Density Dependence

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Density Dependence Independence
kx log10(Nx) log10(Nx1)
px lx1/ lx 1-qx
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Lecture Goals

• explain the rationale and history behind
• density dependence
• density independence
• discuss how mortality factors between different
  life stages/ages combine quantitatively
• explain the concept of killing power and its
  calculation
• explain the use of k-factor analysis to determine
  
• the life stage determining abundance trends
• the density dependence/independent nature of
  mortality in a life stage

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What is density-dependence?

• Mortality rate (qx 1-px) is a function of
  population size (SNx)
• Not absolute numbers surviving
• Not number of individuals dying
• Traditionally associated with A.J. Nicholson
• Australian Ecologist
• Attributed to natural factors whose proportional
  impact on mortality varies with density
• Limited food, Limited space, Disease
• Often subject to intraspecific competition
• Tend to regulate (stabilize) population numbers
• But always??

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What is density-independence?

• Mortality rate (qx 1-px) is not function of
  population size (SNx)
• Numerically a constant proportion die/survive
• The constant can vary randomly through time
• Traditionally associated with Andrewartha and
  Birch
• Australian Ecologists
• Attributed to natural factors unrelated to
  density
• influencing the realized r value (exponential
  model)
• weather, predators, etc.
• No intrinsic regulation

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Beware of pigeon holes (in definitions)!!!
Is weather a density-dependent or independent
factor?
Why? (Explain yourself)
Consider the numbers when discussing quantitative
phenomena!
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Combining Mortalities Between Ages/Stages
Say there are 4 identifiable stages (age,
larvae/pupae, etc.)
Begin with N0 1000 eggs If q0 0 .5, q10.1,
and q20.9 How many from this group will reach N3?
N1 1000 (1-0.5) 500 N2 500 (1-0.1)
450 N3 450 (1-0.9) 45
px lx1/ lx 1-qx
N3 N0 p0 p1 p2
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We define a new value from our life tables k
kx log10(Nx) log10(Nx1)

• Known as killing-power
• represents loss through mortality
• ktotal is the killing power calculated through
  theentire generation
• ktotal log10(N0) log10(Nlast)
• ktotal S kx
• k values are additive
• q (mortality) is NOT additive

x
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Key Factor Analysis

• Identify relevant life stages/ages
• Observe cohort until all are dead to calculate
  the k-value for each stage
• Repeat for many cohorts
• Determine which stages k-values have the
  greatest contribution to the total k-value
• examined across many generations
• key factor
• Examine relationship between k-value (or
  survival) and numbers for the key-factors
• density-dependent or independent?

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An Example Atlantic Salmon (Salmo salar)
Jonsson et al. 1998. The relative role of
density-dependent and density independent
survival in the life cycle of Atlantic salmon
Salmo salar. J. Anim. Ecol. 67751-762
Questions What life stage determines numbers?
(implications for conservation
focus) Density-dependent or independent?
(implications for hatcheries)
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density-dependent (why?)
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(Some) Conclusions

• Mortality appears to be
• Density-dependent during the egg-smolt
  (freshwater) stage
• Density-independent during the smolt-adult (at
  sea) stage
• Mortality/Survival during the freshwater stage
  seems to be responsible for observed variations
  in adult numbers through the years studied.

Implications for Conservation? (Hatchery vs.
Habitat)
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Royama, T. 1996. A fundamental problem in key
factor analysis. Ecology 7787-93.
Criticisms include

• analysis overlooks important factors that do not
  vary over the study period
• consider previous analysis with only 79-82 data
• results can vary with the definition of stages
• especially in insects many shorter stages
  disperse/obscure contribution to K

for judging which factor is major, criteria
are multiple and subtle beyond the simplistic
idea of key factors.
- Royama 1996