneous morphogenesis) Bautiful animations are to be found in: http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm The recipe 10ml 0.48M malonic acid 10ml saturated KBrO 3 20ml 0.6M H 2 SO 4 10ml 0.005M ferrion 0.15 g Ce(NH 4 ) 2 (NO 3 ) 6

15. LOT Summer 2006The return of the laws of form15 Oscillations in time and space (spontaneous morphogenesis) Beautiful animations are to be found in: http://online.redwoods.cc.ca.us/instruct/darnold/DEProj/Sp98/Gabe/intro.htm The system is not at equilibrium: No violation of the 2nd Law of Thermodynamics.

16. LOT Summer 2006The return of the laws of form16 http://hermetic.nofadz.com/pca/bz.htm A computer simulation (cellular automaton) of the B-Z reaction can be run on the website

17. LOT Summer 2006The return of the laws of form17

18. LOT Summer 2006The return of the laws of form18 Ilya Prigogine (1917-2003) n Nobel Prize in Chemistry 1977 n “For his contributions to non-equilibrium thermodynamics, particularly the theory of dissipative structures” “Non-equilibrium may be a source of order. Irreversible processes may lead to a new type of dynamic states of matter which I have called “dissipative structures””. “…a formulation of theoretical methods in which time appears with its full meaning associated with irreversibility or even with “history”, and not merely as a geometrical parameter associated with motion”.

19. LOT Summer 2006The return of the laws of form19 From Prigogine’s Nobel Lecture a single solution for the value 1, but multiple solutions for the value 2.

20. LOT Summer 2006The return of the laws of form20 From Prigogine’s Nobel Lecture a single solution for the value 1, but multiple solutions for the value 2. In this way we introduce in physics and chemistry an “historical”element, which until now seemed to be reserved only for sciences dealing with biological, social, and cultural phenomena.

21. LOT Summer 2006The return of the laws of form21 A central consideration “Every description of a system which has bifurcations will imply both deterministic and probabilistic elements…., the system obeys deterministic laws, such as the laws of chemical kinetics, between two bifurcations points, while in the neighborhood of the bifurcation points fluctuations play an essential role and determine the “branch” that the system will follow.” The theory of bifurcations (catastrophe theory) is due to René Thom (see infra) “The development of the theory permits us to distinguish various levels of time: time as associated with classical or quantum dynamics, time associated with irreversibility through a Lyapounov function and time associated with "history" through bifurcations. I believe that this diversification of the concept of time permits a better integration of theoretical physics and chemistry with disciplines dealing with other aspects of nature”.

22. Some historical landmarks

23. LOT Summer 2006The return of the laws of form23 D’Arcy Wentworth Thompson (1860- 1948) on “The Laws of Form” (1917) n Biologists have overemphasized the role of evolution, and underemphasized the roles of physical and mathematical laws in shaping the form and structure of living organisms. n The Miraldi angle, the Fibonacci series, the golden ratio and the logarithmic spiral. n “Beyond this stage of perfection in architecture, natural selection could not lead; for the comb of the hive-bee, as far as we can see, is absolutely perfect in economising labour and wax”. (Darwin, 1958:249) n ”….the beautiful regularity of the bee's architecture is due to some automatic play of the physical forces.” (D’Arcy Thompson)

24. LOT Summer 2006The return of the laws of form24 The music of the spheres http://au.geocities.com/psyberplasm/ch5.html

25. LOT Summer 2006The return of the laws of form25 The snowflake

26. LOT Summer 2006The return of the laws of form26 A simple mathematical transformation converts one form into the other D’Arcy Thompson’s famous grids

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30. LOT Summer 2006The return of the laws of form30 The central ideas: n You only have to specify 2 or 3 parameters for the grid n And you generate all the superficially “different” forms n Different rates of chemical diffusion may be the key n Same forces, same physical laws, only slightly different lines of minimal resistance n Or directions of a gradient n Or axes of maximal diffusion n (in my terminology) just a little bit of nudging

31. LOT Summer 2006The return of the laws of form31 A straightforward inference n If the action of a gene, or a genetic network, consists in specifying the values of a few parameters for chemical diffusion n And/or activating a few genes at the right time in the right cells n Even the most elaborate forms of life can be explained n As we will see in a moment: in some cases, the “solutions” for a given parametric space can be extremely limited, with sharp discontinuities between them. n Minor quantitative variations can give rise to major qualitative differences.

