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Evolution of Reproductive Tactics: semelparous versus iteroparousReproductive effort (parental investment)Mola mola, white leghorn chicken linesOptimal reproductive tacticsGraphical models of tradeoffs between present vs.future progenyExpenditure per progeny and optimal clutch sizeAltrical vs. precocial, nidicolous vs. nidifugousDeterminant vs. Indeterminant layers (Flicker example)Avian clutch size -- Lack’s parental care hypothesisSeabirds: Albatross egg addition experimentLatitudinal 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 ertDemographic and Environmental Stochasticity
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,
Patterns in Avian Clutch SizesAltrical versus Precocial Nidicolous vs. Nidifugous Determinant versus Indeterminant LayersClassic 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
Chimney Swift, Apus apus David Lack
Seabirds (Ashmole) Boobies,Gannets, Gulls, Petrels, Skuas, Terns, Albatrosses Delayed sexual maturity, Small clutch size, Parental care
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
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 Hazards of Migration Hypothesis Falco eleonora
Evolution of Death RatesSenescence, old age, genetic dustbinMedawar’s Test Tube Modelp(surviving one month) = 0.9p(surviving two months) = 0.92p(surviving x months) = 0.9xrecession 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 of Medawar’s test tubes Peter Medawar
Percentages of people with lactose intolerance
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 = 0when [(K – N)/K] = 0 [(K – N)/K] = 0when N = K dN/dt = rN – (r/K)N2
Inhibitory effect of each individual On its own population growth is 1/K
At equilibrium, birth rate must equal death rate, bN = dNbN = b0 – x N dN = d0 + y N b0 – x N = d0 + y NSubstituting 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 bNand 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
