Population Growth Ch 11 Population Growth 1 Geometric

Population Growth (Ch. 11)

Population Growth • 1) Geometric growth • 2) Exponential growth • 3) Logistic growth

Geometric Growth • Growth modeled geometrically – Resources not limiting – Generations do not overlap • Recall: • 1) = Nt+1 / Nt • 2) = Ro

Geometric Growth • Growth modeled geometrically – Resources not limiting – Generations do not overlap • Equation: Nt = No t – Nt = Number inds. @ time t – No = Initial no. inds. – = Geometric rate of increase – t = Number time intervals

Geometric Growth • Phlox (annual plant) Fig. 11. 3

Exponential Growth • Growth modeled exponentially – Resources not limiting – Generations overlap • Recall: 1) Per Capita Rate of Increase (r) 2) r = (ln Ro) / T 3) r = b – d

Exponential Growth • Equation: d. N / dt = rmax N • d. N / dt means “change in N per unit time” • Recall r: per capita rate of increase (Ch. 10) • rmax: Special case of r (intrinsic rate of increase). b - d under optimum conditions – b = birth rate and d = death rate (rates per individual per unit time) • As N increases, d. N/dt gets larger.

Exponential Growth • For exponential growth: Nt = N 0 ermaxt • • • Nt = No. inds. at time t. N 0 = Initial no. inds. e = Base natural logarithms rmax = Intrinsic rate of increase t = Number time intervals Resources not limiting Geo: Nt = N o t

Exponential Growth: Example • Whooping crane

Exponential Growth: Example • Hunting/habitat destruction • Federally listed Endangered(1967). Down to 22!! Fig. 11. 6

Exponential Growth: Example • Raising birds: costumes avoid imprinting on humans

Exponential Growth: Example • Teaching young birds to migrate (Wisconsin to Florida) 1996

Geometric or Exponential? Nt = N o t Nt = N 0 ermaxt Geometric Exponential Generations

Geometric or Exponential? Nt = N o t Nt = N 0 ermaxt Geometric Exponential Separate Generations Overlap λ=1 Population stable r=0 λ>1 Population growing r>0 λ<1 Population shrinking r<0

Logistic Population Growth • Unlimited resources? ? nothing lasts forever… • As resources depleted: logistic population growth.

Logistic Population Growth • As resources depleted, logistic population growth (generations overlap) – Sigmoid (S-shaped) curve. – Carrying capacity (K): number environment can support. Fig. 11. 8 Ex

Logistic Population Growth • Yeast growth (limited alcohol) • Max. 17% (34 proof) Fig. 11. 9

Logistic Population Growth Equation: d. N/dt = rmax N (1 -N/K) • rmax = Intrinsic rate of increase (ideal conditions) • N = population size @ time t • K = carrying capacity • Or: d. N/dt = rmax N (K-N) K

How does this work? • d. N/dt = rmax N (K-N) K • N small: rmax N (K-0) or ≈ rmax N (1) K At small N, acts like exponential growth! • N big: rmax N (K-K) or ≈ rmax N (0) K At larger N, growth slows: stops at K

Logistic Population Growth 1 -N/K is “scaling factor” When N nears K, d. N/dt nears zero. Fig. 11. 13

Logistic Population Growth • r: actual (realized) reproductive rate (b -d) • Max. @ small N • When N=K, r=0 • So b=d and b-d=0 • Above K? r negative Fig. 11. 14 d. N/dt = rmax. N (1 -N/K)

Concepts! • Population growth (# added per unit time) highest when N=K/2 • Maximum sustainable yield: largest sustainable harvest

Concepts! • N/K: reflects environmental resistance – Factors that limit population size Environmental resistance – Density-dependent factors: depend on density (N/K) • Disease, Resource competition – Density-independent factors: not related density • Natural disasters (hurricane, fire, flood) d. N/dt = rmax. N (1 -N/K)

Organism Size and Population Density • A search for patterns…… Size – Size vs. density (neg. correlation) – Generation time vs. size? Gen time

Generation time vs. size rmax • Positive correlation • Log-log scale size vs. rmax? Size

rmax vs. size • Negative correlation • Note log: log scale

Human Population • How many? • Where? • Age distributions and growth potential How many?

• • • Human Population How many? 7. 09 billion (6/17/13) 7. 02 billion (6/11/12) 6. 925 billion (6/19/11) 6. 448 billion (6/18/05) Check it out now at: • http: //www. census. gov/ipc/www/idb/worldpopinfo. php Where (continent)?

• Where? Human Population Fig. 11. 23 Fig. 11. 22

Human Population • Where?

Human Population • Age distributions and growth potential, 2008 Fig. 11. 24

Human Population • “Population bomb”: potential of population to explode as people age 2000/2001 -Present - New Silent Generation or Generation Z
 1980 -2000 - Millennials or Generation Y
 1965 -1979 Generation X
 1946 -1964 - Baby Boom 1925 -1945 – Silent Generation 1900 -1924 – G. I. Generation

Human Population • Human pop. curve: shape? • What Earth’s K for humans?

Human Population • Depends in part on lifestyle! – Ecological footprint: resource use – Biocapacity: resource supply – Deficit if use>supply: US largest deficit

Course sequence • • • Natural history (Done!) Individuals (Done!) Populations (Done! Except Life Histories) Species interactions (You are here!) Communities/ecosystems Geographic/global ecology

5 main types of interactions among species: Effect on species A Effect on species B Competition - - Predation + - Parasitism + - Commensalism + 0 Mutualism + + Type of interaction

Species Interactions: Competition (Ch. 13)

Competition (Ch. 13) • Definition: – Individuals attempt to gain more resource in limiting supply – (-, -) interaction: both participants get less • Intraspecific: Within species. • Interspecific: Between species.

Competition • Interference Competition: – Individuals interact with each other • Resource (Exploitation) Competition: – Individuals interact with resource