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