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On the Evolution of Phenotypic Plasticity In Spatially Structured Environments. Bruno Ernande Fisheries Department IFREMER Port-en-Bessin, France. Phenotypic plasticity Phenotype = Genotype + Environment z ij = g i + E j

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on the evolution of phenotypic plasticity in spatially structured environments
Bruno Ernande, NMA Course, Bergen

On the Evolution of Phenotypic Plasticity In Spatially Structured Environments

Bruno Ernande

Fisheries Department

IFREMER

Port-en-Bessin, France

definitions
Phenotypic plasticity

Phenotype = Genotype + Environment

zij = gi + Ej

a single genotype can produce different phenotypes according to the environment where it develops and lives

this holds for both spatial and temporal environmental variation

Reaction norm

the systematic profile of phenotypes zij expressed by a single genotype gi in response to a given range of environments Ej

Phenotypic plasticity may be an active process allowing short term adaptation. Can it be selected for?

Bruno Ernande, NMA Course, Bergen

Definitions

Phenotype z

reaction norm

degree of

plasticity

g1

g2

Environment E

prerequisites for phenotypic plasticity to evolve

Phenotype z

g1

g1

g2

Ve

Vp

Vg

g2

Ve

Environment E

Environment E

Bruno Ernande, NMA Course, Bergen

Prerequisites for phenotypic plasticity to evolve
  • To be selected for, phenotypic plasticity needs to
    • enhance fitness of plastic genotypes relative to non-plastic ones
    • be under genetic control
    • exhibit sufficient additive genetic variance in the population
  • Requirements are met in both plants and animals: Schlichting 1986; Sultan 1987; Scheiner 1993; Pigliucci 1996

Vp = Vg + Ve

Vp = Vg + VE + VgE

how to represent reaction norms in models
Character-state reaction norm

{zi1, zi2, zi3, zi4, zi5}: the different character-states are evolving under the constraints imposed by correlations across environments

Falconer 60’s, Via and Lande 1985, Kawecki and Stearns 1993

Polynomial reaction norm

{zi0 , s}: intercept and slope are considered as the evolving traits.

Gavrilets and Scheiner 1993a,b

z

gi

gi

Slope, s

zi0

intercept

E0

E

E

Bruno Ernande, NMA Course, Bergen

How to represent reaction norms in models?

z

zi5

zi4

zi3

zi2

zi1

1

2

3

4

5

how to represent reaction norms in models5
Bruno Ernande, NMA Course, BergenHow to represent reaction norms in models?
  • Reaction norm as a functional trait
    • zi(E): reaction norm is represented by a flexible function which can evolve like a trait
    • Gomulkiewicz & Kirkpatrick 1992
    • This of course the most flexible way to model a reaction norm

z

gi

zi(E)

E

previous models of phenotypic plasticity evolution
Bruno Ernande, NMA Course, BergenPrevious models of phenotypic plasticity evolution
  • Optimality Theory:Ecologically oriented models
    • Geared toward identifying the selective pressures favouring or preventing the evolutionary emergence of phenotypic plasticity
      • from explicit ecological scenarios and
      • a priori trade-offs
    • Based on population dynamics, no genetics: phenotypic evolution
    • Long-term evolution but no evolutionary transients, only evolutionary equilibria
    • No density- nor frequency-dependent populations: interactions between individuals are not accounted for
    • Stearns and Koella 1986; Houston and McNamara 1992; Kawecki and Stearns 1993; Sasaki & de Jong, 1999
previous models of phenotypic plasticity evolution7
Bruno Ernande, NMA Course, BergenPrevious models of phenotypic plasticity evolution
  • Quantitative genetics: Genetically oriented models
    • Aim at identifying the implications of the underlying genetics for the evolutionary emergence of phenotypic plasticity, focusing mainly on genetic constraints such as
      • the lack of additive genetic variance or
      • genetic correlations
    • Based on a statistical description of the population, no detailed ecology
    • Evolutionary transients together with equilibria, but short term evolution (constant additive genetic (co-)variance matrix)
    • No density- nor frequency-dependent populations: interactions between individuals are not accounted for
    • Via and Lande 1985, 1987; Van Tienderen 1991, 1997;Gomulkiewicz and Kirkpatrick 1992; Gavrilets and Scheiner 1993
under investigated aspects
Bruno Ernande, NMA Course, BergenUnder-investigated aspects
  • Density-dependent population dynamics and frequency-dependent selection
    • Would allow to account for phenotypic plasticity triggered by interactions between individuals such as competition for food resources or mates, predation,…
  • Accounting for different types of costs of phenotypic plasticity
    • Maintenance costs: expenses incurred by maintaining the potential for being plastic
    • Production costs: costs paid by a plastic genotype actually producing a given phenotype in excess to those incurred by a fixed genotype producing the same phenotype
  • The consequence of alternative distribution patterns
    • Are individuals distributed randomly across environments or do they select it?
  • The evolutionary implications of a precise environmental setting
    • Frequency of the different environments, the quality of the resource they offer…

