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by: Mr. Chaz Walter


Marketplace > James Madison University > Geology > GEOL 200 > EVOLUTIONARY SYSTEMS
Mr. Chaz Walter
GPA 3.58

Lynn Fichter

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Lynn Fichter
Class Notes
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This 4 page Class Notes was uploaded by Mr. Chaz Walter on Saturday September 26, 2015. The Class Notes belongs to GEOL 200 at James Madison University taught by Lynn Fichter in Fall. Since its upload, it has received 26 views. For similar materials see /class/214115/geol-200-james-madison-university in Geology at James Madison University.




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Date Created: 09/26/15
BAKSNEPPEN MODEL OF EVOLUTION Bak Per and Kim Sneppen 1993 Punctuated Equilibrium and Criticality in a Simple Model of Evolution Physical Review Letters Vol 71 No 24 p 40834086 Programmed by Steve Baedke39 Documentation by Lynn S Fichter The Scientific Argument That Led to the Model From the time of Darwin and to the present day gradualism has been the basis of all modem biological theories of evolution Gradualim argues that evolution takes place by slow steady changes over long periods of time Biologists who study evolution over geologically short time spans years to hundreds of years using population genetics to study gene frequency changes see gradualistic evolution in their experiments In 1972 however paleontologists Niles Eldredge and Steven Jay Gould argued that the fossil record where we observe changes over long time spans tens of thousands to billions of Extinction Intensity For zoic Genera In 106 Time Intervals stages years shows punctuated equilibrium equilibrium stasis or no changeipunctuated by short intervals of very fast change Punctuated events were further supported by David Raup s observations 1992 that extinctions follow a power law distributionismall events are common and insignificant large events are rare and significantiplotting as a straight line on a log graph or altematively like the curve to the right That is extinction is fractalia signature of selforganizedcritical o o N 0 Number of Geologic Stages 0 systems The debate between gradualism and punctuated equilibrium was extremely contentious during the 197039s and 198039s at one 0 80 100 20 60 Percent Extinction seientific meeting punches were thrown by the antagonists This Note Mm the number 0ng extincth controversy has begun to die down a little each side has declared like the Permian are very in equent victory and gone on about their businessimeaning the debate ommmg only Iquot one geoioglmlmge While smaller extinctionsi lt10 occurred in remains unresolved For the most part biologists and we Wigwam geological mg paleontologists are still not meaningfully talking with each other about evolution The BakSneppen Model Per Bak and Kim Sneppen developed their evolutionary model in the early 199039s to test the punctuated equilibrium observations made by Eldredge Gould and Raup Since both punctuated equilibrium and power law extinctions are similar to the sand pile behavior that Bak studied the BakSneppen BS model was designed to see if a stripped down computer based evolutionary model could be designed that would self organize to a critical state and exhibit avalanche behavior that follows a power law distribution If it did that would support punctuated evolution The B S evolutionary model is an ecosystem in which the fitness of each species changes because of its relationships with other species following two simple rules Rule One find the species with the lowest fitness and randomly change its fitness When a species has low tness almost any change is bene cial but because we do not want to build in a rule that will increase tness independent of the model s dynamics we just change tness at random BakrSheppeh Made ovaoluoon r 2 Rule 1w at the same time the lowest t species is changed also randomly change the tness of the species to the immediate le and right Species do not enst in isolotion they are olwoys part ofo mmmumty Therefore o ehonge in one species ehonges the fitness of the species it inteioets With in this case the ones to the right and left And ogoin fitness ehonges ot randam to not build oios into the model The model parameters include the following The model contains some number of species usially 50200 each represented only by its total tness umber ranging om 00 extinction to 10 maximum tness 2 Visually each species is represented by a vertical line The 39 the tness the longer the line up to maximum tness length 10 Only a dot marking the top ofthe see screen capture below but the row end wraps that Ecosystem vertical lines like to the right and the entire circle represents the ecosystem 4 The acting out of Rules One and Two are seen as urnes of dots blinking on and off scattered at rst but later concentiating in zones about 10 to 20 species wide These are the tops of the tness lines changing length as tness changes akrSneDDen lvell n l E x u lzl 877789697375 Na es 5n Nunheiothvslsnehesr gg msmsmaa Geneiaiions LasiAvalance a 2UB5U5U3 ME72 l uzalulutluauzu l l Sie thou h lhiesholdritness r a zsmtalsamtutu 3 D g quot773 2 sttatsuauazfst 2 F RemaveRuleZ Lsioesthvslsnehe ruse 27ll3uuuu2t7laz t 1 aka 35335va m nisiswslmsirsr mt I Bak Sneppen Model of Evolution 3 5 Threshold tness is the highest level the lowest tness has reached to date in the model s run Threshold tness in the model is shown by a horizontal line that rises with time although urries of activity drop below this line with each avalanche 6 An avalanche is the cascade of tness changes below the threshold ie all the blinking dots below the line although this behavior also results in random tness changes above the line An avalanche