?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%2F4957%2F&rft.title=Delayed+Maturation+in+Temporally+Structured+Populations+with+Non-Equilibrium+Dynamics&rft.creator=Van+Dooren%2C+T.J.M.&rft.creator=Metz%2C+J.A.J.&rft.description=In+this+paper+we+study+the+evolutionary+dynamics+of+delayed+maturation+in+semelparous+individuals.+We+model+this+in+a+two-stage+clonally+reproducing+population+subject+to+density-dependent+fertility.+The+population+dynamical+model+allows+multiple%2C+cyclic+and%2For+chaotic+attractors%2C+thus+allowing+it+to+illustrate+how+(i)+evolutionary+stability+is+primary+a+property+of+a+population+dynamical+system+as+a+whole%2C+and+(ii)+that+the+evolutionary+stability+of+a+demographic+strategy+by+necessity+derives+from+the+evolutionary+stability+of+the+stationary+population+dynamical+systems+it+can+engender%2C+i.e.%2C+its+associated+population+dynamical+attractors.+%0D%0A%0D%0AOur+approach+is+based+on+numerically+estimating+invasion+exponents%2C+defined+as+the+theoretical+long-term+average+relative+growth+rates+of+different+mutant+population+densities+in+the+stationary+environment+defined+by+a+resident+population+system.+For+some+combinations+of+resident+and+mutant+trait+values+we+have+to+consider+multivalued+invasion+exponents%2C+which+makes+the+evolutionary+argument+more+complicated+(and+more+interesting)+than+is+usually+envisaged.+Multivaluedness+occurs+(i)++when+more+than+one+attractor+is+associated+with+the+values+of+the+residents'+demographic+parameters%2C+or+(ii)+when+the+setting+of+the+mutant+parameters+makes+the+descendants+of+a+single+mutant+reproduce+exclusively+either+in+even+or+odd+years%2C+so+that+a+mutant+population+is+affected+by+either+subsequence+of+the+fluctuating+resident+densities+only.+%0D%0A%0D%0ANon-equilibrium+population+dynamics+or+random+environmental+noise+select+for+strategists+with+a+non-zero+probability+to+delay+maturation.+When+there+is+an+evolutionary+attracting+pair+of+such+a+strategy+and+a+population+dynamical+attractor+engendered+by+it%2C+this+delaying+probability+is+a+Continuously+Stable+Strategy%2C+this+is+an+Evolutionarily+Unbeatable+Strategy+which+also+is+Stable+in+a+long+term+evolutionary+sense.+Population+dynamical%2C+i.e.%2C+temporary%2C+coexistence+of+delaying+and+non-delaying+strategists+is+possible+with+non-equilibrium+dynamics%2C+but+adding+random+environmental+noise+to+the+model+destroys+this+coexistence.+Adding+random+noise+also+shifts+the+CSS+towards+a+higher+probability+of+delaying+maturation.&rft.publisher=WP-96-070&rft.date=1996-08&rft.type=Monograph&rft.type=NonPeerReviewed&rft.format=text&rft.language=en&rft.identifier=https%3A%2F%2Fpure.iiasa.ac.at%2Fid%2Feprint%2F4957%2F1%2FWP-96-070.pdf&rft.identifier=++Van+Dooren%2C+T.J.M.+%26+Metz%2C+J.A.J.+%3Chttps%3A%2F%2Fpure.iiasa.ac.at%2Fview%2Fiiasa%2F206.html%3E++(1996).++Delayed+Maturation+in+Temporally+Structured+Populations+with+Non-Equilibrium+Dynamics.+++IIASA+Working+Paper.+IIASA%2C+Laxenburg%2C+Austria%3A+WP-96-070+++++