Chapter 10Population Dynamics(Understanding How Populations Work)

Chapter 10Population Dynamics(Understanding How Populations Work)

What Processes Determine What Processes Determine Current Population Size?Current Population Size?

Population size in earlier time period (NPopulation size in earlier time period (Nt-1t-1))

Number of births (B)Number of births (B)

Number of deaths (D)Number of deaths (D)

Number of immigrants (I)Number of immigrants (I)

Number that emigrate (E)Number that emigrate (E)

NNtt = N = Nt-1t-1 + + (B(B−−D)D) + (I + (I−−E)E)

Dynamics of DeathDynamics of Death

SurvivorshipSurvivorship

Age-Specific Survivorship (Lx)Age-Specific Survivorship (Lx)

Def: The proportion of individuals born into a Def: The proportion of individuals born into a population that survive to a specified age x.population that survive to a specified age x.

LLxx = = nnxx / / nn00

xx = age, = age,

nnxx = number of individuals surviving to age x. = number of individuals surviving to age x.

nn00 = number of individuals born into = number of individuals born into population in a single time period (Cohort)population in a single time period (Cohort)

Cohort SurvivorshipCohort Survivorship

Mark all individuals born in a single year Mark all individuals born in a single year (called a cohort). (called a cohort). nn00

Each year, count the number of surviving Each year, count the number of surviving individuals in the cohort. individuals in the cohort. nnxx

LLxx = proportion of original cohort still alive = proportion of original cohort still alive for each age class = x. for each age class = x. = n= nxx / n / n00

Example Calculations for Cohort Example Calculations for Cohort SurvivorshipSurvivorship

AgeAge

ClassClass

Number of Number of

Survivors ( nSurvivors ( nx x )) Survivorship ( LSurvivorship ( Lxx ) )

00 653653 1.0001.000

11 325325 0.4970.497 = 325 / 653= 325 / 653

22 163163 0.2500.250 = 163 / 653= 163 / 653

33 8181 0.1240.124 = 81 / 653= 81 / 653

44 3535 0.0540.054 = 35 / 653= 35 / 653

Survivorship From Age-at-DeathSurvivorship From Age-at-Death

Determine age-at-death for a sample of Determine age-at-death for a sample of dead organisms.dead organisms.

Often based on annual growth structures.Often based on annual growth structures.– Annual tree rings Annual tree rings – Annual layers in fish scales and ear bonesAnnual layers in fish scales and ear bones– Enamel layers in bear teethEnamel layers in bear teeth– Ridges on horns of Dall sheepRidges on horns of Dall sheep

Computing Survivorship From Computing Survivorship From Age-at-DeathAge-at-Death

AgeAge

ClassClass

How Many Died How Many Died at That Ageat That Age

Number of Number of Survivors (nSurvivors (nxx))

Survivor-Survivor-ship (Lship (Lxx))

00 223223 530530 1.0001.000

11 145145 307 307 = 530-223= 530-223 0.5790.579

22 8989 162 162 = 307-145= 307-145 0.3060.306

33 5858 73 73 = 162-89= 162-89 0.1380.138

44 1515 15 15 = 73-58= 73-58 0.0280.028

TotalTotal 530530

Computing Survivorship From Computing Survivorship From Age-at-DeathAge-at-Death

AgeAge

ClassClass

How Many Died How Many Died at That Ageat That Age

Number of Number of Survivors (nSurvivors (nxx))

Survivor-Survivor-ship (Lship (Lxx))

00 223223 530530 1.0001.000

11 145145 307 307 = 530-223= 530-223 0.5790.579

22 8989 162 162 = 307-145= 307-145 0.3060.306

33 5858 73 73 = 162-89= 162-89 0.1380.138

44 1515 15 15 = 73-58= 73-58 0.0280.028

TotalTotal 530530

Three Types of Survivorship Curves

LogarithmicScale

Mortality due to Mortality due to predation affects old predation affects old more than young)more than young)

Type 2 Survivorship Curve: Constant Mortality Rate

Winter mortality due Winter mortality due to to freezingfreezing affects all affects all ages equallyages equally

Mortality due to Mortality due to environment environment affects all ages affects all ages equallyequally

Type 3 Survivorship Curve:Perennial Plant Species

Mortality due to predation Mortality due to predation affects seeds and affects seeds and seedlings more than seedlings more than mature plantsmature plants

Dynamics of BirthDynamics of Birth

Age-Specific Birth Rate (mAge-Specific Birth Rate (mxx))

Definition:Definition: The average number of young The average number of young born to female organisms of a specific age x.born to female organisms of a specific age x.

