Overall mean: 75'2% 11'4%

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• Overall mean 75.2 11.4
• Multiple choice 45.9 8.7 (75)
• Essay 1 14.8 2.7 (75)
• Essay 2 14.5 3.0 (75)
• Answers will be posted later today (glass case on
  3rd floor Felmley)
• Complaints

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Mortality rates idealized patterns

• TYPE I Low mortality rate for most of life,
  followed by rapid mortality near end of life time
• Humans (sometimes), some other mammals
• TYPE II Constant mortality rate across entire
  life
• Birds
• TYPE III Extremely high mortality rate early,
  followed by low mortality later in life
• Invertebrates, fish, plants

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Idealized Survivorship curves
Type I
Type II
Type III
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Real survivorship curves

• Often represent combinations of the idealized
  survivorship curves
• High mortality rate early in life accelerating
  mortality rate late in life
• Example Spruce budworm

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Spruce budworm survivorship
Number Alive
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Adding birth to life tables

• mx fecundity at age x
• note bx in text (important)
• SEMELPAROUS Each individual reproduces once,
  then dies
• Salmon, annual plants, many insects, Agave
• ITEROPAROUS Each individual reproduces gt1 time
• Humans, most mammals birds, trees, barnacles

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Life table for barnacle
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Net reproductive rate (R0)

• Multiply probability of being alive (lx) by
  offspring produced at that age (mx)
• Yields mean number of offspring produced at age x
  (across entire cohort)
• Sum across all ages ?x0 lxmx R0
• Net reproductive rate
• Number of age 0 offspring produced by an average
  member of the cohort (lifetime)

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Life table for barnacle
R0Sx0 lxmx1.2852
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Interpreting R0

• Number of age 0 offspring produced by an average
  member of the cohort (lifetime)
• If R0 1 then individuals replace themselves,
  and population does not change
• R0 gt 1 implies population is increasing
• R0 lt 1 implies population is decreasing

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Problem

• Female Mice
• 50 of survive from one year to the next
• Give birth to 3 female offspring / year, starting
  in yr. 1
• After 3 breeding seasons, death by old age
• construct life table
• calculate R0

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End 14th lecture
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Cohort Generation Time (Tc)

• Note Gc in text
• For this population, how long between birth of
  parents and birth offspring?
• Overlapping generations
• Must average across all offspring, all parents
• ?x0 xlxmx / ?x0 lxmx Tc
• Numerator - weighted sum of time at birth
• Denominator - total births per individual (R0)

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Life table for barnacle
3.9345Sx0xlxmx
R0Sx0 lxmx1.2852
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Calculate Tc

• Tc ?x0 xlxmx / ?x0 lxmx
• 3.9345 / 1.2852
• 3.1003 years
• average generation time

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Uses of life tables

• Projecting population growth in age structured
  populations
• Total births across the entire population depends
  on mx and on the age distribution
• Total deaths across the entire population depends
  on lx and the age distribution
• must have the life table plus the age distribution

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An age distribution
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Stable age distribution

• For a constant life table (lx and mx), the
  population rapidly approaches a characteristic
  distribution of ages
• Stable age distribution
• all age classes increase at the same rate
• can be calculated from life table (later)
• typically attained in a few generations

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Population rate of increase

• At stable age distribution, population changes
  according to
• Nt N0 ert
• N0 individuals at time 0
• Nt individuals at time t
• e 2.71828 (base of natural logarithm)
• t time
• r per capita rate of increase

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Population growth

• Per capita rate of increase r dN / Ndt
• Population growth dN/ dt rN
• Exponential growth
• also known as Geometric growth
• At stable age distribution, r can be calculated
  from a life table

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Nt N0 ert

• if r 0.5 and N0 100
• N1 N0 ert 100(e0.51) 100(1.648) ? 165
• N2 N0 ert 100(e0.52) 100(2.718) ? 271
• N3 N0 ert 100(e0.53) 100(4.482) ? 448
• N4 N0 ert 100(e0.54) 100(7.389) ? 739
• N5 N0 ert 100(e0.55) 100(12.182) ? 1218
• multiplicative increase (?1.648 er )
• finite rate of increase er ?

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Exponential vs. arithmetic
Slope dN/dt
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Calculating r from a life table

• Assume stable age distribution, constant lx and
  mx
• Sx0 e-rx lx mx 1
• cannot solve for r algebraically
• find r by trial and error

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End 15th lecture