32. LOT Summer 2006The return of the laws of form32 Enter mathematical biology n Differential equations for growth, extinction and stable oscillations Vito Volterra 1860-1940 Alfred J. Lotka 1880-1946

33. LOT Summer 2006The return of the laws of form33 A forerunner: the Belgian Pierre François Verhulst (1804-1849)

34. LOT Summer 2006The return of the laws of form34 Solutions to Verhulst’s logistic equation

35. LOT Summer 2006The return of the laws of form35 Solutions to Verhulst’s logistic equation Carrying capa- city of the medium

36. LOT Summer 2006The return of the laws of form36 Alfred J. Lotka and “physical biology” (1924) n “… a viewpoint, a perspective, a method of approach, … a habit of thought…which has hitherto received its principal development and application outside the boundaries of biological science….. Namely: the study of fundamental equations whereby evolution is conceived as redistribution of matter.” (pp. 41-42). (my emphasis) n sustainable rates of growth, birth and mortality rates, equilibria between species, biochemical cycles and rates of energy transformations, the evolution of human means of transportation.

37. LOT Summer 2006The return of the laws of form37 The Lotka-Volterra equations y = n. of predators x = n. of prey , ,  population parameters

38. LOT Summer 2006The return of the laws of form38 The Lotka-Volterra equations y = n. of predators x = n. of prey , ,  population parameters The ratios between the parameters decide whether there is extinction, stable oscillations, transients etc.

39. LOT Summer 2006The return of the laws of form39 An attractor: a dynamically stable state (mimicry is another application)

40. LOT Summer 2006The return of the laws of form40 Limit cycles

41. LOT Summer 2006The return of the laws of form41 One limit cycle and one attractor

42. LOT Summer 2006The return of the laws of form42 The central ideas: n Extremely complex dynamic patterns n Closed orbits, limit cycles n Qualitatively different regimes determined by slight variations in parametric values n Discontinuous transitions in spite of a continuum of parameters’ change n Attractors n Critical and super-critical bifurcations n A lot of nudging in these systems

43. LOT Summer 2006The return of the laws of form43 Limits of all these approaches n Poaverty of the mathematical tools (see René Thom 1975) n The “age of specificity” was yet to come n The microscopic determinants were unknown n Diffusion and catalysis were the only available concepts n No “real” genetics n No idea of a genetic blueprint n No idea of gene regulation n No idea of genes as switches n No idea of gene networks

44. LOT Summer 2006The return of the laws of form44 Enter the mighty Turing n The Chemical Basis of Morphogenesis (1952) n Reaction-diffusion processes n “A system of chemical substances, called morphogens, reacting together and diffusing trough a tissue, is adequate to account for the main phenomena of morphogenesis” n Th[is] investigation is chiefly concerned with the onset of instability”. n A sphere and then gastrulation n An isolated ring of cells and then stationary waves n A two-dimensional field and then dappling

45. LOT Summer 2006The return of the laws of form45 The purpose of Turing’s paper: n “Is to discuss a possible mechanism by which the genes of a zygote may determine the anatomical structure of the resulting organism” n “The theory does not make any new hypotheses; it merely suggests that certain well-known physical laws are sufficient to account for many of the facts.” (my emph.) n..morphogens (Waddington’s evocators) diffusing into a tissue somehow persuade it [sic] to develop along different lines than would have been followed in its absence.”

46. LOT Summer 2006The return of the laws of form46 A most revealing statement: n “The genes themselves may also be considered to be morphogens. But they certainly form rather a special class. They are quite indiffusible. Moreover, it is only by courtesy that genes can be regarded as separate molecules. It would be more accurate (at any rate at mitosis) to regard them as radicals of the giant molecules known as chromosomes. n “The function of genes is presumed to be purely catalytic. They catalyze the production of other morphogens, which in turn may only be catalysts.”

