E x = Expectation of further life:

rmax, generation time and body size

Exponential 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 # 1413 October 2015

Great Tit Parus major

David 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 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


Daylength Hypothesis

Prey Diversity Hypothesis

Spring Bloom or Competition Hypothesis


Nest Predation Hypothesis Alexander Skutch ––––––>


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 allele

precession of time of expression of the effects of a

beneficial allele

Peter Medawar

Age Distribution ofMedawar’s test tubes

Percentages of people with lactose intolerance

Joint Evolution of Rates of Reproduction and Mortality

Donald Tinkle

Sceloporus

Joint Evolution of Rates of Reproduction and Mortality

Donald Tinkle

Sceloporus

J - shaped exponential population growth

http://www.zo.utexas.edu/courses/THOC/exponential.growth.html

http://www.zo.utexas.edu/courses/THOC/exponential.growth.html

Instantaneous rate of change of N at time t

is total births (bN) minus total deaths (dN)

dN/dt = bN – dN = (b – d )N = rN

Nt = N0 ert (integrated version of dN/dt = rN)

log Nt = log N0 + log ert = log N0 + rt

log R0 = log 1 + rt (make t = T)

r = log or = er (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 swift

Delayed reproduction in seabirds, especially albatrossesLatitudinal Gradients in Avian Clutch Size

Daylength HypothesisPrey Diversity HypothesisSpring Bloom or Competition Hypothesis Nest Predation Hypothesis (Skutch)Hazards of Migration Hypothesis

Evolution of Death Rates

Senescence, old age, genetic dustbinMedawar’s 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 allele

S - shaped sigmoidal population growth

Verhulst-Pearl Logistic Equation: dN/dt = rN [(K – N)/K]

S - shaped sigmoidal population growth

K NK K

—( N K( —

(

1

Verhulst-Pearl Logistic Equation

dN/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/K

ra = rmax – rmax K)N/(

Derivation of Verhulst–Pearl 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 Verhulst–Pearl 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)N2

Note: N2 is N*N = probability of contact

Density Dependence versus Density IndependenceDramatic Fish Kills, Illustrating Density-Independent Mortality___________________________________________________ Commercial Catch Percent

–––––––––––––––––––––Locality Before After Decline___________________________________________________Matagorda 16,919 1,089 93.6Aransas 55,224 2,552 95.4Laguna Madre 12,016 149 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 _______________________________________________________________________________________ Climate Variable and unpredictable; uncertain Fairly constant or predictable; more certain

Mortality Often catastrophic, nondirected, More directed, density dependentdensity independent

Survivorship Often Type III Usually Types I and IIPopulation size Variable 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 necessary

Intra- and inter- Variable, often lax Usually keenspecific competitionSelection favors 1. Rapid development 1. Slower development

2. High maximal rate of 2. Greater competitive ability increase, rmax 3. Early reproduction 3. Delayed reproduction4. Small body size 4. Larger body size5. Single reproduction 5. Repeated reproduction6. Many small offspring 6. Fewer, larger progeny

Length of life Short, usually less than a year Longer, usually more than a year

Leads to Productivity EfficiencyStage in succession Early Late, climax__________________________________________________________________

From Pianka (1970) American Naturalist

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E x = Expectation of further life: