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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!!!
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