population growth (ch. 11). population growth 1) geometric growth 2) exponential growth 3) logistic...
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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) / T3) 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.
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
Geo:Nt = No 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?
Geometric Exponential
Generations
Nt = N0 ermaxtNt = No t
Geometric or Exponential?
Geometric Exponential
Separate Generations Overlap
λ = 1 Population stable r = 0
λ > 1 Population growing r > 0
λ < 1 Population shrinking r < 0
Nt = No tNt = 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.
Ex
Fig. 11.8
Logistic Population Growth• Yeast growth (limited alcohol)
• Max. 17% (34 proof)
Fig. 11.9
Logistic Population GrowthEquation: 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 Growth1-N/K is “scaling factor”
When N nears K, dN/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
dN/dt = rmaxN (1-N/K)
Fig. 11.14
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 = rmaxN (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
Siz
e
Generation time vs. size
• Positive correlation• Log-log scale
size vs. rmax? Size
r max
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. 11.22
Fig. 11.23
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 Z1980-2000 - Millennials or Generation Y1965-1979 - Generation X1946-1964 - Baby Boom1925-1945 – Silent Generation1900-1924 – 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 onType 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