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

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 Growth

Density Dependence versus Density IndependenceDensity Dependent versus Density Independent SelectionEquilibrium, Opportunistic, and Fugitive Speciesr-strategists versus K-strategists

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

Density Dependence versus Density Independence

Dramatic Fish Kills, Illustrating Density-Independent Mortality_______________________________________________________ Commercial Catch Percent

–––––––––––––––––––––Locality Before AfterDecline_______________________________________________________

Matagorda 16,919 1,089

93.6

Aransas 55,224 2,552

95.4

Laguna 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.

Parus major

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 certainMortality Often catastrophic, nondirected, More directed, density dependent

density independent Survivorship Often Type III Usually Types I and IIPopulation size Variable in time, nonequil- Fairly constant in time,

ibrium; usually well below equilibrium; 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 necessaryization each year

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

progenyLength of life Short, usually less than a year Longer, usually more than a year Leads to Productivity EfficiencyStage in succession Early Late, climax_______________________________________________________________________________________________________________________________

_

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___________________________________________________________________

Numbers of Populations in Various Categories____________________________________________

Positive Positive Negative Negative NegativeTaxon (P<.05) (Not sig.) (Not sig.) (P<.10) (P < .05) Total ___________________________________________________________________ Inverts 0 0 0 0 4 4Insects 0 0 7 1 7 15Fish 0 1 2 0 4 7Birds 0 2 32 16 43 93Mammals 1* 0 4 1 13 19 Totals 1* 3 45 18 71 138___________________________________________________________________* 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

Microtines: Voles and lemmings: 4 year cycles Fabled lemming marches into the sea

Snowy owls

Disney’s “White Wilderness” movie

Dennis Chitty Charles Krebs A. Sinclair

Population “Cycles”

• 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?”