14.2 Measuring and Modeling Population Change

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14.2 Measuring and Modeling Population Change
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Carrying capacity

• The maximum number of organisms that can be
  sustained by available resources over a given
  period of time
• Is dynamic because environmental conditions are
  always changing

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Population growth factors

• Population dynamics changes in population
  characteristics
• The main determinants are
• natality (birth rate)
• mortality (death rate)
• Immigration (individuals moving in)
• Emigration (individuals moving out)

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Population change

• (births immigration) - (deaths emigration)
  x100
• initial population size
• (BI)-(DE)/ n x 100

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• CLOSED POPULATION
• A population whose growth is influenced only by
  natality and mortality
• OPEN POPULATION
• A population whose growth is influenced by
  natality, mortality and migrations

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Factors affecting Birth rate

• Fecundity theoretical maximum number of
  offspring that could be produced by a species in
  one lifetime

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• Fertility the number of offspring actually
  produced by an individual during its lifetime.
• affected by food supply, disease, mating success,
  etc.

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Type I survivorship

• Type I species that have a high survival rate of
  the young, live out most of their expected life
  span and die in old age.
• Example Elephants are slow to reach sexual
  maturity and have few offspring. They have a long
  life expectancy

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Type III survivorship

• Type III species that have many young, most of
  which die very early in their life.
• Example Plants, oysters and sea urchins.

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Type II survivorship

• Type II species that have a relatively constant
  death rate throughout their life span. Death
  could be due to hunting or diseases.
• Examplescoral, squirrels, honey bees and many
  reptiles.

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Biotic potential

• maximum reproductive rate under ideal conditions
  (intrinsic rate of natural increase)
• Example Under ideal conditions, a population of
  bacteria can grow to more than 10 in 24 h.
• Limiting Factor the name applied to an essential
  resource that is in short supply or unavailable,
  and prevents an organism from achieving this
  potential

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Geometric Growth

• - births take place at one time of the year
  (i.e., breeding season), but deaths may occur all
  year
• - population grows rapidly during breeding
  season, declines throughout year until next
  breeding season
• - constant growth rate must be compared by
  looking at same time each year
• - annual growth rate can be determined
• - line of best fit (on graph) produces J-curve
• - examples seals, deer, salmon

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Geometric growth

• A population that grows rapidly during breeding
  season, then declines through the year until the
  next breeding season

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• Populations with geometric growth curves
  experience a constant growth rate
• Determine growth rate with formula
• ? N(t1)/N(t)
• where ? (lambda) represents the geometric growth
  rate
• N(t1) represents the population size in a given
  year
• N(t) represents the population size at the same
  time in the previous year. (See page 663)

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• This equation can be generalized and rearranged
  to find population size at any given time
• N(t) N(0) ?t
• See page 633-634, Sample Problem

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Exponential growth

• reproduction is continuous throughout year (i.e.,
  no breeding season)
• - constant growth rate
• - instantaneous growth rate can be determined,
  more complex than ageometric formula
• - examples yeast, bacteria, humans
• In natural populations, exponential growth does
  not continue indefinitely because of limited
  amounts of energy, water, shelter, space

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• Can use a modified form of exponential growth
  formula to estimate doubling time.
• See Sample Problem p.665

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• Both geometric and exponential growth models
  produce similar graphs, known a J-curves.

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Logistic Growth Curve
Stationary phase - stabilizing
Log phase very rapid growth
Lag phase small population size, therefore slow
population growth
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r- and k- species

• Depending on their reproductive strategies,
  species can be characterized as r or k species.
• r is the instantaneous rate of population
  increase while k is the carrying capacity.

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• The r-species possess characteristics of high
  biotic potential, rapid development, early
  reproduction, single period of reproduction per
  individual, short life cycle, and small body
  size.
• Populations of r-species usually remain below the
  carrying capacity and are regulated by
  density-independent factors

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• k-species possess characteristics of low biotic
  potential, slow development, delayed
  reproduction, multiple periods of reproduction
  per individual, long life cycle and larger body
  size.
• populations of k-species are usually maintained
  near the carrying capacity and regulated by
  density dependent factors

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• In disrupted habitats r-species are more common
  while k-species are common in stable habitats.
  Many of our agricultural pests are r-species.
  Most organisms however actually have attributes
  that fit both r and k species.