Population Biology Defining the individual
Transcript of Population Biology Defining the individual
11/12/2008
1
Population Biology
• Essential to understand human populations
• Essential to understand endangered species
• Essential to understand pests
• Essential to understand other economically
important species
Defining the individual
• Unitary
– Individuals are discrete
– Less plasticity
• Modular
– Individuals reproduce by modules
– More plasticity
– Ramets and genets
– biomass
Populations Spatial Scale: Extent
Spatial Scale: Resolution Geographic Range
11/12/2008
2
Density and Dispersion
Life table analysis
• Cohort
• Survival
• Fedundity
• Mortality
11/12/2008
3
Simple Cohort Life Table
Interval (days)
Number
surviving (ax)
Proportion of original
surviving (lx)
Proportion of
orginal cohert
dying during
interval (dx)
Mortality rate
per day (qx) Log10 lx
Cohort fecundity
Fx
Average
fecundity per
survivor (mx)
Proportion of
original fecundity
(lxmx)
0-63 996 1.000 0.329 0.006 0.000
63-124 668 0.671 0.374 0.013 -0.173
124-184 295 0.296 0.105 0.007 -0.528
184-215 190 0.191 0.014 0.003 -0.720
215-264 176 0.177 0.004 0.002 -0.753
264-278 172 0.173 0.005 0.002 -0.763
278-292 167 0.168 0.008 0.004 -0.776
292-306 159 0.160 0.005 0.002 -0.797 53 0.333 0.053
306-320 154 0.155 0.007 0.003 -0.811 485 3.149 0.487
320-334 147 0.148 0.042 0.025 -0.831 803 5.461 0.806
334-348 105 0.105 0.083 0.106 -0.977 973 9.264 0.977
348-362 22 0.022 0.022 1.000 -1.656 95 4.309 0.095
362- 0 0.000
0.000
0.200
0.400
0.600
0.800
1.000
1.200
Proportion Surviving
-1.800
-1.600
-1.400
-1.200
-1.000
-0.800
-0.600
-0.400
-0.200
0.000
Cohort Life Table
Static Life Table
11/12/2008
4
Parus major
Great TitsIteroparity and the age-dependent
reproduction
11/12/2008
5
Reproductive rates (R0, λ, r)
• Basic reproductive rate
• Fundamental net reproductive rate
– If prefer the symbol: λ
– If λ > 1 the population increases if < 1 the
population decreases
– Does not separate between survival and
reproduction
Reproductive rates (R0, λ, r)
• Note that R0 = λ T
• and ln(R0)= T ln(λ)
• And ln(λ) = ln(R0)/T
• ln(λ) = r
• So r=ln(R0)/T
• r is the intrinsic rate of natural increase
• If r > 0 the population grows, if < 0 then
population declines and if r = 0 then?
The nature of population growth
• Exponential
• Excel exercise (using Nt = N0R^t)
Matrices
• A matrix is a rectangular arrangement of data in the form m x n where m is the number of rows and n is the number of columns
• Capital letters are used: A
• An element or entry is any datum of the matrix and lowercase is typically used
• The position of the element is denoted with subscripts ij where i is the row and j is the column.
– Example: a12,3 would be found in the 12th row, 3 third column
• A vector is a m x 1 or 1 x n matrix
Leslie or Population Projection Matrix
In this example
There are three age classes
Fx is the fecundity of cohort x
Sx is the survival of cohort x to cohort x+1
Population vector
In this example:
Three age classes
Nx is the number in each age class
11/12/2008
6
Matrix multiplication
x nt=1 =
= nt=1 =
Population Change
The resultant vector is the new population
broken down by age structure
The new population is the sum of each of the age groups. In this case, Nt+1 = 112
Remember that λ is and the original
population was or 100 0
1
N
N t+=λ
so λ is 112/100 or 1.12
And? What do we do with this beast?
• A useful tool for seeing what happens to populations in the future
• Can incorporate stochasticity
– Gives a range instead a single value
• Can estimate the parameters that drive the results using a sensitivity analysis
– Important to figure out what to protect for endangered species or
– What to target for pest species
Leslie Projection Matrices
• Used to see what would happen under
different scenarios
• Can be expanded (gets ugly fast)
– Include spatial structure
– React to disease
– Competitors
– Etc
– Carrying capacity
Carrying Capacity
• Ideal populations
– Everything needed is provided
– Populations increase exponentially
• Real populations
– Population has some limit set by the environment
– This upper limit is carrying capacity
– Highest density “allowed” by the environment
– Real populations may show exponential growth up to, over, or near the carrying capacity
Carrying Capacity
• In most cases, exceedingly difficult to measure– May be easy on a small scale where a limiting factor is
easily monitored• Rock structure for sessile organisms
• Nesting sites for albatross
– Limiting factor can be biotic and abiotic
– Typically a mix of factors
– Ecology, being ecology, makes for complexities• Species that limit some species are themselves limited by
other species that are limited by other species that are limited by other species that are limited by other species that are limited by other species and so on
11/12/2008
7
Carrying Capacity Carrying capacity
Density Independent vs. Density
Dependent GrowthPopulus Exercises
Bottom-up or top-down?
• Bottom up
– Nutrients
– Water
– Nesting sites
– Trophic levels below
• Top down
– Predators
– Parasites
– Trophic levels above
11/12/2008
8
Age Structure and Populations Human Populations
r and K
“r-selected “species maximize“K-selected” species maximize
11/12/2008
9
r and K selection
Robert MacArthurE. O. Wilson
R and K selection Characteristics
r-strategist K-strategist
Climate variable constant or predictable
Population size variable, recolonization at equilibrium
Competition variable, lax keen
Lifespan short, <1yr long, slower development
Size small larger
Reproduction much energy toward, rapid, large number of progeny
delayed reproduction, few offspring
Leads to high productivity efficiency
Modern view of r and K selection