population ecology readings: ch 9 – population structure ch 10 – life tables, pp. 239-249 ch 11-...
TRANSCRIPT
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