1. Evolution of Reproductive Tactics:
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

2. 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

3. Evolution of Reproductive Tactics Semelparous versus Interoparous Big Bang versus Repeated Reproduction Reproductive Effort (parental investment) Age of First Reproduction, alpha, a Age of Last Reproduction, omega, 

4. Iteroparous organism

5. Semelparous organism

9. Patterns in Avian Clutch Sizes Altrical versus Precocial Nidicolous vs
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

10. Great Tit
Parus major
David Lack

11. European Starling,
Sturnus vulgaris
David Lack

12. Chimney Swift, Apus apus
David Lack

13. Seabirds (Ashmole)
Boobies, Gannets, Gulls, Petrels, Skuas, Terns, Albatrosses
Delayed sexual maturity, Small clutch size, Parental care

14. Albatross Egg Addition Experiment
An extra chick added to each
of 18 nests a few days after
hatching. These nests with two
chicks were compared to 18 other
natural “control” nests with only
one 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.
Diomedea immutabilis

15. Latitudinal Gradients in Avian Clutch Size

16. Latitudinal Gradients in Avian Clutch Size
Daylength Hypothesis
Prey Diversity Hypothesis
Spring Bloom or Competition Hypothesis

17. 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

18. Latitudinal Gradients in Avian Clutch Size
Nest Predation Hypothesis
Alexander Skutch ––>

19. Latitudinal Gradients in Avian Clutch Size
Hazards of Migration Hypothesis
Falco eleonora

20. Evolution of Death Rates Senescence, old age, genetic dustbin Medawar’s Test Tube Model p(surviving one month) = p(surviving two months) = p(surviving x months) = 0.9x recession of time of expression of the overt effects of a detrimental allele precession of time of expression of the positive effects of a beneficial allele
Peter Medawar

21. Age Distribution of
Medawar’s test tubes
Peter Medawar

22. Percentages
of people
with lactose
intolerance

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

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

25. S - shaped sigmoidal population growth

26. Verhulst-Pearl Logistic Equation
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

27. Inhibitory effect of each individual
On its own population growth is 1/K

30. At equilibrium, birth rate must equal death rate, bN = dN
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 – d r = (x + y) K or K = r/(x +y)

32. 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