Post on 16-Jan-2016
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
QuickTime™ and a decompressor
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