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N = 5290 Species

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  • rmax, generation time and body sizeExponential population growthDemographic and environmental stochasticityOptimal reproductive tacticsSemelparity versus iteroparityReproductive effort (parental investment)Expenditure per progenyParent-offspring conflict

    Patterns in Avian Clutch SizesAltrical versus PrecocialNidicolous vs. NidifugousDeterminant vs. Indeterminant LayersOpen Ground NestersOpen Bush Nesters Open Tree Nesters Hole NestersNest attentiveness and male feedingFlicker egg removal experiment

    N = 5290 Species Lecture # 158 March 2016

  • Great Tit Parus majorDavid Lack

  • Parus major

  • European Starling, Sturnus vulgaris

  • Chimney Swift, Apus apus

  • Seabirds (N. Philip Ashmole)

    Boobies, Gannets, Gulls, Petrels, Skuas, Terns, Albatrosses Delayed sexual maturity, Small clutch size, Parental care

  • Boobies, Gannets, Gulls, Petrels, Skuas, Terns, Albatrosses Delayed sexual maturity, Small clutch size, Parental care

  • Albatross Egg Addition Experiment Diomedea immutabilisAn 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

    Nest Predation Hypothesis Alexander Skutch >

  • Latitudinal Gradients in Avian Clutch Size

    Hazards of Migration HypothesisFalco eleonora

  • Evolution of Death Rates Senescence, old age, genetic dustbin Medawars 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 effects of a beneficial allele Peter Medawar

  • Age Distribution ofMedawars test tubes

  • Percentages of people with lactose intolerance

  • Joint Evolution of Rates of Reproduction and MortalityDonald Tinkle Sceloporus

  • Joint Evolution of Rates of Reproduction and MortalityDonald Tinkle Sceloporus

  • J - shaped exponential population growth

  • Instantaneous rate of change of N at time t is total births (bN) minus total deaths (dN)dN/dt = bN dN = (b d )N = rNNt = N0 ert (integrated version of dN/dt = rN)log Nt = log N0 + log ert = log N0 + rtlog R0 = log 1 + rt (make t = T)r = log l or l = er (l is the finite rate of increase)

  • Once, we were surrounded by wilderness and wild animals, But now, we surround them.

  • Lack - Avian clutch size and parental careGreat tit, starling, chimney swiftDelayed reproduction in seabirds, especially albatrossesLatitudinal Gradients in Avian Clutch SizeDaylength HypothesisPrey Diversity HypothesisSpring Bloom or Competition Hypothesis Nest Predation Hypothesis (Skutch)Hazards of Migration HypothesisEvolution of Death RatesSenescence, old age, genetic dustbin Medawars Test Tube Model recession of time of expression of overt effects of a detrimental allele precession of time of expression of effects of a beneficial alleleS - shaped sigmoidal population growthVerhulst-Pearl Logistic Equation: dN/dt = rN [(K N)/K]

  • S - shaped sigmoidal population growthK NK K( N K((1

  • Verhulst-Pearl Logistic EquationdN/dt = rN {1 (N/K)} = rN [(K N)/K]

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

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

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

    dN/dt = rN (1 N/K) = rN (r/K)N2

    dN/dt = 0 when [(K N)/K] = 0

    [(K N)/K] = 0 when N = K

  • Inhibitory effect of each individualon its own population growth is 1/Kra = rmax rmax K)N


  • Derivation of VerhulstPearl logistic equation

    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)

  • = r/(x+y)

  • Derivation of the Logistic Equation

    Derivation of the VerhulstPearl logistic equation. 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 before, r/K for (x + y), multiplying through by N, and rearranging terms, dN/dt = rN (r/K)N2Note: N2 is N*N = probability of contact

  • Density Dependence versus Density IndependenceDramatic Fish Kills, Illustrating Density-Independent Mortality___________________________________________________ Commercial CatchPercentLocalityBeforeAfterDecline___________________________________________________Matagorda16,9191,089 93.6Aransas55,2242,552 95.4Laguna Madre12,016 149 92.6___________________________________________________Note: These fish kills resulted from severe cold weather on the Texas Gulf Coast in the winter of 1940.

  • Fugitive species

  • Some of the Correlates of r- and K-Selection _______________________________________________________________________________________ r-selection K-selection _______________________________________________________________________________________ ClimateVariable and unpredictable; uncertain Fairly constant or predictable; more certainMortalityOften catastrophic, nondirected, More directed, density dependentdensity independent SurvivorshipOften Type III Usually Types I and IIPopulation sizeVariable in time, nonequilibrium; Fairly constant in time,ibrium; usually well below equilibrium; at or nearcarrying capacity of environment; carrying capacity of theunsaturated communities or environment; saturatedportions thereof; ecologic vacuums; communities; no recolonizationrecolonization each year necessaryIntra- and inter-Variable, often laxUsually keenspecific competitionSelection favors1. Rapid development1. Slower development2. High maximal rate of2. Greater competitive ability increase, rmax 3. Early reproduction3. Delayed reproduction4. Small body size4. Larger body size5. Single reproduction5. Repeated reproduction6. Many small offspring6. Fewer, larger progenyLength of lifeShort, usually less than a year Longer, usually more than a year Leads toProductivityEfficiencyStage in successionEarlyLate, climax__________________________________________________________________ From Pianka (1970) American Naturalist


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