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) = N t+1 / N t 2) = R o

Geometric Growth Growth modeled geometrically –Resources not limiting –Generations do not overlap Equation: N t = N o t –N t = Number time t –N o = 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 R o ) / T 3)r = b – d

Exponential Growth Equation: dN / dt = r max N dN / dt means “change in N per unit time” Recall r: per capita rate of increase (Ch. 10) r max : 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.

Exponential Growth For exponential growth: N t = N 0 e r max t N t = No. inds. at time t. N 0 = Initial no. inds. e = Base natural logarithms r max = Intrinsic rate of increase t = Number time intervals Resources not limiting Geo: N t = 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? GeometricExponential Generations N t = N 0 e r max t N t = N o t

Geometric or Exponential? GeometricExponential SeparateGenerationsOverlap λ = 1Population stabler = 0 λ > 1Population growingr > 0 λ < 1Population shrinkingr < 0 N t = N o t N t = N 0 e r max t

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. Ex Fig. 11.8

Logistic Population Growth Yeast growth (limited alcohol) Max. 17% (34 proof) Fig. 11.9

Logistic Population Growth Equation: dN/dt = r max N (1-N/K) r max = Intrinsic rate of increase (ideal conditions) N = population time t K = carrying capacity Or: dN/dt = r max N (K-N) K

How does this work? dN/dt = r max N (K-N) K N small: r max N (K-0) or ≈ r max N (1) K At small N, acts like exponential growth! N big: r max N (K-K) or ≈ r max 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

Logistic Population Growth r: actual (realized) reproductive rate (b-d) small N When N=K, r=0 So b=d and b-d=0 Above K? r negative dN/dt = r max N (1-N/K) Fig

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

Concepts! 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 = r max N (1-N/K) N/K: reflects environmental resistance –Factors that limit population size

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

Generation time vs. size Positive correlation Log-log scale size vs. r max ? Size r max

r max 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) billion (6/19/11) billion (6/18/05) Check it out now at: Where (continent)?

Human Population Where? Fig Fig

Human Population Where?

Human Population Age distributions and growth potential, 2008 Fig

Human Population “Population bomb”: potential of population to explode as people age 2000/2001-Present - New Silent Generation or Generation Z Millennials or Generation Y Generation X Baby Boom – Silent Generation – 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 Type of interaction species A species B Competition - - Predation + - Parasitism + - Commensalism + 0 Mutualism + +

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