Adaptive Dynamics workshop, 2002 Evolution of reaction norms of age and size at maturity Bruno Ernande, Mikko Heino, and Ulf Dieckmann ModLife European Research Training Network Adaptive Dynamics Network. International Institute for Applied Systems Analysis. A-2361 Laxenburg. Austria.

Adaptive Dynamics workshop, 2002 ∎ Phenotype=Genotype+Environment Introduction 1: Phenotypic plasticity - a single genotype G can produce different phenotypes P according to the environment E where it develops and lives  phenotypic plasticity - the systematic profile of phenotypes expressed by a genotype in response to the environment  reaction norm Ultimately, phenotypic plasticity should be the best way for individuals to adapt their phenotype to the current environment they are facing! E P G degree plasticity reaction norm

Adaptive Dynamics workshop, 2002 Introduction 2: What about constraints? ∎ If phenotypic plasticity was so advantageous, it should be more widespread in the wild. There must be some constraints … Costs of phenotypic plasticity (DeWitt et al. 1998): -maintenance costs -production costs ‘Trade-off’ between environments (Via and Lande 1985; Gomulkiewicz qnd Kirkpatrick 1992):  individuals ‘cannot’ do equally well in all environments  should lead to some genetic constraints between different points of the reaction norm How should we introduce such constraints in models of the evolution of reaction norms and what is their effect?

Adaptive Dynamics workshop, 2002 Concepts of reaction norms ∎ Another view: reaction norms with individual status as a determinant Py Px E1 E2 E3 growth 1 growth 2 growth 3 size age e.g. age and size at maturity {Py(Px(E1),Py(Px(E2)),Py(Px(E3))} E P G 1234 P(E1) P(E2) P(E3) P(E4) ∎ The historical view: reaction norms with an explicit environmental determinant {P(E1),P(E2),P(E3),P(E4),P(E5)}

Adaptive Dynamics workshop, 2002 Concepts of reaction norms ∎ Another view: reaction norms with individual status as a determinant Py Px {Py(Px1),Py(Px2),Py(Px3)} E P G 1234 P(E1) P(E2) P(E3) P(E4) ∎ The historical view: reaction norms with an explicit environmental determinant {P(E1),P(E2),P(E3),P(E4),P(E5)} Py(Px1) Py(Px2) Py(Px3) Px1Px1Px2Px3

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 1 ∎ Resource utilization efficiency determines asymmetric competition realized carrying capacity Resource utilization efficiency matching, m(e)

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 1 ∎ Resource utilization efficiency determines asymmetric competition realized carrying capacity ∎ Fitness of a mutant Resource utilization efficiency matching, m(e)

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 1 ∎ Resource utilization efficiency determines asymmetric competition realized carrying capacity ∎ Fitness of a mutant ∎ Selection gradient Resource utilization efficiency matching, m(e)

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 1 ∎ Resource utilization efficiency determines asymmetric competition realized carrying capacity ∎ Fitness of a mutant ∎ Selection gradient ∎ Canonical equation Resource utilization efficiency matching, m(e)

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 2 ∎ Analytical results: everything is determined locally and model behaves as if we were considering a collection of isolated populations

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 2 ∎ Analytical results: everything is determined locally and model behaves as if we were considering a collection of isolated populations ∎ Introduction of costs as a constraint: Costs introduce some ‘trade-off’ between environments

Adaptive Dynamics workshop, 2002 A generic model with environmental determinants 3 ∎ Costs prevent perfect matching ∎ and allow ‘global’ evolutionary branching

Adaptive Dynamics workshop, 2002 A model with individual status as a determinant: Reaction norm of age and size at maturity 1 Random distribution Habitat selection Larval stage Immature stage Mature stage S M (1) S I (1) S L (1) S M (2)S M (3) S L (2)S L (3) S I (2)S I (3) E1E2E3 S M (1)S M (2)S M (3)Mature stage Reproduction Metamorphosis Maturation E age

Adaptive Dynamics workshop, 2002 A model with individual status as a determinant: Reaction norm of age and size at maturity 1 Random distribution Habitat selection Larval stage Immature stage Mature stage S M (1) S I (1) S L (1) S M (2)S M (3) S L (2)S L (3) S I (2)S I (3) E1E2E3 S M (1)S M (2)S M (3)Mature stage Reproduction Metamorphosis Maturation E age

Adaptive Dynamics workshop, 2002 A model with individual status as a determinant: Reaction norm of age and size at maturity 2 ∎ Maturation process: environments also differ in growth rate Size age Size at metamorphosis E1 E2 E3 a M (E1,E3)a M (E2,E3) S M (E2,E3) S M (E1,E3)

Adaptive Dynamics workshop, 2002 A model with individual status as a determinant: Reaction norm of age and size at maturity 2 ∎ Maturation process: environments also differ in growth rate Size age Size at metamorphosis E1 E2 E3 E4 a M (E1,E4) a M (E2,E3) S M (E1,E4) S M (E2,E3)

Adaptive Dynamics workshop, 2002 A model with individual status as a determinant: Reaction norm of age and size at maturity 3 ∎ Selection gradient: with i.e. the immature environment having such a growth rate that when combined with the growth rate in the larval environment e L leads to the point S m (a m ) of the reaction norm ‘Trade-off’ between environments emerges from the multiplicity of growth trajectories leading to the same point of the reaction norm

Adaptive Dynamics workshop, 2002 Remarks and questions ∎ Is that a general feature of reaction norms with individual status as a determinant? ∎ More generally, is there any general pattern for evolutionarily emergent constraints? ∎ What is the relationship with genetic constraints as antagonistic pleiotropy?