47. LOT Summer 2006The return of the laws of form47 A vicious circle? n “Eventually, presumably, the chain leads to some morphogens whose duties are not purely catalytic”. n (a breakdown into smaller molecules that increase the osmotic pressure in the cell) n “The genes might thus be said to influence the anatomical form of the organism by determining the rates of those reactions which they catalyze. n … the genes themselves may [thus] be eliminated from the discussion.” n Hormones and skin pigments are other kinds of morphogens

48. LOT Summer 2006The return of the laws of form48 In essence n The physics and the chemistry of the reaction- diffusion processes is all we need n The genes speed up certain processes, and that’s all. n We can ignore them in the model. n A “leg-evocator morphogen” may be present in a certain region of the embryo, or diffuse into it. n The distribution of that evocator in space and time can be regarded as fixed n We then pay attention only to the reactions “set in train by it.” n That’s how a leg will develop in that region.

49. LOT Summer 2006The return of the laws of form49 The toolkit: n Standard equations of diffusion, and of periodical oscillations n The law of mass action n Standard catalytic reactions n Rates of diffusion of the morphogenes (the cell walls being a screen, with pores)

50. LOT Summer 2006The return of the laws of form50 A puzzle: spherical symmetry n How do we “break” that symmetry (to get a horse) n Casual symmetry-breaks can become permanent and be amplified n Noise and instability can produce differences in the rate of migration of morphogens n Standing waves can be generated n A ring of N cells with only two morphogens n There is a “chemical wave-length” that does not depend on the dimension of the ring n It will be attained “whenever possible” but there will be constraints and approximations.

51. LOT Summer 2006The return of the laws of form51 Stationary waves of finite wavelength n The truly interesting case. n Stable morphogenetic processes n Disturbances near the time when instability is zero are the only ones which have any appreciable definitive effect. n Under certain conditions, the most quickly growing component may get a lead over its closest competitor. n If a homogeneous one-morphogen system first undergoes random disturbances without diffusion, then undergoes diffusion without disturbance, then we have dappling

52. LOT Summer 2006The return of the laws of form52 Dappling in 2D as the result of one morphogen

53. LOT Summer 2006The return of the laws of form53 Concentration of one morphogen (Y) in a ring of cells “Variety with quick cooking”

54. LOT Summer 2006The return of the laws of form54 Concentration of one morphogen (Y) in a ring of cells with two morphogens Initial Transient final

55. LOT Summer 2006The return of the laws of form55 Spots and Stripes n Activator and inhibitor factors with different diffusion rates can interact to produce regular spots/stripes (Turing 1952).

56. LOT Summer 2006The return of the laws of form56 Biological instances n The case of the sea-anemone Hydra and of the leaves of the woodruff (Asperula odorata)

57. LOT Summer 2006The return of the laws of form57 Spherical harmonics: gastrulation n Spherical Laplacian operator (vibrating strings in three dimensions) with two morphogens n The concentrations of the two morphogens are proportional, both being surface harmonics of the same degree n n The skeletons of radolaria are instances n As the size of the sphere (the blastula) increases, the wavelength of the concentration is constant n If there is a perturbation, a pattern of breakdown of homogeneity is created n It is axially symmetric around the perturbation

58. LOT Summer 2006The return of the laws of form58 Gastrulation n The blastula grows with axial symmetry, but n At a greater rate at one end of the axis than at the other end. n Chemical instability combines with mechanical instability (elasticity of the tissue) n Gastrulation ensues n The axis is random in this theory, but biological processes may well determine a privileged direction (the animal pole) n Turing anticipates the use of digital computers to simulate some model situations