How these factors are driving the potential evolution of phenotypic plasticity, how do they interact and what is their relative importance?

the modelling approach
Bruno Ernande, NMA Course, BergenThe modelling approach
  • We use adaptive dynamics theory (Metz et al. 1992; Dieckmann & Law 1996; Metz et al. 1996; Geritz et al. 1998) and its recent extension to function-valued traits
  • Properties and assumptions:
    • Selection gradient derived from explicit ecological scenarios
    • Phenotypic model (clonal model), no genetics
    • Long term evolution of phenotypic plasticity: mutation driven (slow mutation rate, small mutational steps)
    • Describes adaptive transient states together with evolutionary equilibria
    • Allows to account for interactions between individuals
      • density-dependent population dynamics and
      • frequency-dependent selection

Ernande & Dieckmann 2004 JEB

the basics
Bruno Ernande, NMA Course, BergenThe basics
  • Individuals are living across a range of environments e that can represent:
    • abiotic parameters (temperature, salinity, amount of nitrates…)
    • biotic characteristics (species or densities of preys, of predators, types of competitors )
  • The phenotype p can vary across environmental types e according to a function p(e)which is a reaction norm
  • Determinants of environmental heterogeneity:
    • How frequent are the different environmental types? Frequency of occurenceo(e)
    • What is the quality of the different environments? Intrinsic carrying capacityk(e)
    • How sensitive to phenotypic variation is the performance of organisms in each type of environment? Sensitivity to maladaptations(e)

Ernande & Dieckmann 2004 JEB

model structure

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Distribution strategy

of the individuals

Environment

Population

Growth rate

+

REACTION NORM

Costs of

Phenotypic Plasticity

Maintenance, production

FITNESS

Long term growth rate of a

rare mutant in a resident population

Bruno Ernande, NMA Course, Bergen

Model structure

Ernande & Dieckmann 2004 JEB

resource utilization efficiency

Phenotype

Environment

REACTION NORM

Bruno Ernande, NMA Course, Bergen

Resource utilization efficiency

Resource utilization

efficiency

Ernande & Dieckmann 2004 JEB

resource utilization efficiency13

along an environmental gradient

sensitivity

s(e)

matching,m(e)

s(e)

p(e)

Bruno Ernande, NMA Course, Bergen

Resource utilization efficiency
  • In each environment e, a matching phenotype m(e) maximizes efficiency of resource utilization Ep(e)(harvesting, handling, digestibility,…)

in a given environmente

1

Efficiency,Ep(e)

0

m(e)

Phenotype,p(e)

Ernande & Dieckmann 2004 JEB

resource competition
Bruno Ernande, NMA Course, BergenResource competition

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Environment

REACTION NORM

Ernande & Dieckmann 2004 JEB

resource competition15

2

k(e)

a=0

a<1

E>0

a=1

Competition coefficient, A(E)

1

Realized carrying capacity,kp(e)

E<0

a>1

degree of

asymmetry

0

0

0

0

1

Difference in efficiency,E

Efficiency,Ep(e)

Bruno Ernande, NMA Course, Bergen

Resource competition
  • Competition for resources
    • logistic density-dependence with a coefficient of competition A(E) and a realized carrying capacity kp(e), both depending on the resource utilization efficiency.

Ernande & Dieckmann 2004 JEB

alternative distribution strategies
Bruno Ernande, NMA Course, BergenAlternative distribution strategies

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Distribution strategy

of the individuals

Environment

REACTION NORM

Ernande & Dieckmann 2004 JEB

alternative distribution strategies17

Occurrence,o(e)

  • Ideal Free Distribution:
    • Individuals can detect intrinsic quality of the different environments

Quality,k(e)

Efficiency,Ep(e)

Distribution,dp(e)

Occurrence,o(e)

  • Optimal Foraging:
    • Individuals can both detect intrinsic quality of the different environments and distribute according to theirefficiency.

Quality,k(e)

Efficiency,Ep(e)

Distribution,dp(e)

Bruno Ernande, NMA Course, Bergen

Alternative distribution strategies

Occurrence,o(e)

  • Random Distribution:
    • No selective control over local habitat

Quality,k(e)

Efficiency,Ep(e)

Distribution,dp(e)

Environment, e

Ernande & Dieckmann 2004 JEB

population growth rate

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Distribution strategy

of the individuals

Environment

Population

Growth rate

REACTION NORM

Bruno Ernande, NMA Course, Bergen

Population growth rate

Ernande & Dieckmann 2004 JEB

costs of phenotypic plasticity
Bruno Ernande, NMA Course, BergenCosts of phenotypic plasticity

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Distribution strategy

of the individuals

Environment

Population

Growth rate

REACTION NORM

+

Costs of

Phenotypic Plasticity

Maintenance, production

Ernande & Dieckmann 2004 JEB

costs of phenotypic plasticity20
Costs increase with departure from the developmental base-line.