From direct observation of number of young From direct observation of number of young produced by females.produced by females.

Fecundity schedule: Fecundity schedule: Age-specific birth rates Age-specific birth rates for entire lifetime.for entire lifetime.

Interactions Between Interactions Between Survivorship and Birth RatesSurvivorship and Birth Rates

Net Reproductive Rate (RNet Reproductive Rate (R00))

Definition:Definition: Average offspring from an Average offspring from an individual organism individual organism during entire during entire lifetimelifetime..

RR00 = Sum for all age classes {L= Sum for all age classes {Lxx m mxx}}

WHERE: x = age and LWHERE: x = age and Lxx and m and mxx are age-specific are age-specific survivorship and birth rates.survivorship and birth rates.

Computing Net Reproductive Computing Net Reproductive Rate (RRate (R00))

AgeAgeClassClass

Survivorship Survivorship LLxx

Birth RateBirth Ratemmxx LLxx m mxx

00 1.0001.000 00 00

11 0.5790.579 55 2.952.95

22 0.3060.306 1010 3.063.06

33 0.1380.138 1111 1.521.52

44 0.0280.028 99 0.260.26

TotalTotal RR00 = = 7.797.79

Generation Time ( T )Generation Time ( T )

Definition:Definition: Average time from birth to Average time from birth to when it reproduces.when it reproduces.

= average age of mothers= average age of mothers

TT = Sum (Age)(L= Sum (Age)(Lxx)(m)(mxx) / R) / R00

Computing Generation Time (T)Computing Generation Time (T)

AgeAge(X)(X)

Survivorship Survivorship LLxx

Birth RateBirth Ratemmxx LLxx m mxx X LX Lxx m mxx

00 1.0001.000 00 00 00

11 0.5790.579 55 2.952.95 2.952.95

22 0.3060.306 1010 3.063.06 6.126.12

33 0.1380.138 1111 1.521.52 4.564.56

44 0.0280.028 99 0.260.26 1.041.04

TotalTotal RR00 = = 7.797.79 14.6714.67

T = 14.67 / 7.79 = 1.88T = 14.67 / 7.79 = 1.88

Per Capita Rate of Increase (r)Per Capita Rate of Increase (r)

The difference Birth Rate The difference Birth Rate − Death Rate− Death Rate

+ r means births exceed deaths, so + r means births exceed deaths, so population size is increasing.population size is increasing.

− − r means births are less than deaths, r means births are less than deaths, population size is decreasing.population size is decreasing.

Estimating r From a Life TableEstimating r From a Life Table

r = Ln (Rr = Ln (R00) / T) / T

““Ln” indicates the Ln” indicates the natural logarithm natural logarithm function.function. Net Net

Reproductive Reproductive RateRate

Generation Generation TimeTime

End of Part 1:End of Part 1:Population DynamicsPopulation Dynamics

Population DynamicsPopulation DynamicsPart 2Part 2

Understanding Population Understanding Population Growth RateGrowth Rate

Ln (RLn (R00))rr == __________ TT

High net reproductive rate results in high r(rapid population growth)

Small generation time results in high r .

20 yrs20 yrs 20 yrs20 yrs 20 yrs20 yrs

Effect of Generation TimeEffect of Generation Time

60 yrs60 yrs

30 yrs30 yrs 30 yrs30 yrs

Effect of Generation TimeEffect of Generation Time

60 yrs60 yrs

Effect of Net Reproductive RateEffect of Net Reproductive Rate

How to Increase RHow to Increase R00 = Sum L = Sum Lxx m mxx??

Increase survivorship:Increase survivorship: Longer-lived Longer-lived individuals have more opportunities for individuals have more opportunities for reproduction during life time. reproduction during life time.

