Finish PopulationDynamics (Ch. 10)

Fecundity Schedule for Phlox drummondii

Age (days) nx lx mx lxmx xlxmx

0-299 996 1.00

299-306 158 0.16

306-313 154 0.15

313-320 151 0.15

320-327 147 0.14

mx = Age-specific fecundity: Average number seeds produced by individual in age category.

nx= number survivors lx = survivorship

Fecundity Schedule for Phlox drummondii

Age (days) nx lx mx lxmx xlxmx

0-299 996 1.00 0.0000

299-306 158 0.16 0.3394

306-313 154 0.15 0.7963

313-320 151 0.15 2.3995

320-327 147 0.14 3.1589

mx = Age-specific fecundity: Average number seeds produced by individual in age category.

i.e. plants 300 days old produce on average 0.3394 seeds

Fecundity Schedule for Phlox drummondii

Age (days) nx lx mx lxmx xlxmx

0-299 996 1.00 0.0000 0.0000

299-306 158 0.16 0.3394 0.0532

306-313 154 0.15 0.7963 0.1231

313-320 151 0.15 2.3995 0.3638

320-327 147 0.14 3.1589 0.4589

Ro= lxmx

x = age intervallx = proportion pop. surviving to age xmx = Age-specific fecundity: Average number seeds produced by individual in age category.

Sum these!

Annual Plant• Phlox drummondii (hermaphrodite)

– Ro = Net reproductive rate; Average number seeds produced by individual during life

– If > 1, population increasing– If = 1, population stable– If < 1, population declining

Annual Plant

Is pop. stable, increasing, decreasing?

Annual Plant• Non-overlapping generations: can estimate

growth rate (per unit time).

• Geometric Rate of Increase, lambda ():

Annual Plant• Non-overlapping generations: can estimate

growth rate.

• Geometric Rate of Increase, lambda (): = Nt+1 / Nt

– Nt+1 = Size population future time

– Nt = Size population earlier time

Annual Plant• Geometric Rate of Increase, lambda ():

– Start 996 plants: 2.4177 seeds/individual (Table 10.1)

– 996 x 2.4177 = 2,408 seeds start next year = Nt+1 / Nt

= 2,408 / 996 = 2.41

= Ro for annual plant (generations do not overlap & reproduction not continuous)

Estimating Rates when Generations Overlap

Who am I? Hermaphrodite?

Estimating Rates when Generations Overlap

• Common Mud Turtle (Kinosternon subrubrum)• Data:

– survivorship in age class (years)– reproductive info for each age class

How can a turtle reproduce?• Need Females! Population mix males &

females

• Not all reproduce

• Clutch Size: # eggs laid by female/nest

• How many nests/year (or time period)?

mx= (% fem) x (% reproducing) x (clutch size) x (# nests)

• Table 10.2– Trick: Pop.

has males & females, so calculate production females by females

• Sum col. 4 in Table 10.2 (lxmx), R0 = 0.601

• Stable, increasing, decreasing?

Other population parameters

• Common Mud Turtle– Average generation time (T): Average time from

egg to egg between generations

Fecundity Schedule for Kinosternon subrubrum

Age (yrs) nx lx mx lxmx xlxmx

1 996 1.00 0.0000 0.0000 = 1 x 0.00

2 158 0.16 0.3394 0.0532 = 2 x 0.05

3 154 0.15 0.7963 0.1231

4 151 0.15 2.3995 0.3638

5 147 0.14 3.1589 0.4589

T= xlxmx /Ro

x = age intervallx = proportion pop. surviving to age xmx = Age-specific fecundity: Average number eggs/seeds produced by individual in age category.

Sum these!

