BIOL 3500

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Lecture 8

• BIOL 3500
• Chapter 10 Population Growth

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Learning Objectives

• Contrast
• Crude vs. gross vs. net reproductive rates
• Recall
• Which letter goes with each life table column
• Define
• Finite multiplication rate

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Birth Rate

• Crude birth rate of births / 1000 individuals
• Problems
• Includes males!
• Not all females have equal fecundity

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Age-Specific Birthrates

• Eliminate males
• Divide females into age classes
• Record births per female as bx

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Why Sum?

• Summing bx gives number of births, assuming age 6
  is reached
• Gross reproductive rate
• Is this valid?

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Accounting for Survival

• Not all females live to final age class
• To adjust our estimate, multiply survivorship
  fecundity
• Note difference between age classes
• Net reproductive rate is the result R0

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Age-Specific Mortality, Survival, and Birthrates

• Can you tell me which letter goes with each?

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Projection Table

• Imagine a hypothetical population
• Only count females
• 10 of age 1
• They have 20 babies

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Building the Projection

• How many moms will survive?
• How many babies will survive?

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Heres the Table

• Population gets larger

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Age Distribution

• Which year is age structure stabilized?

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Calculating Lambda

• Lambda total population / previous total
• Called the finite multiplication rate
• Q What is 1.20 times 30?
• To estimate population size, Nt N0?t

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7th Inning Stretch
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Effect of Lambda
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St. Paul Island, AK

• 4 males, 22 females introduced in 1910
• Population declined to 8 in 1950
• What happened to lambda?

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Defining r

• r is obtained from the natural log of lambda
• Why is this necessary?
• Lambda of 0.887 and 1.127 are changing at same
  rate (hard to see this)
• Their equivalent r is -0.120 and 0.120
• Book has this backwards!

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Whats the Difference?

• Lambda
• Based upon discrete time intervals
• r is instantaneous
• Like slope dN/dT

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Population Growth Models

• Population ecologists use mathematical models to
  describe natural phenomena
• Exponential growth
• Logistic growth
• In both, G growth rate (dN/dt)

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Exponential Growth

• Population increases by a constant factor, every
  generation
• Be able to recite
• G rN
• Example bacteria doubling
• Increase by factor of two every generation

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Conditions for Exponential Growth

• Occurs under ideal conditions
• Infinite resources
• Food
• Space
• Territories
• No limitations on numbers
• No predators
• No pollution

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Bacteria Grow Exponentially
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Exponential Growth Rate

• Larger population faster growth

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Problems with Exponential Growth Model

• Can only be applied to small set of circumstances
• Infinite resources
• No limitation on numbers
• Most populations dont meet these criteria
• If they do, only for limited time

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Logistic Growth Model

• Like exponential growth, describes a population
• Unlike exponential growth, includes limitation of
  resources
• When resources plentiful, population grows
• When resources are limited, population stops
  growing, or shrinks
• Logistic Growth Equation
• Be able to recognize
• G rN (K-N)/K

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Carrying Capacity

• Carrying capacity (k) is the number of
  individuals an area can support
• May be determined by
• Food
• Territories
• Water
• Nutrients

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Fur Seals

• St. Paul Islands, AK
• Before 1925 population low
• Unlimited hunting
• 1925 to 1935 population grew dramatically
• Hunting heavily regulated
• After 1935, population reached carrying capacity
  of island, stopped growing

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Fur Seals

• Carrying capacity reached after 1935

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Exponential vs. Logistic Growth

• Exponential growth dN/dt rN
• Logistic growth dN/dt rN (k-N)/K

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Carrying Capacity

• Represented by K
• What is slope when population reaches carrying
  capacity?

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Monroe County, West Virginia
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Different Fluctuations
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Two Cycling Populations

• Hares controlled by food availability (aspen
  twigs)

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Extinction of Heath Hens

• Once plentiful
• 1908 only 50 left on Marthas Vineyard
• 1916 a bad year
• Environmental uncertainty
• Fire destroyed necessary grassland habitat
• Harsh winter
• Hungry goshawks (birds of prey)
• Poultry disease
• 1928 bad luck
• Demographic uncertainty
• 13 birds left
• Only 2 females
• 1932 extinction

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Extinction of the Heath Hen

• Population declined due to hunting habitat loss
• Required grasslands, which were lost to farming
• In the Wild website
• Note conservation efforts