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

Lecture # 1519 October 2017

Evolution of Senescence

•Recession of time of expression of the overt effects of a detrimental allele

• Precession of time of expression of the effects of a beneficial allelle

Varanus komodoensis

Joint Evolution of Rates of Reproduction and Mortality

Donald Tinkle

Sceloporus

Joint Evolution of Rates of Reproduction and Mortality

Donald Tinkle

Sceloporus

Inverserelationshipbetween rmax

and generation time, T

Threshold ofAnnuality

J - shaped exponential population growth

http://www.commondreams.org/view/2011/03/07-0http://www.zo.utexas.edu/courses/THOC/exponential.growth.html

Once, we were surrounded by wilderness and wild animals, But now, we surround them.

http://www.commondreams.org/view/2011/03/07-0

S - shaped sigmoidal population growth

K NK K

—( N K( —

(

1

Pearl-Verhulst Logistic Equation

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 (1 – N/K) = rN – (r/K)N2

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) or (x+y) = r/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 before, r/K for (x + y), multiplying through by N, and rearranging terms, dN/dt = rN – (r/K)N2

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 Coastin the winter of 1940.

Parus major

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 nearcarrying capacity of envi- carrying capacity of theronment; unsaturated com- environment; saturatedmunities 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 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__________________________________________________________________

Dr. Kirk WinemillerTexas A & M. Univ.

Molamola

GambusiaSharks, skates,and RaysMosquito Fish

Sturgeon

Dr. Kirk WinemillerTexas A & M. Univ.

Cocoa Nut Tree

Sequoia Tree

Dandelion

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 Taxa__________________________________________________________

Numbers of Populations in Various Categories Positive Positive Negative Negative Negative

Taxon (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 7Reptiles 0 0 0 5 19 24Birds 0 2 32 16 43 93Mammals 1* 0 4 1 13 19 Totals 1* 3 45 23 90 162___________________________________________________________* Homo sapiens

http://www.commondreams.org/view/2011/03/07-0http://www.snopes.com/disney/films/lemmings.aspMicrotus

Notice apparent 10-year periodicity

Hudson Bay Company

Hudson Bay CompanyHudson's Bay was incorporated on 2 May 1670, with a royal charter from King Charles II.The charter granted the company a monopoly over the region drained by all rivers and streams flowing into Hudson Bay in northern Canada. The area gained the name "Rupert's Land" after Prince Rupert, the first governor of the company appointed by the King. This drainage basin of Hudson Bay constitutes 1.5 million square miles, comprising over one-third of the area of modern-day Canada and stretches into the present-day north-central United States. The specific boundaries were unknown at the time. Rupert's Land would eventually become Canada's largest land "purchase" in the 19th century.

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

Sunspot Hypothesis (Sinclair et al. 1993. Am. Nat.)

10 year cycle embedded within 30-50 year periods

Maunder minimum: 1645-1715

Three periods of high sunspot maxima:

1751-1787 1838-1870 1948-1993

Canadian Government Hare survey 1931-1948

Hare cycle synchronized across North America

Yukon: 5 km strip, tree growth rings (N = 368 trees)

One tree germinated in 1675 (>300+ years old)

Hares prefer palatable shrubs,

but will eat spruce

leaving dark tree ring marks

Anthony Sinclair

Charles J Krebs

CH4

C02

°C

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

Other Food Quality Hypotheses:

Microtus: palatability <–––> toxic (Freeland 1974)

Snowshoe hares: Plant chemical defenses against herbivory

Could optimal reproductive tactics beinvolved in driving population cycles?

Chitty’s “Genetic Control” Hypothesis

Dennis Chitty

http://www.commondreams.org/view/2011/03/07-0http://www.snopes.com/disney/films/lemmings.aspMicrotus