Latitudinal Gradients in Avian Clutch Size
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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?”