The total costs of the reaction norm are proportional to its variance around the developmental base-line.

Three types of costs

maintenance costs independent of the distribution of the individuals

production costs depending fully on the distribution

mixed cost

Distribution,dp(e)

Maintenance

Production

Bruno Ernande, NMA Course, Bergen

Costs of phenotypic plasticity

Phenotype, p(e)

Environment, e

Ernande & Dieckmann 2004 JEB

invasion fitness of a mutant
Bruno Ernande, NMA Course, BergenInvasion fitness of a mutant

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Distribution strategy

of the individuals

Environment

Population

Growth rate

REACTION NORM

+

Costs of

Phenotypic Plasticity

Maintenance, production

FITNESS

Long term growth rate of a

rare mutant in a resident population

Ernande & Dieckmann 2004 JEB

canonical equation
Bruno Ernande, NMA Course, BergenCanonical equation
  • Fitness of a rare mutant p’ in a resident population p:
  • Adaptive dynamics of a function valued trait p are are given by:

Dieckmann & Heino 2001

with p(e,e’): the mutational variance-covariance function,

gp(e): the selection gradient in environmental type eis the functional derivative of the fitness function f(p’,p) at trait p’ = p.

frequency-dependence

Ernande & Dieckmann 2004 JEB

evolutionary trajectories
Bruno Ernande, NMA Course, BergenEvolutionary trajectories

Resource utilization

efficiency

  • Competition:
  • Asymmetry
  • Realized carrying capacity

Phenotype

Environment

Distribution strategy

of the individuals

Environment

Population

Growth rate

REACTION NORM

+

Costs of

Phenotypic Plasticity

Maintenance, production

FITNESS

Long term growth rate of a

rare mutant in a resident population

Ernande & Dieckmann 2004 JEB

evolutionary equilibria
Bruno Ernande, NMA Course, BergenEvolutionary equilibria
  • Evolutionary equilibria p* or evolutionary singularities are attained when:
  • This is possible when
    • the selection gradient vanishes at p*, gp*(e’) = 0

 Selection induced-equilibria.

    • the mutational variance-covariance function p*2(e,e’) is singular at p*

 Covariance induced equilibria.

Ernande & Dieckmann 2004 JEB

selection induced equilibria

R.D.

I.F.D.

O.F.

Bruno Ernande, NMA Course, Bergen

Selection-induced equilibria
  • Evolutionary singularities are characterized by a balance between two opposing forces:
    • one toward the matching phenotype m(e) with a weight
    • the other toward the cost-free generalist phenotype with a weight
  • The weights of the two forces depend on the distribution strategy of the individuals:

Ernande & Dieckmann 2004 JEB

evolutionary effect of the different types of costs
As costs are shifting from maintenance to production type (i.e.  increases), the effects of:

the frequency of occurenceo(e) of the different environmental types in case of all distribution strategies,

the intrinsic carrying capacity k(e) in case of Ideal Free Distribution and Optimal Foraging.

on the shape of the reaction norm disappear.

Bruno Ernande, NMA Course, Bergen

Evolutionary effect of the different types of costs

m(e)

Ernande & Dieckmann 2004 JEB

evolutionary effect of the distribution strategies
The effect of carrying capacity differs according to the kind of distribution strategy considered:

in case of Random Distribution, better matching evolve in poor environments

in of Ideal Free Distribution and Optimal Foraging, better matching evolves in good environmental types

Bruno Ernande, NMA Course, Bergen

Evolutionary effect of the distribution strategies

m(e)

Ernande & Dieckmann 2004 JEB

evolutionary branching of reaction norms
If costs of plasticity and sensitivity are higher

Directional selection

monomorphic maladapted reaction norm

Selection turns disruptive

evolutionarily non-stable

Protected dimorphism in reaction norm:

Evolution of Trophic Specialization.

Bruno Ernande, NMA Course, Bergen

Evolutionary branching of reaction norms

Monomorphic

Dimorphic1

Dimorphic 2

conclusions
Bruno Ernande, NMA Course, BergenConclusions
  • Evolution of phenotypic plasticity can be driven by frequency-dependent interaction between conspecifics allow for branching of reaction norms and apparition of polymorphism in the degree of phenotypic plasticity.
  • Considering different type of costs of phenotypic plasticity have a drastic effect on the shape of reaction norm: interact in an intricate manner with the environmenal setting;
  • Distribution strategy of the individuals is a crucial factor: changes the effect of the quality of the environments and the susceptibility for branching in reaction norms
  • Promising developments:
    • the systematic exploration of branching points in reaction norms,
    • the evolutionary competition between generalist, specialist and “plasticist”: the coevolution between distribution patterns and phenotypic plasticity,
    • development of a model in case of a temporally fluctuating environment.