Natural Selection, ultimate inventor, efficiency expert Debates and Progress in Ecology Levels of Approach in Biology Proximate versus Ultimate Factors, mechanism vs. strategy Avian migration, day length, pituitary secretions, Wanderlust Celestial Navigation Winter as a long-term predictable agent of mortality Monarch-Viceroy butterflies example, cardiac glycosides Warning coloration, aposematic coloration, mimicry Nature versus Nurture, “environmentally-induced” polymorphism Thrush anvil, snail green-brown color polymorphism Gecko foot hairs, setae, spatulae, Van der Waal’s forces Attachment and detachment

Figure 8.1

Testosterone Figure 8.1

Testosterone Figure 8.1

Vital Statistics of Populations Deme (Mendelian Population) Demography (assume all individuals equal) Population Parameters (emergent properties) Mean and Variance IndividualPopulation Male or FemaleSex Ratio Has Babies or notBirth Rates Alive or DeadDeath Rates Given AgeAge Structure Fixed GenotypeGene Frequencies Growth Rates Density

Life tables: Horizontal versus vertical samples Cohort Segment Time Birth Age Figure 8.2

Figure 8.3

Life Tables Discrete versus Continuous Ages Pivotal Age assumption (age classes) q x = force of mortality (fraction dying during age interval) q x = age-specific death rate Survivorship curves l x = fraction of initial cohort that survives to age x l y / l x = probability of living from age x to age y E x = Expectation of further life

Type 1: Rectangular Type 2: Diagonal Type 3: Inverse Hyperbolic Xantusia vigilis Uta stansburiana sheep Figure 8.4

Sceloporus olivaceus Eumeces fasciatus Xantusia vigilis Eumeces fasciatus Palm tree Euterpe globosa Figure 8.5

Fecundity, Tables of Reproduction m x = age-specific fecundity Two conventions: females only, or count both males and females but weight each as one-half (only progeny entering age class zero are counted) Gross reproductive rate (GRR) is the sum of m x over all ages However, because some females will die before having all their possible babies, must calculate realized fecundity which is simply l x m x (the fraction of females surviving times their fecundity) Realized fecundity, l x m x, is summed over all ages to get the Net Reproductive Rate, R 0 (also called the Replacement Rate of the Population)

The Romneys

2 ——> 20

20 x 20 = 400

2 ——> x 20 = x 20 = 8,000

2 ——> x 20 = x 20 = 8,000 8,000 x 20 = 160,000 Exponential Population Growth!

2 ——> x 20 = x 20 = 8,000 8,000 x 20 = 160,000 Exponential Population Growth!

2 ——> x 20 = x 20 = 8,000 8,000 x 20 = 160,000 Exponential Population Growth! (Home of Duggers and Romneys)

Pediculus humanus Figure 8.6

Deme, demography, vital statistics of populations Population parameters, mean and variance “Life” Tables: Cohort vs. Segment Samples Age and sex specificity Homocide example: Chicago vs. England Numbers dying in each age interval Discrete vs. continuous approaches Force of Mortality q x Age-specific survivorship l x Type I, II, III survivorship (rectangular, diagonal, inverse hyperbolic)

Expectation of further life, Age-specific fecundy, m x Age of first reproduction, alpha,  — menarche Age of last reproduction, omega,  Realized fecundity at age x, l x m x Net Reproductive rate Human body louse, R 0 = 31 Generation Time, T =  xl x m x Reproductive value, v x Stable vs. changing populations Residual reproductive value

T, Generation time = average time from one gener- ation to the next (average time from egg to egg) v x = Reproductive Value = Age-specific expectation of all future offspring p.143, right hand equation (4) “dx” should be “dt”

In populations that are expanding or contracting, reproductive value is more complicated. Must weight progeny produced earlier as being worth more in expanding populations, but worth less in declining populations. The verbal definition is also changed to “the present value of all future offspring” p.146, left hand equation (5) left out e -rt term

v x = m x +  (l t / l x ) m t Residual reproductive value = age-specific expectation of offspring in distant future v x * = (l x+1 / l x ) v x+1

Intrinsic rate of increase (per capita, instantaneous) r = b - d r max and r actual — l x varies inversely with m x Stable (stationary) age distributions Leslie Matrices (Projection Matrix) Dominant Eigenvalue = Finite rate of increase

Illustration of Calculation of E x, T, R 0, and v x in a Stable Population with Discrete Age Classes _____________________________________________________________________ AgeExpectation Reproductive Weighted of Life Value Survivor-Realizedby Realized E x v x Age (x) shipFecundityFecundityFecundity l x m x l x m x x l x m x _____________________________________________________________________ Sums2.2 (GRR) 1.00 (R 0 ) 2.78 (T) _____________________________________________________________________ E 0 = (l 0 + l 1 + l 2 + l 3 + l 4 + l 5 )/l 0 = ( ) / 1.0 = 3.4 / 1.0 E 1 = (l 1 + l 2 + l 3 + l 4 + l 5 )/l 1 = ( ) / 0.8 = 2.4 / 0.8 = 3.0 E 2 = (l 2 + l 3 + l 4 + l 5 )/l 2 = ( ) / 0.6 = 1.6 / 0.6 = 2.67 E 3 = (l 3 + l 4 + l 5 )/l 3 = (error: extra terms) ) /0.4 = 1.0 / 0.4 = 2.5 E 4 = (l 4 + l 5 )/l 4 = (error: extra terms) ) /0.4 = 0.6 / 0.4 = 1.5 E 5 = (l 5 ) /l 5 = 0.2 /0.2 = 1.0 v 1 = (l 1 /l 1 )m 1 +(l 2 /l 1 )m 2 +(l 3 /l 1 )m 3 +(l 4 /l 1 )m 4 +(l 5 /l 1 )m 5 = = 1.25 v 2 = (l 2 /l 2 )m 2 + (l 3 /l 2 )m 3 + (l 4 /l 2 )m 4 + (l 5 /l 2 )m 5 = = 1.40 v 3 = (l 3 /l 3 )m 3 + (l 4 /l 3 )m 4 + (l 5 /l 3 )m 5 = = 1.65 v 4 = (l 4 /l 4 )m 4 + (l 5 /l 4 )m 5 = = 0.65 v 5 = (l 5 /l 5 )m 5 = 0.1 ___________________________________________________________________________ Table 8.1 p. 144 delete extra terms (red)

Figure 8.7