How to Increase R0 = Sum Lx How to Increase R0 = Sum Lx mx?mx?

Increase survivorship: Longer-lived individuals have more opportunities for reproduction during life time.

Increase birth rates: Increase number of offspring produced by individuals in each age class.

Question: Can an organism do both ???

How to Decrease T ?How to Decrease T ?

Rapid Growth Rate:Rapid Growth Rate: Organisms reach Organisms reach sexually mature body size sooner.sexually mature body size sooner.

Question: What is required to do this ?Question: What is required to do this ?

Reproduce at a smaller body size:Reproduce at a smaller body size: Less time required to reach sexual Less time required to reach sexual maturity.maturity.

Any disadvantages to this ?Any disadvantages to this ?

How to Decrease T ?How to Decrease T ?

Rapid Growth Rate:Rapid Growth Rate: Organisms reach Organisms reach sexually mature body size sooner.sexually mature body size sooner.

Question: What is required to do this ?Question: What is required to do this ?

Reproduce at a smaller body size:Reproduce at a smaller body size: Less time to reach sexual maturity.Less time to reach sexual maturity.

Any disadvantages to this ?Any disadvantages to this ?

Body Size and Generation Time

Larger species takelonger to grow to

mature size.

Larger species oftenreproduce throughout

long life span.

Higher average ageof reproducing

individuals

Trade – OffsTrade – Offs(Assuming Limited Resources)(Assuming Limited Resources)

Allocating resources to reproduction Allocating resources to reproduction reduces resources available for adult reduces resources available for adult survivorship (immune system, fat survivorship (immune system, fat reserve).reserve).

mmxx LLxx

Trade - OffsTrade - Offs

Reproducing at an earlier age (smaller Reproducing at an earlier age (smaller body size) means more individuals body size) means more individuals reproduce before they die. reproduce before they die.

Trade - OffsTrade - Offs

Reproducing at an earlier age (smaller Reproducing at an earlier age (smaller body size) means more individuals body size) means more individuals reproduce before they die. reproduce before they die.

However:However:– Small adults produce small offspring with Small adults produce small offspring with

lower Lx than large offspring.lower Lx than large offspring.– Smaller parents and offspring at Smaller parents and offspring at

disadvantage in competition for resources disadvantage in competition for resources with larger individuals (lower Lx and mx)with larger individuals (lower Lx and mx)

r - vs K - Selected Life Historyr - vs K - Selected Life History

r - selected traitsr - selected traits– Short generation timeShort generation time– Small adult body sizeSmall adult body size– Short life spanShort life span– High birth ratesHigh birth rates– Small offspringSmall offspring– Low survivorship of Low survivorship of

offspringoffspring– Low Parental CareLow Parental Care– Type III SurvivorshipType III Survivorship

K - selected traitsK - selected traits– Long generation timeLong generation time– Large adult body sizeLarge adult body size– Long life spanLong life span– Low birth ratesLow birth rates– Large offspringLarge offspring– High survivorship of High survivorship of

offspringoffspring– High Parental CareHigh Parental Care– Type I SurvivorshipType I Survivorship

DispersalDispersal(Immigration and Emigration)(Immigration and Emigration)

Causes of DispersalCauses of Dispersal– Over-population and depletion of resourcesOver-population and depletion of resources– Environmental change alters habitat qualityEnvironmental change alters habitat quality– Organisms carried by wind or water currents Organisms carried by wind or water currents – Spatial/Temporal variation in resourcesSpatial/Temporal variation in resources

– Human transportHuman transport

Importance of DispersalImportance of Dispersal

Gene flow among separate populationsGene flow among separate populations

Re-colonization of empty habitatsRe-colonization of empty habitats

Enhances utilization of shifting or Enhances utilization of shifting or ephemeral resourcesephemeral resources

PROBLEM:PROBLEM: Exotic species Exotic species

Dispersing/sedentary stages of organisms

Northward Expansion of Tree Species After Continental Glaciers Receded 12,000 yrs BP

Exotic Species:

Invasion of Africanized Honeybees

Expansion of Collared Doves into Europe

Due to occasional long-distancedispersal of young doves insearch of new territories.

Why did the collared dove notoccur in Europe before ???

The EndThe End