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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

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Density and Dispersion

Life table analysis

• Cohort

• Survival

• Fedundity

• Mortality

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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

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Parus major

Great TitsIteroparity and the age-dependent

reproduction

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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

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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

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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

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Age Structure and Populations Human Populations

r and K

“r-selected “species maximize“K-selected” species maximize

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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