Evolution of Reproductive Tactics:

semelparous versus iteroparous

Reproductive effort (parental investment)

Mola mola, white leghorn chicken lines

Optimal reproductive tactics

Graphical models of tradeoffs between present vs.future progeny

Expenditure per progeny and optimal clutch size

Altrical vs. precocial, nidicolous vs. nidifugous

Determinant vs. Indeterminant layers (Flicker example)

Avian clutch size -- Lack’s parental care hypothesis

Seabirds: Albatross egg addition experiment

Latitudinal gradients in avian clutch size

Age of first reproduction, alpha, —

menarche

Age of last reproduction, omega,

Reproductive value vx , Expectation of

future offspring

Stable vs. changing populations

Present value of all expected future

progeny

Residual reproductive value

Intrinsic rate of increase (little r, per capita = b - d)

J-shaped exponential runaway population growth

Differential equation: dN/dt = rN = (b - d)N, Nt = N0 ert

Demographic and Environmental Stochasticity

Evolution of Reproductive Tactics

Semelparous versus Interoparous

Big Bang versus Repeated Reproduction

Reproductive Effort (parental

investment)

Age of First Reproduction, alpha,

Age of Last Reproduction, omega,

Iteroparous organism

Semelparous organism

Patterns in Avian Clutch Sizes

Altrical versus Precocial

Nidicolous vs. Nidifugous

Determinant versus

Indeterminant Layers

Classic Experiment (1887):

Flickers usually lay 7-8 eggs,

but in an egg removal experiment,

a female laid 61 eggs in 63 days

Great Tit Parus major

David Lack

European Starling, Sturnus vulgaris

David Lack

QuickTime™ and a decompressor

are needed to see this picture.

Chimney Swift, Apus apus

David Lack

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are needed to see this picture.

Seabirds (Ashmole)

Boobies, Gannets, Gulls, Petrels, Skuas, Terns, Albatrosses

Delayed sexual maturity, Small clutch size, Parental care

Albatross Egg Addition Experiment

Diomedea immutabilis

An extra chick added to eachof 18 nests a few days afterhatching. These nests with twochicks were compared to 18 othernatural “control” nests with onlyone chick. Three months later, only 5 of the 36 experimental chicks survived from the nests with 2 chicks, whereas 12 of the 18 chicks from single chick nests were still alive. Parents could not find food enough to feed two chicks and most starved to death.

Latitudinal Gradients in Avian Clutch Size

Latitudinal Gradients in Avian Clutch Size

Daylength Hypothesis

Prey Diversity Hypothesis

Spring Bloom or Competition Hypothesis

Latitudinal Gradients in Avian Clutch Size

• Daylength Hypothesis

• Prey Diversity Hypothesis (search images)

• Spring Bloom or Competition Hypothesis

• Nest Predation Hypothesis (Skutch)

• Hazards of Migration Hypothesis

Latitudinal Gradients in Avian Clutch Size

Nest Predation Hypothesis Alexander Skutch ––>

Latitudinal Gradients in Avian Clutch Size

QuickTime™ and a decompressor

are needed to see this picture.

QuickTime™ and a decompressor

are needed to see this picture.

Hazards of Migration Hypothesis

Falco eleonora

Evolution of Death Rates Senescence, old age, genetic dustbin

Medawar’s Test Tube Model p(surviving one month) = 0.9 p(surviving two months) = 0.92

p(surviving x months) = 0.9x

recession of time of expression of the overt effects of a detrimental alleleprecession of time of expression of the positive effects of a beneficial allele

Peter Medawar

Age Distribution ofMedawar’s test tubes

Peter Medawar

Percentagesof people with lactoseintolerance

20001500100050000

1000

2000

3000

4000

5000

6000

7000

Population, ml

Human population growth

Year, AD

Population, millions

What starts off slow, finishes in a flash . . .

20001500100050000

1000

2000

3000

4000

5000

6000

7000

Population, ml

Human population growth

Year, AD

Population, millions

What starts off slow, finishes in a flash . . .

S - shaped sigmoidal population growth

Verhulst-Pearl Logistic Equation

dN/dt = rN – rN (N/K) = rN – {(rN2)/K}

dN/dt = rN {1– (N/K)} = rN [(K – N)/K]

dN/dt = 0 when [(K – N)/K] = 0

[(K – N)/K] = 0 when N = K

dN/dt = rN – (r/K)N2

Inhibitory effect of each individualOn its own population growth is 1/K

At equilibrium, birth rate must equal death rate, bN = dN

bN = b0 – x N

dN = d0 + y N

b0 – x N = d0 + y N

Substituting K for N at equilibrium and r for b0 – d0

r = (x + y) K or K = r/(x +y)

Derivation of the Logistic Equation

Derivation of the Verhulst–Pearl logistic equation

is easy. Write an

equation for population growth using the actual

rate of increase rN

dN/dt = rN N =

(bN – dN) N

Substitute the equations for bN and dN into this

equation

dN/dt = [(b0 – xN)

– (d0 + yN)] N

Rearrange terms,

dN/dt = [(b0 – d0 ) –

(x + y)N)] N

Substituting r for (b – d) and, from above, r/K for

(x + y), multiplying

through by N, and rearranging terms,

dN/dt =

rN – (r/K)N2