Table 10.2:• T = 6.4 /

0.601 = 10.6 years

T = xlxmx / Ro

Other population parameters• Common Mud Turtle

• Per Capita Rate of Increase (r)• r = rate population change per individual per unit

time

r = (ln Ro) / T

– ln = natural log• Also:• r is births per individual per unit time (b) minus

deaths per individual per unit time (d)• r = b - d

Estimating Rates when Generations Overlap

• Common Mud Turtle

r = (ln Ro) / T

r = ln (0.601) / 10.6

r = -0.05– rate population change per individual per unit time

If r > 0, population increasing

If r = 0, population stable

If r < 0, population decliningMakes sense:r = b - d

Organism Size and Population Density

• A search for patterns………….(recall size vs. density)

body size

population density (log)

(log)

hi

hi

lo

lo

Organism Size and Population Density

• A search for patterns………….(recall size vs. density)

• Generation time vs. size?– Also log-log scale

Gen time (T)

Siz

e

Generation time vs. size

• Positive slope• Log-log scale

Use of population dynamics info• Control invasive species (who am I?)

2008 map

Use of population dynamics info• Prevent extinction rare species (who are we?)

200 or fewer individuals in wild

Use of population dynamics info• Managing harvested species

• Ex, orange roughy

Slimehead family!New ZealandFishery areas

Use of population dynamics info• Long lived (150 years)

– Breed when 25-30 yr old

• Harvest only large fish (allow some to breed)?

Population Density

Immigration Emigration

Dispersal• Important to population

dynamics

• Immigration: add individuals

• Emigration: lose individuals

Dispersal• Hard to study:

• 1) tracking movements adults

• 2) dispersal phase may be small

wolf

Bee!

Dispersal• Africanized Honeybees

– Killer bees...

Dispersal• Africanized Honeybees

– Honeybees (Apis mellifera)• subspecies

• Africanized disperse faster than European honeybees.

Dispersal• Africanized Honeybees

They are Here!!

• First in Mobile AL, Aug 2004!

• 28 US fatalities 2010 near Albany GA

Aug 2004, first

• Most species don’t disperse fast....

When Do Organisms Disperse?

• Eggs/ Sperm/ Seed (e.g. pollen, soft corals, burrs)

• Larvae/Juveniles (e.g. Corals, Fish, spiders)

• Adults (e.g. Cats, Butterflies, birds)

Immobile adults must disperse as Juveniles, Zygotes or Gametes!

Dispersal & Climate Change• Organisms spread northward 16,000 years

ago (retreat of glaciers)– Evidence: preserved pollen in sediments.

Changes in Response to Climate Change

– Tree species: Movement slow 100 - 400 m/yr.

Fig. 10.6

– Climate envelope: area with appropriate climate conditions

American Pika(Ochotona princeps)

Climate Change– Climate envelope: area with

appropriate climate conditions

– Will envelopes move too fast?

– Assisted migration: human help to prevent extinctions

Torreya taxifolia

Dispersal in Response to Changing Food Supply

• Holling: numerical responses to increased prey– Increased prey density led to

increased predator density

This figure from Ch. 7 showed functional responses

Dispersal in Response to Changing Food Supply

• Numerical response: dispersal + increased reproduction

Vole

KestrelOwl

Dispersal in Response to Changing Food Supply

• Predators moved to areas of more dense prey

Fig. 10.7

Dispersal in Rivers and Streams

Dispersal in Rivers and Streams

• Current (flow of water) causes drift (movement downstream)

• Adaptations to maintain position:– 1) Streamlined bodies/strong swimmers

Jumping salmon

Dispersal in Rivers and Streams

• Adaptations to maintain position:– 2) Bottom-dwelling: avoid current– 3) Adhesion: hang on!

Alabama hogsuckerEtowah darter

Dispersal in Rivers and Streams

• Still get washed downstream in flash floods (spates).

James River VA, 1985

Dispersal in Rivers and Streams

• Colonization cycle: interplay downstream & upstream dispersal

Dispersal in Rivers and Streams

• Cool story: Costa Rican river snail moves upstream in migratory wave (to 1/2 million snails!)