59. LOT Summer 2006The return of the laws of form59 The ur-morphoge_ netic event in the development of the embryo

60. LOT Summer 2006The return of the laws of form60 Summing up: The third factor view n The primary “engine” are physical and chemical processes of a perfectly canonical kind n Biology only adds something like privileged axes, selective catalysts, morphogens n The universal “basis” of morphogenesis is genuinely universal. n Biology adds a “nudging” (in my terminology) n Maybe what natural selection does is selecting those “nudges” n 30,000 genes can do a lot of nudging of the basic processes involved

61. LOT Summer 2006The return of the laws of form61 Where are we n “Mighty” equations and all-covering laws of physics and chemistry n But no specificity n 1953 the double helix n 1960 genes as switches n 1960 the structure of myoglobin (Kendrew) and hemoglobin (Perutz) n 1961 the genetic code (Niremberg and Matthaei, Crick and Brenner) n 1970 Monod: what is true of E. coli is true of the elephant n 1977 Jacob: Evolution and tinkering

62. LOT Summer 2006The return of the laws of form62 A strange maverick: René Thom (1923-2002) (Fields medal 1958) n Originated by the French mathematician Rene Thom in the 1960s, catastrophe theory is a special branch of dynamical systems theory. It studies and classifies phenomena characterized by sudden shifts in behavior arising from small changes in circumstances. n Catastrophes are bifurcations between different equilibria, or fixed point attractors. Due to their restricted nature, catastrophes can be classified based on how many control parameters are being simultaneously varied. For example, if there are two controls, then one finds the most common type, called a "cusp" catastrophe. If, however, there are more than five controls, there is no classification. n For 4 controls there are exactly 7 elementary catastrophes n “If one must choose between rigour and meaning, I shall unhesitatingly choose the latter”.

63. LOT Summer 2006The return of the laws of form63 The 7 elementary catastrophes n Catastrophes in systems with only one state variable: n The fold n The cusp n The swallowtail n The butterfly n Catastrophes in systems with two state variables n The hyperbolic umbilic n The elliptic umbilic n The parabolic umbilic n http://perso.orange.fr/l.d.v.dujardin/ct/eng_index.html (Lucien Dujardin) http://perso.orange.fr/l.d.v.dujardin/ct/eng_index.html

64. LOT Summer 2006The return of the laws of form64 Structural Stability and Morphogenesis English edition 1975 With a foreword by C. H. Waddington (Benjamin Publisher) Ren é Thom

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67. LOT Summer 2006The return of the laws of form67 Thom’s lexical semantics n 12 kinds of verbs in all languages n All based upon: Ending, being, beginning, changing n Capturing, failing, emitting, rejecting, crossing, stirring, giving, sending, taking, fastening, cutting n Concepts have a “regulation figure” a logos analogous to that of living beings. n A grammatical category C is semantically denser than another grammatical category C’ if a regulation of a concept of C involves mechanisms intervening in the regulation of C’. n Since the verb is indispensible for the stability of the substantive, it is less dense than the noun.

68. LOT Summer 2006The return of the laws of form68 Theta roles (arguments) n There cannot be more than 4 arguments for a verb n In all the languages of the world n This is the result of the topology of actions

69. LOT Summer 2006The return of the laws of form69 A strange linguistic theory (see also books by Jean Petitot) n Morphogenetic fields determine semantics and syntax (capture, assimilation etc.) n The stability of the subject is a central constraint n In the “emission of the sentence” (sic) the elements are emitted in the order of increasing density. n The normal order is VOS n Because in a transitive interaction the object may perish, while the subject survives n Other orders are (topological) transformations of this basic order n Dictated by the necessity of communication

70. The modern return of the laws of form

71. LOT Summer 2006The return of the laws of form71 Invariants of locomotion The Journal of Experimental Biology (2006) Vol. 209, pp. 238-248 Unifying constructal theory for scale effects in running, swimming and flying Adrian Bejan (Duke University) and James H. Marden (Upenn) “Animal locomotion is no different than other flows, animate and inanimate: they all develop (morph, evolve) architecture in space and time (self- organization, self-optimization), so that they optimize the flow of material.” (p. 246) Older theories: potentially common constraints Constructal theory: universal design goals, from which principles for optimized locomotion can be deduced. These can explain the nature of the constraints

