Evolutionary Constraints

No evolutionary response

Mechanisms and constraintsMechanisms and constraints

Budgets and trade-offs

Ecological Settings

Specialization

Evolutionary Constraints

No Evolutionary Constraints

Conover et al. 2009

Genetic Variation and Evolution

Trait twoEvolutionarily

Convergence Stable

Traits

Trait one

Genetic Variation

Initial Population

Selection

Response

Selective

advantage

Selective

disadvantage

No response

The breeders equation for selection response R = Gβ

Two Possibilities:

Some variation cannot be produced (G is degenerate)

(Stabilizing) selection prevents change (β = 0)

(Maynard Smith et al. 1985)

Any organism has to obey the laws of physics

and chemistry

Mechanical/Physical constraints

produce allometric patterns

• E.g. limits on body size in organisms that

breathe through trachea

• Gravity pulls everything down

Meganeura moryi

Gigantic proto-Odonata

because of

different composition

atmosphere during Carboniferous

(Dudley 1998)

Levels of organization

Environment

Genes Phenotype Performance Fitness

Developmental

ConstraintsEcological Constraints

Physical Constraints

Ecological Constraints

Available options depend on the

environment

High (Unavoidable?) Cost of

Reproduction when

β(E)

1) Carrying eggs

2) Predators are present

3) Visibility is high

Daphnia pulex

Organisms resemble their ancestors

Species are not independent samples

Historical or Phylogenetic Constraints

Species are not independent samples

Some traits evolved already in the past and not recently

Primates cannot occupy all herbivore niches

Muller et al. 2011

Waved albatross

Phoebastria irrorata

All Procellariiformes lay a single egg per clutch

Phylogenetic patterns

One often models evolution along a tree assuming R = GβSpecies traits will change or not, but also the genetic variance-covariance G

Steppan et al. 2002

Phylogenetic patterns

From Begon et al. 2005

Life -History Invariants

(Fishbase, Maturity table)

Selection and constraint produce allometric

patterns

α: age at maturity/first clutchM: average adult mortality rate

Average female adult life

span 1/M

Life -History invariants: αM

Charnov, E. L. (1993)Female age at maturity

Life -History invariants such as αM

Are the result of selection and constraints

Life -History Invariants: αMCharnov, E. L. (1993)

α: age at maturity/first clutchM: average adult mortality rateZ(x): instantaneous mortality at age x

Average female adult

life span 1/M

))(exp()(exp)(

0

αφαα

−=

−= ∫ dxxZSS(α): survival to

maturity

)()(

)()(

0

αα

αφαφ

α

ZanddxxZ =∂

∂= ∫

Female age at maturity

)()(0 αα VSR =Lifetime Reproductive Succes R0

V(α): average total number of offspring for individuals that reach maturity

If all density dependence is on very young juveniles, then we can assume that evolution maximizes R0

R is maximized when ...R0 is maximized when ...

R0 is maximized when ...

0ln

0 00 =∂

∂⇔=

∂

∂

αα

RR

0)(ln)(ln

0ln 0 =

∂

∂+

∂

∂⇔=

∂

∂

α

α

α

α

α

VSR

Life -History Invariants: αMCharnov, E. L. (1993)

R0 is maximized when ...

)()(ln

αα

αZ

V=

∂

∂

If mortality does not change a lot after

This can now explain our pattern, if we believe that d is taxon-specific

If mortality does not change a lot after maturation, Z(α) is the adult mortality

rate M.

Md

Md

Z

d

α

α

αα

α

=⇔

=⇔

=∂

∂

/

)(ln

Assume that V(α) = αdd specifies a power law for number

of offspring

"The illusion of invariant quantities in life histories"

Age at maturity α and average adult life span A,

average total life span T

u is a uniform random number

α = uT and A = (1-u)T

R2 will be high if A is highly variable.

