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Demographic dynamics and evolution of parental care. Cinthia „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“. Group 5. Male parenting. Rare behaviour.

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demographic dynamics and evolution of parental care

Demographic dynamics and evolution of parental care

Cinthia „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“

Group 5

slide3

Male parenting

Rare behaviour

Iporangaia

pustolosa

slide4

Caringmales

  • Attractfemales
  • Increase offspring survival
  • Decreased bodyconditions
  • Non-caringmales
  • Lessattractivetofemales
  • Betterbodyconditions
questions
Questions
  • How does female preference affect the dynamics?
  • Is male parental care evolutionarystable?
slide6

hatching

abandon-

ment

death

NC

NN

death

mating

birth

male dynamics
Male dynamics

r-f2

r-f1

r-fk

r

r

r

f0

f2

f1

fk-1

NN

NC(1)

NC(2)

NC(k)

γαp

μ

μ

μ

μ

γ

f – mating rate

r – fraction of hatching clutches

μ – death rate

γ – abandonment rate

α– number of viable male offspring per clutch

p – probability of survival for abandonned clutches

mating
Mating

male mating pool:

NN

NC(1) * r

NC(2) * r

...

NC(k-1) * r

female mating pool:

F = ε *Nt

β0

β1

β2

βk-1

ε – fraction of available females

βi– femalepreference for classi

mating1
Mating

number of matings in each class:

where

=> sum of all matings = F

one model to rule them all
One model to rule them all

No analyticalsolutions

Numericalsimulations

γ – abandonment rate

μ – death rate

r – fraction of hatching clutches

f – mating rate

one model to rule them all1
One model to rule them all

Abandonning males

Birthofabandonedeggs

Released males

Birthofcaredeggs

Availablefemales

α – number of viable male offspring per clutch

p – probability of survival for abandoned clutches

K – carrying capacity

ε – fraction of females available for mating

assumptions
Assumptions

Death rate is

constant

Bodycondition does notaffect male survival

Abandonment rates are constant

Lastclassalwaysabandons

Mating rate is a functionoffemalepreference

Femaleavailability is proportional to numberof males

Each male has max. one

clutch at a time

parameter values
Parametervalues

r = 0.2

μ = 0.2

γ = 0.1

α =10

p =0.3

K= 500

ε = 0.3

β = varying

slide15

k = 3

b0 = b1 = b2 = 1

class collapse
„class collapse“

NN = NN = NN = NN

NCt = NCt = NCt = NCt

class collapse1
„class collapse“

Abandonning males

Birthofabandonedeggs

Released males

Birthofcaredeggs

= - F

Availablefemales

class collapse2
„class collapse“

No analyticalsolutions

Numericalsimulations

= F

class collapse4
„class collapse“

Equilibria:

Nc = 0 Nn = 0

=> which fixed point is stable depends on parameters

evolution of male care
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
slide29

dashed – bad fathers

solid – good fathers

=> good fathers go extinct

egg mortality = 0.2

gammabad = 0.8

gammagood = 0.2

slide30

dashed – bad fathers

solid – good fathers

=> bad fathers go extinct

egg mortality = 0.2

gammabad = 0.8

gammagood = 0.2

slide31

dashed – bad fathers

  • solid – good fathers
  • good fathers go extinct
  • equal to no preference

egg mortality = 0.2

gammabad = 0.8

gammagood = 0.2

slide32

dashed – bad fathers

  • solid – good fathers
  • bad fathers go extinct
  • dynamics change

egg mortality = 0.2

gammabad = 0.8

gammagood = 0.2

conclusion
Conclusion

How does female preference affect the dynamics?

  • no change in ratio of NN/NC
  • change in the distribution of the NC-classes
conclusions
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
what s next
What’s next?

NN

NC1

NC2

NC3