72. LOT Summer 2006The return of the laws of form72 The ingredients: n Locomotion = streams of mass flow n Accomplishing the most for unit of energy consumed n Morphing of river basins, atmospheric circulation, design of ships, submarines etc. n Maximum range speed = U-shaped curve of cost vs speed n One very narrow range of speeds that maximize the ratio of distance traveled to energy expended n Stride/stroke frequencies versus net force output (for running, swimming and flying) n Predicts and explains the emergence of central tendencies

73. LOT Summer 2006The return of the laws of form73 The ingredients: n M b = body mass n  b = body density n g = gravitational acceleration n L b = body length = (M b /  b ) 1/3 n  = coefficient of friction

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75. LOT Summer 2006The return of the laws of form75 From small insects to large mammals, the force produced when moving at optimal speed is a multiple of body weight (applies to running, swimming and flying)

76. LOT Summer 2006The return of the laws of form76 The return (brief list) n Diffusion equations for gene frequencies n The Hardy-Weinberg equilibrium n Parental investment n Arborization structures (the fourth power law) n Foraging (more anon) n Biological motion (the 2/3 power law) n Connectivity in the cortex n Locomotion (crawling, walking, running, swimming and flying) n The distribution of white matter and grey matter in the brain n Birdsongs n Quorum-sensing (cell-to-cell and to tissue coordination) n Kissing chromosomes and genetic waves

77. LOT Summer 2006The return of the laws of form77 Foraging n Obviously crucial for reproductive fitness n On a par with fecundity, morbidity and mortality rates n Essential variables: n Energy spent per unit mass of food collected n Energy for “handling” n Typical distance covered in the average day/season n Individual strategies / collective strategies n Patterns of food sharing vs. competition n Generalists vs. specialists n Anatomical and physiological constraints n Ecological constraints (Anna Dornhaus UofA)

78. LOT Summer 2006The return of the laws of form78 Foraging n More refined factors: n Probability of finding better food sources versus value of a forgone available source and energy spent in a further search n Reliability of routine strategies vs. new strategies n Amount of information transmitted to / received from other individuals n Hardwired habits vs. learning n Species specifications vs. individual variation and innovation n Implicit “programs” versus cognitive capacities (mental representations?)

79. LOT Summer 2006The return of the laws of form79 Dechaume-Moncharmont, F.-X., Dornhaus, A., Houston, A. I., McNamara, J. M., Collins, E. J., & Franks, N. R. (2005). The hidden cost of information in collective foraging. Proceedings of the Royal Society (B Series), 272, 1689-1695. Foraging strategies as a function of the probabilities of finding a source Probab for a pro-active searcher Probab for a re-active searcher p s * = optimal proportion of pro-active searchers t = duration of food availability

80. LOT Summer 2006The return of the laws of form80 Several counter-intuitive predictions n But well confirmed by data on honey bees n In the wild and in laboratory conditions. Under certain environmental conditions, the optimum strategy for a social insect colony is pure independent foraging. This prediction holds even when potential recruits would benefit from information gained from successful foragers by having a higher probability of finding food than they would as independent foragers. This is because of the costs of waiting for information in the recruitment process. Most intriguingly, such hidden costs are sufficiently important to have noticeable effects even when the food source is available for many days.

81. LOT Summer 2006The return of the laws of form81 Several counter-intuitive predictions Recruitment is not always adaptive, even when the recruits have a higher probability of finding food. There is not necessarily a direct link between an increase in individual performance after information transfer and collective energy gain over the whole foraging period.

82. LOT Summer 2006The return of the laws of form82 Why do we care? n Even “simple” species seem to have found the optimal foraging strategy in different ecological conditions n Something that can only be captured by quite sophisticated mathematical computations. n How do we explain this fact? n Have they blindly explored a huge variety of alternatives, n And natural selection has rewarded the best ones? n Or are we witnessing the instantiation of some general optimization principles? n Do we need genes “for” optimal foraging?