(Nee et al. 2005)

1

u

A u

α=

−

2 var[ln( )]

var[ln( )] var ln1

AR

uA

u

=

+ −

ln( ) ln( ) ln( ) ln(1 )a A u u= + − −

"The illusion of invariant quantities in life histories"

We believe that the best way forward ... is to develop procedures to

compare the relative variation in the proposed invariant across

(Nee et al. 2005)

compare the relative variation in the proposed invariant across

species to variation in other … not necessarily invariant, measures.

...

Classifications of Constraints: What a Mess

Physical Constraints

Genetic Constraints

PhysiologicalPhylogenetic

Constraints

Constraints (Roff 1992)

Ecological

Trade- Offs (Roff 2002)

No response –

Species Variation Selection

Albatross X

Daphnia X XDaphnia X X

Dragonfly X X

The developmental perspective

is essential

Example Variation Selection

Gene regulation

networks

X X

networks

Metabolic

networks

X X

Macromolecules X X

Wagner 2011

Simple genotype-phenotype maps used to investigate constraints

No response –

Genotype networks

Each colour is a

phenotype

Wagner 2011

phenotype

Effects:

Genotype space

G-P mapping

Selection on robustness

(for/against)

Apparent phenotype Y - Underlying trait X

Make smooth genotype-phenotype maps

Barbara Stadler has worked the ingredients to do this analysis

for discrete genotype spaces

Phenotypic trait vector Y

underlying traits X of an allele or a haplotype of alleles

Apparent phenotype Y - Underlying trait X

heterozygote of X1 and X2

homozygote of X

Y symmetric in arguments

( )21

XXY ,

( ) ( )XXYXZ ,=

( ) ( )1221

XXYXXY ,, =

Phenotypic trait vector Z

underlying traits X of an allele or a haplotype of alleles

Apparent phenotype Y - Underlying trait X

Z

X

allelic traits → organismal traits → fitness

Apparent phenotype Y - Underlying trait X

devo eco

evo

Phenotypic trait vector Z

underlying traits X of an allele or a haplotype of alleles

Z

The map Y(X) is locally approximately linear

X

.

.

.

.

Invasion fitness

fitness of the phenotype of a mutant heterozygote Y in a population with phenotype Z of the resident allele (genotype)

),( ZYr

fitness of a mutant X' in a population of alleles with trait X

( ) ( ) ( )( )XZXXYXX ,,',' r=ρ

Invasion fitness gradient

( ) ( )XX

XZXXYX

X

=∂

∂=∇

'

),,'('

)(' rρ

( )( )XZXZX r')(1

)(' ∇∇=∇ ρ ZYZ∂

=∇ ),()(' rr( )( )XZXZX r')(2

1)(' ∇∇=∇ ρ

ZY

ZYY

Z

=∂

∂=∇ ),()(' rr

fitness gradient =

phenotypic effects of allele × ecological effects of phenotype

devo eco

Evolutionary Dynamics

( )( ))('))((2

1)(

)(trtt

dt

d

tXZXZGX

X∇∇=

devo ecoscaling for

( )( )

( )( ))('2

1)(

)('))(())((2

1)(

)(

)(

trtdt

d

trtttdt

d

t

t

T

XZGZ

XZXZGXZZ

Z

X

∇=

∇∇∇=

devo ecoscaling for

available variation

Evolutionarily Stable Configuration

• evolves in the same way in any environment, independent of ecology

• evolution driven by internal coherence and system performance

• performance is for a proper function (raison d'être)• performance is for a proper function (raison d'être)

Example: iguanians use their tongue as a prehensile organ

(Wagner and Schwenk 2000)

One type of internal selection

Evolutionarily Stable Configuration

∇Z(X*) = 0 for all loci involved

or: loci are either at an internal ESS

performance is for a proper function (raison d'être)

→ Z is one-dimensional = e.g. capture rate→ Z is one-dimensional = e.g. capture rate

performance z

tongue traitsx*

∇'r(z) > 0

Internal selection 2: interactions

between developmental modules

constrain evolution

Galis et al. 2006

Germband

Aminoserosa

Head region minus

gnathal segments

Fig. 1. Extended (a) and segmented (b) Fig. 1. Extended (a) and segmented (b)

germband stages in Drosophila.

The germband (blue) refers to the part of the

embryo that will give rise to the metameric

regions: gnathal segments of the head region

(Md, mandible; Mx, maxilla; Lb, labium),

thoracic segments (T1–3) and abdominal

segments (A1–8). The amnioserosa (red) is an

extra-embryonic membrane. The extended

germband stage starts ~.6.5 h after fertilization

and the segmented germband stage ends at

~10.5 h after fertilization.

Are phenotypes constrained because they are robust?

Not in this case. Galis et al. 2002

Germband

Aminoserosa

Head region minus

gnathal segments

Fig. 1. Extended (a) and segmented (b)

germband stages in Drosophila.

The germband (blue) refers to the part of the The germband (blue) refers to the part of the

embryo that will give rise

to the metameric regions: gnathal segments of

the head region (Md,

mandible; Mx, maxilla; Lb, labium), thoracic

segments (T1–3) and

abdominal segments (A1–8). The

amnioserosa (red) is an extra-embryonic

membrane. The extended germband stage

starts ~.6.5 h after fertilization

and the segmented germband stage ends at

~10.5 h after fertilization.

Internal selection due to

interactions causing

effects on many

phenotypes

Developmental hourglass Prud’homme and Gompel 2010

Summary

• The time scale considered is important

• R = G β• R(E) = G(E) β(E) !if populations remain in the same environment!

• Constraints can arise from lack of variation and from stabilizing

selection

• Depending on the traits one focuses on, the interpretation shifts• Depending on the traits one focuses on, the interpretation shifts

(variation ↔ selection)

• Genotype networks and genotype-phenotype maps

• Internal selection: one raison d’etre ↔ interactions cause effects on

many phenotypes

• Some classifications of constraints arise more from the perspective

of the researcher than the evolving system

References

Charnov, E. L. 1993. Life History Invariants. Oxford University Press

Conover, D.O., S.B. Munch, and S.A. Arnott (2009) Reversal of evolutionary downsizing caused by

selective harvest of large fish. Proceedings of the Royal Society of London. Series B: Biological Sciences

276:2015-2020.

Dudley, R. 1998. Atmospheric oxygen, giant Paleozoic insects and the evolution o aerial locomotor

performance. Journal of Experimental Biology 201: 1043-1050.

Galis, F. , T.J.M. van Dooren and J.A.J. Metz (2002). Conservation of the segmented germband stage:

robustness or pleiotropy? Trends Genet. 18 (10), 504-509.

Galis F., T.J.M. van Dooren, Feuth, H., Ruinard, S., Witkam, A., Steigenga, M.J., Metz, J.A.J.,

Wijnaendts, L.C.D. (2006). Extreme selection against homeotic transformations of cervical vertebrae in

humans.Evolution 60 (12):2643-2654.humans.Evolution 60 (12):2643-2654.

Maynard Smith, J., R. Burian, S. Kaufman, P. Alberch, J. Campbell et al., 1985. Developmental

constraints and evolution. Q. Rev. Biol. 60: 265–287.

Muller et al. 2011. Phylogenetic constraints on digesta separation: Variation in fluid throughput in the

digestive tract in mammalian herbivores. Comparative biochemistry and physiology. Part A, Molecular &

integrative physiology. 06/2011;

Nee S et al. The illusion of invariant quantities in life histories. Science. 2005 Aug 19; 309(5738):1236-9

Prud’homme and Gompel 2010

Roff, D.A. 1992. The Evolution of Life Histories: Theory and Analysis. Chapman and Hall, New York.

Roff, D.A. 2002. Life History Evolution. Sinauer Associates, Sunderland, MA.

G. von Dassow, E. Meir, E. M. Munro, and G. M. Odell (2000) The segment polarity network is a robust

developmental module. Nature 406: 188-92.

Wagner 2011. Genotype networks shed light on evolutionary constraints. Trends in Ecology & Evolution.

doi:10.1016/j.tree.2011.07.001

Wagner, G. P. and K. Schwenk (2000) Evolutionarily Stable Configurations: functional integration and the

evolution of phenotypic stability. Evolutionary Biology 31:155-217.