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## Population Growth (Ch. 11)

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**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: • Per Capita Rate of Increase (r) • r = (ln Ro) / T • r = b – d**Exponential Growth**• Equation: dN / dt = rmax N • dN / 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, dN/dt gets larger.**Geo:**Nt = No t Exponential Growth • For exponential growth: Nt = N0 ermaxt • Nt = No. inds. at time t. • N0 = Initial no. inds. • e = Base natural logarithms • rmax = Intrinsic rate of increase • t = Number time intervals • Resources not limiting**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 = No t Nt = N0 ermaxt**Geometric or Exponential?**Nt = No t Nt = N0 ermaxt**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:dN/dt = rmax N (1-N/K) • rmax = Intrinsic rate of increase (ideal conditions) • N = population size @ time t • K = carrying capacity • Or: dN/dt = rmax N (K-N) K**How does this work?**• dN/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, dN/dt nears zero. Fig. 11.13**Logistic Population Growth**dN/dt = rmaxN (1-N/K) • 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**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) dN/dt = rmaxN (1-N/K)**Organism Size and Population Density**• A search for patterns…… • Size vs. density (neg. correlation) • Generation time vs. size? Size Gen time**Generation time vs. size**• Positive correlation • Log-log scale rmax 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)?**Human Population**• Where? 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 Effect on Type of interaction species A species B Competition - - Predation + - Parasitism + - Commensalism + 0 Mutualism + +**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