Lab 5

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Lab 5

• Leslie Matrix Modeling
• Populations with Multiple Age Classes

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Todays Goal

• Create Leslie Matrix population models that
  incorporate age-specific survival and recruitment
  for multiple age classes and multiple species

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Objectives

• Using timelines and estimated population
  parameters No, F, P, and K, you will create
  Leslie matrix models of 4 species with different
  life history characteristics
• Your models should incorporate
• times of census and birth
• multiple age classes (N0, N1, N2,)
• age-specific survival (P) and recruitment rates
  (F)
• density dependence
• harvest management intervention with a stable
• age distribution (120 years)

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Objectives (cont.)

• Using your models, you will
• Evaluate how populations approach K
• Evaluate the effects of a constant harvest rate
  on a population and its relation to K
• Observe how non-linear dynamics appear to operate
  in these linear models

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Population Modeling so far

• Moose modeling lab
• Simple exponential model using r and ? to
  determine Nt
• Simple logistic model using r, ? and K to
  determine Nt
• Deer Contraception lab
• Explicit natality and season specific survival
  rates
• determine population growth rate
• Juvenile and adult age classes
• Incorporation of terms for culling and
  contraception
• management
• All individuals counted as adults have the same
  survival and
• natality rates
• Age structure introduced adults and neonates
  having
• differential survival rates and only adults
  reproduced

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What this looked like

• Adults1 (Adults0Survivaladults)
• Neonates1 Adults0SurvivaladultsNatalityadults
  Survivalneonates
• Only 2 age classes adult and neonate
• Only adults reproduced

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More realistic modeling

• In nature, many age classes are present with
  survival and natality
• A population with age structure is represented as
  a vector (a single column)
• Horizontal position indicates age class as
  indicated by N0 to N3
• Numbers indicate population size in each age class

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Matrix Modeling
A matrix includes recruitment and survival for
multiple age classes
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A Sample Matrix
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Calculation
T0
Sample Matrix
X
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Calculation (cont.)
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New vector for year T1

• Vector represents new population size
• Can be done iteratively for T2......TN using the
  same matrix
• Also, were only modeling females here

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Finding Stable Age Distribution
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• Tip for calculating density dependence
• In lab 3 we calculated density dependence as
  (K-N) / K
• However in the simple logistic model N never
  exceeds K, thus (K-N) / K is always a positive
  number
• Using a Leslie Matrix model N may exceed K,
  therefore the density dependence function will
  become a negative number when this overshoot
  occurs

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• Tip for calculating density dependence
• Because we cannot have a negative density
  dependence, which would imply a negative number
  of recruits added to the population, we will set
  the density dependence function equal to zero
  whenever it becomes negative
• This can be done using the IF function in Excel,
  which has the format
• IF(logical test, value if true, value
  if false)

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Your Assignment for Today

• Work in groups of 4
• One person in each group will create a Leslie
  matrix model for 1 of the 4 species
• grizzly bear
• coyote
• gray partridge
• California condor
• This lab will require a full report in JWM
  submission format
• Include in your discussion a comparison of
  population model for the different species and
  answers to all of the questions in the lab