begins as soon as any species tness drops below the threshold and lasts as long as any activity remains below the threshold The length of the avalanche is the number of mutations that occur between the beginning of the avalanche and the threshold tness being exceeded again The end of an avalanche results in the threshold line rising to a new lowest tness Applications and Implications Does any interesting behavior arise from such a simple system especially behavior that mimics biological behavior We do not expect random processes to produce an organized outcome random events should remain well random unorganized Organization takes purpose design or at least causes that have a preferential deterministic direction And there is no natural selection here to drive the system What the BS model illustrates is that even random processes can result in selforganization to a critical state Threshold tness rises rapidly at rst then exponentially slows until it reaches about 066 the critical state from which level extinction avalanches sweep back and forth through the ecosystem None of the changes observed in the system are designed however to increase the critical threshold or lead to extinction avalanches but the dynamics of the model lead inevitably to self organized criticality A change in one species is analogous to dropping a grain of sand onto the sand pile sometimes one grain causes an avalanche sometimes it takes a lot of grains to build to the next threshold and another avalanche The avalanches follow a powerlaw distribution 0 I O Punctuated Equilibrium The DEVII s STAIRCASE Punctuated equilibrium in the BS model is seen in V THE fATE 0f 39Nd39V39dUAl SPECIES the Devil s Staircase plot to the right The Devil39s quot I F I staircase shows the accumulated activity of one species undergoing a series of evolutionary changes Horizontal lines are times of stasis when tness is not changing 39 100 39 Vertical jumps are punctuated mutations note these come 1n bundles mult1ple avalanches over short t1me punctuational change Accumulated Activity m l39 m 1 m intervals In reality there are many more mutation steps in each bundle than the graph can show One can think of the number of changes as representing the amount of physical change in the animal such as size The quotpunctuated equilibriumquot nature of the curve is evident in O I l I I l the long times of stasis followed by jumps in activity 0 100 p 200 300 Generations PowerLaw Extinctions At the critical point 066 avalanches sweep back and forth through the ecosystem see Activity Pattern graph on the last page Dynamics of the BakSneppen Evolutionary Model Periodically even BakSneppen Model ovaolution 4 stable species get swept up in an avalanche and go extinct only to be replaced by another species with different tness The deeper significance of extinction avalanches is that the extinctions have no identifiable cause Yes just one random mutation below the threshold sets off the extinction avalanche But that is just the pointiit is random with no identifiable cause Just one of many minor changes The result is an avalanche of extinctions and new species generation that may go on for just a few generations or millions of generations before the avalanche is over We are always looking for the cause of an extinction the smoking gun that killed off all those species But extinctions are not necessarily caused by some external event such as an asteroid impact or a dramatic climatic change Such events may of course destabilize a critical system enough to precipitate an extinction but the BS model implies that such external events are not necessary A real system not at the critical state may experience an external trigger without it precipitating an avalanche while a system at the critical state is sensitive dependent enough it may experience an avalanche even without an extemal trigger The trigger may simply be the ap of the butterfly wingithe extinction of a single speciesithat results in an avalanche that propagates through the entire system Extinction is inherent just within the dynamics of evolution Personal Implications In his book How Nature Works Bak explains the implications of selforganized criticality this way There is not much that an individual can do to protect himherself from these disasters Fate plays a decisive role for the sandpile inhabitant It is the criticality that makes life complicated and the accidents of where you live The sandpile theory self organized criticality is irresistible as metaphor The formation of a person s identity is analogous to the formation of the sand pile A personality reaches the critical state then the impact of each new experience reverberates throughout the whole person both directly and indirectly by setting the stage for future change Because these changes are subject to sensitive dependence each person s history and personality is unique This leads to a couple of questions Imagine that the BS model is a society with those having higher fitness being higher on the socialwealth ladder and those with low fitness or caught up in an avalanche say a war being poor less fortunate souls What are the implications of the BakSneppen model for these questions 1 Watch the individuals above the threshold How stable are they How much do they contribute to raising the threshold line to the next level Can you think of anyone or any group in our society analogous to the people above the threshold 2 Get personal Pick out one individual above the threshold line and identify with it39 imagine it is you How safe are you in this avalanche prone world How much control do you have over your destiny Are there any innocent victims in this society Is there any way to protect yourself in such a world


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