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SUMMARY:Bernoulli Lecture II - Populations and communities as fluid on a l
 andscape:  rising to the challenge of long-term environmental change\, pas
 t\, present\, and future
DTSTART:20140807T161500
DTEND:20140807T171500
DTSTAMP:20260929T050425Z
UID:5171c6e9b6a055c3bb6f51d873002312d4fc0c4c56e88467141317b9
CATEGORIES:Conferences - Seminars
DESCRIPTION:Peter Chesson\nAll natural populations and communities occupy 
 spatially heterogeneous landscapes.  Individual fitnesses vary in space\,
  and the contributions to population growth from different localities can 
 be profoundly unequal even though directed dispersal\, and retention of or
 ganisms in favorable localities\, reduce the potential inequalities.  Ela
 borate methods have been developed for solving models of population and co
 mmunity dynamics on heterogeneous landscapes\, but to be science rather th
 an technology\, they must also impart understanding. Scale transition theo
 ry aims to provide this understanding through concepts that explain how th
 e rules for population dynamics on local spatial scales interact with hete
 rogeneity between localities\, leading to novel outcomes on larger spatial
  scales. These novel outcomes include changes in population densities\, st
 abilization of population dynamics\, and promotion of species coexistence.
  \nScale transition theory is founded on the idea of nonlinear averaging:
  the average of a nonlinear function is in general different from the aver
 age of the nonlinear function.  Jensen’s inequality is a simple instanc
 e of nonlinear averaging where the function is convex and the average of t
 he function is uniformly greater than the function of the average.  More 
 generally\,  the function is multidimensional and not necessarily convex.
   A product of two variables is a simple but extremely important example 
 of a nonlinear function of multiple variables.  The average of the produc
 t is the product of the averages (the function of the average)\, plus the 
 covariance between the two variables in space.  Two key concepts emerge f
 rom this simple observation: (1) fitness-density covariance\, which explai
 ns how fitness at the landscape scale differs from the simple spatial aver
 age of local scale fitness\, and (2) covariance between environment and co
 mpetition\, which explains how the ability of an organism to benefit from 
 favorable environmental conditions can be limited by competition.  Both c
 oncepts have powerful roles showing how population stabilization and speci
 es coexistence can emerge from the interaction between nonlinearities and 
 spatial heterogeneity.  Another concept\, nonlinear competitive variance\
 , shows how different nonlinear reactions to the same underlying spatially
  varying density-dependent processes can profoundly change higher scale dy
 namics.\nScale transition theory can be applied to models using quadratic 
 approximations related to moment closure techniques. However\, exact appro
 aches are being developed.  In general these exact approaches require num
 erical evaluation of the key quantities\, but still provide general unders
 tanding through elucidation of the role of the key ideas in specific insta
 nces.  Other approximations use spatially implicit models and Laplace tra
 nsforms to provide detailed understanding of the interactions between diff
 erent kinds of spatial variation and nonlinear functions. \nRecent develo
 pments in scale transition theory abandon the usual stationary assumptions
  that the environment repeats statistically in time and space\, allowing r
 ealistic landscapes\, and the consequences of temporal nonstationarity\, i
 ncluding long-term climate change\, to be studied rigorously with mathemat
 ical models\, extending traditional theory to richer more realistic domain
 s.
LOCATION:BI A0 448 https://plan.epfl.ch/?room==BI%20A0%20448
STATUS:CONFIRMED
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