?url_ver=Z39.88-2004&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4497%2F&rft.title=Adaptive+Dynamics%3A+A+Geometrical+Study+of+the+Consequences+of+Nearly+Faithful+Reproduction&rft.creator=Metz%2C+J.A.J.&rft.creator=Geritz%2C+S.A.H.&rft.creator=Meszena%2C+G.&rft.creator=Jacobs%2C+F.J.A.&rft.creator=Heerwaarden%2C+J.S.+van&rft.description=We+set+out+to+explore+a+class+of+stochastic+processes%2C+called+%22adaptive+dynamics%22%2C+which+supposedly+capture+some+of+the+essentials+of+the+long-term+biological+evolution.+These+processes+have+a+strong+deterministic+component.+This+allows+a+classification+of+their+qualitative+features+which+in+many+aspects+is+similar+to+classifications+from+the+theory+of+deterministic+dynamical+systems.+But+they+also+display+a+good+number+of+clear-cut+novel+dynamical+phenomena.+%0D%0A%0D%0AThe+sample+functions+of+an+adaptive+dynamics+are+piece-wise+constant+function+from+R_%2B+to+the+finite+subsets+of+some+%22trait%22+space+X+in+R%5Ek.+Those+subsets+we+call+%22adaptive+conditions%22.+Both+the+range+and+the+jumps+of+a+sample+function+are+governed+by+a+function+s%2C+called+%22fitness%22%2C+mapping+the+present+adaptive+condition+and+the+trait+value+of+a+potential+%22mutant%22+to+R.+Sign(s)+tell+us+which+subsets+of+X+qualify+as+adaptive+conditions%2C+which+mutants+can+potentially+%22invade%22%2C+leading+to+a+jump+in+the+sample+function%2C+and+which+adaptive+condition(s)+can+result+from+such+invasion.+%0D%0A%0D%0AFitness+supposedly+satisfy+certain+constraints+derived+from+their+population%2Fcommunity+dynamical+origin%2C+such+as+the+fact+that+all+mutants+which+are+equal+to+some+%22residents%22%2C+i.e.%2C+element+of+the+present+adaptive+condition%2C+have+zero+fitness.+Apart+from+that%2C+we+suppose+that+s+is+as+smooth+as+can+be+possibly+condoned+by+its+community+dynamical+origin.+Moreover%2C+we+assume+that+a+mutant+can+differ+but+little+from+its+resident+%22progenitor%22.+%0D%0A%0D%0AIn+sections+1+and+2+we+describe+the+biological+background+of+our+mathematical+framework.+In+section+1+we+deal+with+the+position+of+our+framework+relative+to+present+and+past+evolutionary+research.+In+section+2+we+discuss+the+community+dynamical+origin+of+s%2C+and+the+reasons+for+making+a+number+of+specific+simplifications+relative+to+the+full+complexity+seen+in+nature.+%0D%0A%0D%0AIn+sections+3+and+4+we+consider+some+general%2C+mathematical+as+well+as+biological%2C+conclusions+that+can+be+drawn+from+our+framework+in+its+simplest+guise%2C+that+is%2C+when+we+assume+that+X+is+1-dimensional%2C+and+that+the+cardinality+of+the+adaptive+conditions+stays+low.+The+main+result+is+a+classification+of+the+adaptively+singular+points.+These+points+comprise+both+the+adaptive+point+attractors%2C+as+well+as+the+points+where+the+adaptive+trajectory+can+branch%2C+thus+attaining+its+characteristic+tree-like+shape.+%0D%0A%0D%0AIn+section+5+we+discuss+how+adaptive+dynamics+relate+through+a+limiting+argument+to+stochastic+models+in+which+individual+organisms+are+represented+as+separate+entities.+It+is+only+through+such+a+limiting+procedure+that+any+class+of+population+or+evolutionary+models+can+eventually+be+justified.+Our+basic+assumptions+are+(i)+clonal+reproduction%2C+i.e.%2C+the+resident+individuals+reproduce+faithfully+without+any+of+the+complications+of+sex+or+Mendelian+genetics%2C+except+for+the+occasional+occurrence+of+a+mutant%2C+(ii)+a+large+system+size+and+an+even+rarer+occurrence+of+mutations+per+birth+event%2C+(iii)++uniqueness+and+global+attractiveness+of+any+interior+attractor+of+the+community+dynamics+in+the+limit+of+the+infinite+system+size.+%0D%0A%0D%0AIn+section+6+we+try+to+delineate%2C+by+a+tentative+listing+of+%22axioms%22%2C+the+largest+possible+class+of+processes+that+can+result+from+the+kind+of+limiting+considerations+spelled+out+in+section+5.+And+in+section+7+we+heuristically+derive+some+very+general+predictions+about+macro-evolutionary+patterns%2C+based+on+those+weak+assumptions+only.+%0D%0A%0D%0AIn+the+final+section+8+we+discuss+(i)+how+the+results+from+the+preceding+sections+may+fit+into+a+more+encompassing+view+of+biological+evolution%2C+and+(ii)+some+directions+for+further+research.&rft.publisher=WP-95-099&rft.date=1995-09&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4497%2F1%2FWP-95-099.pdf&rft.identifier=++Metz%2C+J.A.J.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F206.html%3E%2C+Geritz%2C+S.A.H.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F1281.html%3E%2C+Meszena%2C+G.%2C+Jacobs%2C+F.J.A.%2C+%26+Heerwaarden%2C+J.S.+van++(1995).++Adaptive+Dynamics%3A+A+Geometrical+Study+of+the+Consequences+of+Nearly+Faithful+Reproduction.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-95-099+++++