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Latitudinal Gradients in Avian Clutch Size

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- Daylength Hypothesis
- Prey Diversity Hypothesis (search images)
- Spring Bloom or Competition Hypothesis
- Nest Predation Hypothesis (Skutch)
- Hazards of Migration Hypothesis
Please study Handouts 1, 2, 3, and 4 in preparation for next Thursday’s exam

Evolution of Death Rates, Senescence, old age, genetic dustbinMedawar’s Test Tube Model, Lactose intolerance 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

Pearl-Verhulst Logistic Equation: Sigmoidal Population GrowthDensity Dependence versus Density Independence

Density Dependent versus Density Independent Selection

Equilibrium, Opportunistic, and Fugitive Species

r-strategists versus K-strategists

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

S - shaped sigmoidal population growth

Verhulst-Pearl Logistic EquationdN/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 NdN = 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

Dramatic Fish Kills, Illustrating Density-Independent Mortality

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Commercial Catch Percent

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LocalityBeforeAfterDecline

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Matagorda 16,9191,089 93.6

Aransas55,2242,552 95.4

Laguna Madre12,016 149 92.6

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Note: These fish kills resulted from severe cold weather on the

Texas Gulf Coast in the winter of 1940.

Parus major

Fugitive species

Some of the Correlates of r- and K-Selection

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r-selectionK-selection

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ClimateVariable and unpredictable; uncertain Fairly constant or predictable; more certain

MortalityOften catastrophic, nondirected, More directed, density dependent

density independent

SurvivorshipOften Type IIIUsually Types I and II

Population sizeVariable in time, nonequil-Fairly constant in time,

ibrium; usually well belowequilibrium; at or near

carrying capacity of envi-carrying capacity of the

ronment; unsaturated com-environment; saturated

munities or portions thereof; communities; no recolon-

ecologic vacuums; recolon-ization necessary

ization each year

Intra- and inter-Variable, often laxUsually keen

specific competition

Selection favors1. Rapid development1. Slower development

2. High maximal rate of2. Greater competitive ability

increase, rmax

3. Early reproduction3. Delayed reproduction

4. Small body size4. Larger body size

5. Single reproduction5. Repeated reproduction

6. Many small offspring6. Fewer, larger progeny

Length of lifeShort, usually less than a year Longer, usually more than a year

Leads toProductivityEfficiency

Stage in successionEarlyLate, climax

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Kirk Winemiller

From Molles and Cahill, Ecology: Concepts and Applications

Population Regulation [Ovenbird example]

Frequencies of Positive and Negative Correlations Between Percentage

Change in Density and Population Density for a Variety of Populations

in Different Animal Groups

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Numbers of Populations in Various Categories

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Positive Positive Negative Negative Negative

Taxon(P<.05) (Not sig.) (Not sig.) (P<.10) (P < .05) Total

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Inverts 0 0 0 0 4 4

Insects 0 0 7 1 7 15

Fish 0 1 2 0 4 7

Birds 0 2 32 16 43 93

Mammals 1* 0 4 1 13 19

Totals 1* 3 45 18 71 138

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* Homo sapiens (the “sap”)

Negative correlations between percentage change in density and population density for a variety of populations in different animal groups except for Homo the sap 4 and 10 year population “cycles” microtines and snowshoe hares Sunspot Hypothesis — dark tree ring marks Time Lags Stress Phenomena Hypothesis Predator-Prey Oscillations Epidemiology-Parasite Load Hypothesis Food Quantity Hypothesis Nutrient Recovery Other Food Quality Hypotheses Genetic Control Hypothesis – Optimal reproductive tactics Could optimal reproductive tactics drive population cycles?

Notice apparent 10-year periodicity

Snowy owls

Microtines: Voles and lemmings: 4 year cycles

Fabled lemming marches into the sea

Disney’s “White Wilderness” movie

Dennis Chitty Charles Krebs A. Sinclair

- Sunspot Hypothesis
- Time Lags
- Stress Phenomena Hypothesis
- Predator-Prey Oscillations
- Epidemiology-Parasite Load Hypothesis
- Food Quantity Hypothesis
- Nutrient Recovery
- Other Food Quality Hypotheses
- Genetic Control Hypothesis
Bb:Read Krebs et al. “What drives the 10-year cycle of snowshoe hares?”