Demographic dynamics and evolution of

parental care

Group 5Cinthia „the fixed point girl“Cristian „less equations“Danilo „not a spider“Katharina „of the many colours and the pretty boxes“Marcos „saving us from starvation“Vitor „the evil spirit“

Male parenting

Iporangaiapustolosa

Rare behaviour

Caring males• Attract females• Increase offspring survival• Decreased body conditions

Non-caring males• Less attractive to females• Better body conditions

Questions

• How does female preference affect the dynamics?

• Is male parental care evolutionary stable?

NC NN

deathdeath

birth

mating

abandon-ment

hatching

one model to

rule th

em all

NN NC(1) NC

(k)NC(2)

μ μ μ μ γ

r r rf0 f1 f2 fk-1

r-f1r-f2 r-fk

Male dynamics

rα

γαp

f – mating rater – fraction of hatching clutchesμ – death rateγ – abandonment rate

α – number of viable male offspring per clutchp – probability of survival for abandonned clutches

Mating

male mating pool:

NN

NC(1) * r

NC(2) * r

...NC

(k-1) * r

female mating pool:

F = ε * Ntβ0

β1

β2

βk-1

ε – fraction of available femalesβi – female preference for class i

Matingnumber of matings in each class:

where

=> sum of all matings = F

γ – abandonment rateμ – death rater – fraction of hatching clutchesf – mating rate

One model to rule them all

One model to rule them all

Birth of abandoned eggs

Released males

Birth of cared eggs

Available females

α – number of viable male offspring per clutchp – probability of survival for abandoned clutchesK – carrying capacity ε – fraction of females available for mating

Abandonning males

Death rate is constant

Assumptions

Body condition does not affect male survival

Abandonment rates are constant

Female availability is proportional to number of males

Mating rate is a function of female preference

Last class always abandons

Each male has max. oneclutch at a time

Parameter valuesr = 0.2μ = 0.2γ = 0.1α =10p =0.3K= 500 ε = 0.3β = varying

k = 3b0 = b1 = b2 = 1

How does female preference affect the number of individuals in the caring classes?

How does female preference affect the number of individuals in the caring classes?

How does female preference affect the number of individuals in the caring classes?

How does female preference affect the number of individuals in the caring classes?

How does female preference affect the number of individuals in the caring classes?

How does female preference affect the number of individuals in the caring classes?

„class collapse“

NN = NN =NN = NNNCt = NCt =NCt = NCt

„class collapse“Abandonning males

Birth of abandoned eggs

Released males

Birth of cared eggs

Available females= - F

„class collapse“

= F

„class collapse“

Equilibria:

Nc = 0 Nn = 0

=> which fixed point is stable depends on parameters

„class collapse“

Evolution of male care• Different mortality of abandoned eggs• Female preference (body condition & care)• two populations with three caring classes each

2 times 4 equations different abandonment rates

– good fathers: gamma = 0.2

– bad fathers: gamma = 1

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Non-cared egg mortality

pro

po

rtio

n o

f go

od

fath

ers

Evolution of care vs. egg mortality

0 50 100 150 200

0

50

100

150

200

250

300

350

No female choice

time

Nu

mb

er

of i

nd

ivid

ua

ls dashed – bad fatherssolid – good fathers=> good fathers go extinct

egg mortality = 0.2gammabad = 0.8gammagood = 0.2

0 50 100 150 200

0

50

100

150

200

250

300

Females choose for caring males

time

Nu

mb

er

of i

nd

ivid

ua

ls

dashed – bad fatherssolid – good fathers=> bad fathers go extinct

egg mortality = 0.2gammabad = 0.8gammagood = 0.2

0 50 100 150 200

0

50

100

150

200

250

300

350

Females choose for better body condition

time

Nu

mb

er

of i

nd

ivid

ua

ls

dashed – bad fatherssolid – good fathers good fathers go extinct equal to no preference

egg mortality = 0.2gammabad = 0.8gammagood = 0.2

0 50 100 150 200

0

50

100

150

200

250

Females choose for caring males AND body condition

time

Nu

mb

er

of i

nd

ivid

ua

ls

dashed – bad fatherssolid – good fathers bad fathers go extinct dynamics change

egg mortality = 0.2gammabad = 0.8gammagood = 0.2

ConclusionHow does female preference affect the dynamics?

no change in ratio of NN/NC change in the distribution of the NC-classes

Conclusions

Is male parental care evolutionary stable?

success of parental care is dependent on survival rate of the abandoned eggs

female preference can determine if „good“ or „bad“ fathers evolve

0.0 0.2 0.4 0.6 0.8 1.0

0.0

0.2

0.4

0.6

0.8

1.0

Non-cared egg mortality

pro

po

rtio

n o

f go

od

fath

ers

0 50 100 150 200

0

50

100

150

200

250

300

350

No female choice

time

Nu

mb

er

of i

nd

ivid

ua

ls

0 50 100 150 200

0

50

100

150

200

250

300

Females choose for caring males

time

Nu

mb

er

of i

ndiv

idu

als

What’s next?

NNNC1

NC2

NC3

My preciousss!!!