Population ecology readings:

Ch 9 – population structure

Ch 10 – Life Tables, pp. 239-249

Ch 11- Exponential and Logistic Growth

DEF: Populations are individuals of the same species that live together in time and space

POPULATION ECOLOGYWhy here and why now?

(1) Populations have emergent structures….

- Wolf packs; cooperative hunting, deferred reproduction

individuals populationsAre born and die birth rates and mortality ratesDisperse immigration and emigration rates

Extinctionpopulation structures (e.g., clumping)Evolve

POPULATION ECOLOGYWhy here and why now?

(2) Many important processes related to, in particular, mortality and reproduction are Density Dependent as opposed to beingDensity Independent.

Abiotic forces are density independent: - Fire kills irrespective of the number of trees - Saguaros: Frost kills irrespective of the number of cacti - Cold weather kills irrespective of the number of squirrels

Biotic forces are density dependent: - Competition: your food availability depends on how many mouths there are - Predation: predators seek food patches containing many prey - Escaping predation depends on group defense - Mutualisms: seed production depends on the number of pollinators

Are these statementsalways true?

Hence, we want to characterize the number of individuals

Populations: Abundance or Density( # individuals) (# individuals/area)

Survival of indivs:Reproduction of indivs: }

Project abundance/densityinto the future Growth Rate

Building Life Tables:

(1) Follow a population (or given group of indivs – a cohort) from birth to death

(2) Follow a population of known-age indivs for a shorter period of time and record deaths and births as a function of age

Terms:

X = Age (days, weeks, years) of individuals

NX = Number of individuals alive at the start of age X

lX = Proportion of the initial population that is alive at the BEGINNING of age X. ****l0 = 1.0

mX = The number of daughters born to an average female during the interval X to X+1.

Because only females contribute to population growth, life tables only track female individuals

X NX lX mX

0 100 1.0 01 50 0.5 12 25 0.25 33 12 0.12 24 0 0 0

What do we have?

(1) Maximum lifespan is 4 years

Age # survivor maternity

X NX lX mX

0 100 1.0 01 50 0.5 12 25 0.25 33 12 0.12 24 0 0 0

(2) We can plot the natural logarithm of NX (or lX) versus age to examine survivorship: (book plots Nx on a Log scale)

age X

ln(NX) Population experiences constant survivorship with age: ~ ½ the population dies at each interval

Age # survivor maternity

This is in contrast with populations that senesce:

age X

ln(NX)E.g., Humans, whales

or, experience greatest mortality early in life

age X

ln(NX)

E.g., Most insects, many plants

X NX lX mX

0 100 1.0 01 50 0.5 12 25 0.25 33 12 0.12 24 0 0 0

(3) Reproductive effort (per individual) is greatest at midlife

Age # survivor maternity

But even better, we can calculate a population growth rateand determine whether the population is increasing or declining

X NX lX mX

0 100 1.0 01 50 0.5 12 25 0.25 33 12 0.12 24 0 0 0

Age # survivor maternity

lXmX

00.50.750.240

lXmX = the number of daughters each initial female can expect to give birth to during the interval X to X+1.

X NX lX mX

0 100 1.0 01 50 0.5 12 25 0.25 33 12 0.12 24 0 0 0

Age # survivor maternity

lXmX

00.50.750.240

The difference between lXmX and mX is the former accounts for mortality. E.g., m2 = 3 and L3m3 = 0.75.

0.75 < 3 because 75% of females die before the age of 2

lXmX

00.50.750.240

Expected # daughters between ages 0 – 1Expected # daughters between ages 1 – 2Expected # daughters between ages 2 – 3Expected # daughters between ages 3 - 4

If we add all these up, we get the expected number of daughters over a females lifetime

That sounds Useful !!! And IT IS

The sum of lXmX is called the Net Reproductive Rate, R0

R0 = (lXmX) is the expected number of daughters born to each female during her lifetime.

It is true that many females do not reproduce, those that do have many daughters in their lifetime – what we are examining is the reproductive output of the average female.

Given that each female dies in her lifetime (-1 female) if R0 = 1 daughter, then she exactly replaces herself in her lifetime

Has the population therefore grown or declined??

If R0 = 1 the population is neither growing or declining, rather population size is stable.

If, however, R0 > 1 the population is growing

And, if R0 < 1 the population is declining

R0 = 1.25 = 25% population increase/generation **R0 = 0.67 = 33% population decrease/generation **

** True in special circumstances (e.g., annual plants)

Why are Life Tables Useful??

We can tell at a glance: (1) patterns of survivorship, (2) at what age reproductive potential is “stored”, (3) The direction and magnitude of population change

Furthermore, we can understand the effects of changes inage-specific death or maternity whether by accidental orby design.

Peter and RosemaryGrant’s study of Darwin’s Finches

Life Tables – the COHORT approach

1 2 3 4 5 6 7 8 9 10 11

1 2 3 4 5 6 7 8 9 10 11

Age in years

1987

1983

Per

cent

age

of f

inch

es

0

25

50

0

25

50

droughts

La Niña

drought1977See Fig. 10.19

in your text

Bottom-heavyIncreasing

populations

Top-heavydeclining

populations

TheSTATIC approach

X NX lX mX

0 100 1.0 01 50 0.5 1.02 25 0.25 3.03 13 0.13 1.04 6 0.06 0.55 3 0.03 06 0 0 0

--------------------------------------------------------

R0 = 0.865

R0 = 1.38

X NX lX mX

0 100 1.0 01 50 0.5 1.02 10 0.1 3.03 5 0.05 1.04 3 0.03 0.55 1 0.01 06 0 0 0

Hunters target young adults

X NX lX mX

0 100 1.0 01 50 0.5 1.02 25 0.25 3.03 13 0.13 1.04 0 0 0.5

Hunters target old adults

Constant mortalityrate with age and reproductivesenescence

R0 = 1.41

X NX lX mX

0 100 1.0 01 20 0.20 02 10 0.10 2.53 5 0.05 2.54 2 0.02 3.05 1 0.01 3.06 0 0 0

X NX lX mX

0 100 1.0 01 40 0.4 02 20 0.2 2.53 10 0.1 2.54 5 0.05 3.05 2 0.02 3.06 0 0 0

X NX lX mX

0 100 1.0 01 20 0.20 02 15 0.15 2.53 11 0.11 2.54 8 0.08 3.05 6 0.06 3.06 0 0 0

--------------------------------------------------------

Increase survival of hatchlings Increase survival of adultsR0 = 0.96 R0 = 1.07

Constant mortality (50%)rate with age and increasing reproductiveoutput with age

R0 = 0.465

Fundamental Niche

Realized Niche R0 > 1.0

R0 < 1.0

The Niche concept place in a Population Framework

predation

competition

Factor One

Fac

tor

Tw

o