Chapter 10 Population Dynamics (Understanding How Populations Work)

Chapter 10Population Dynamics(Understanding How Populations Work)

HomeworkHomeworkChapter 9Chapter 9

Question AQuestion A

Interactions that cause clumped dispersion?Interactions that cause clumped dispersion?

Patchy variation in habitat qualityPatchy variation in habitat quality

– Physical environmentPhysical environment

– Resource availabilityResource availability

Limited dispersal of young from parentsLimited dispersal of young from parents

Social behavior (flock, school, herd), often as Social behavior (flock, school, herd), often as a predation avoidance adaptation.a predation avoidance adaptation.


Interactions that cause regular dispersion?Interactions that cause regular dispersion?

Competition for space or resources.Competition for space or resources.

Interactions that cause random dispersion?Interactions that cause random dispersion?

Neutral or NO interactionNeutral or NO interaction

Interaction of limited dispersal of young Interaction of limited dispersal of young (causing clumped dispersion) with (causing clumped dispersion) with competition among the young (causing competition among the young (causing mortality and shift to regular dispersion)mortality and shift to regular dispersion)

Question BQuestion B

How might variation in environment (soil type) How might variation in environment (soil type) affect dispersion in plants?affect dispersion in plants?

Patchy variation of soil nutrients, water, or Patchy variation of soil nutrients, water, or physical environment cause plants to occur in physical environment cause plants to occur in patches (clumped dispersion).patches (clumped dispersion).

How might interactions among plants affect How might interactions among plants affect dispersion?dispersion?

Competition for space & resources causes Competition for space & resources causes regular dispersion.regular dispersion.

Question C (Part 1)Question C (Part 1)

What was the main finding of studies by What was the main finding of studies by Damuth (1981) & Peters & Wassenberg (1983)?Damuth (1981) & Peters & Wassenberg (1983)?

Density of animal species decreases Density of animal species decreases with increasing body size.with increasing body size.


Which of the 3 types of rarity described by Which of the 3 types of rarity described by (Rabinowitz 1981) is related to the findings of (Rabinowitz 1981) is related to the findings of Damuth (1981), Peters & Wassenberg (1983)? Damuth (1981), Peters & Wassenberg (1983)?

Species with large body size have small Species with large body size have small local local population sizepopulation size (within habitats). (within habitats).


Example of endangered species affected Example of endangered species affected by pattern described by by pattern described by (Damuth 1981), (Damuth 1981),

Peters & Wassenberg 1983)?Peters & Wassenberg 1983)? – ElephantElephant– TigerTiger– RhinocerosRhinoceros– Mountain gorillaMountain gorilla– PandaPanda– Blue, Right whaleBlue, Right whale

Question DQuestion D

Total of 30 whales photo “marked”.Total of 30 whales photo “marked”.

50 whales observed later, of which 10 50 whales observed later, of which 10 were photo “marked”.were photo “marked”.– M =M =– n =n =– m =m =

30305050

1010

Population = 30 (50 + 1) = 139 Size (N) (10 + 1)

Question EQuestion E

Total of 30 white oak in ten 0.05 ha plots.Total of 30 white oak in ten 0.05 ha plots.

Density = Total oak / Total plot areaDensity = Total oak / Total plot area

= 30 / 0.5= 30 / 0.5

= 60 white oak / ha= 60 white oak / ha

Density = 60/10,000Density = 60/10,000 = 0.006 white oak / m = 0.006 white oak / m22

Which density value is better?Which density value is better?

Density per hectare is in whole numbers, rather Density per hectare is in whole numbers, rather than a small fraction of a tree.than a small fraction of a tree.

Question FQuestion F

Average 64 zebra mussels / 0.01 mAverage 64 zebra mussels / 0.01 m22 plot. plot.

Density = Avg Mussels / plot areaDensity = Avg Mussels / plot area

= 64 / 0.01 m= 64 / 0.01 m22

= 6400 zebra mussels / m= 6400 zebra mussels / m22

Density = 6400 x 10,000 Density = 6400 x 10,000 = 64,000,000 / ha= 64,000,000 / ha

Which density value is better?Which density value is better?

Density per mDensity per m22 is a more manageable number is a more manageable number than millions of mussels per ha.than millions of mussels per ha.

Question GQuestion G

Average 12 velagers / 0.1 ml water.Average 12 velagers / 0.1 ml water.

Density = Avg Velagers / Volume (liter)Density = Avg Velagers / Volume (liter)

= 12 / 0.0001 liter = 12 / 0.0001 liter

= 120,000 velagers / liter= 120,000 velagers / liter

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

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 equally)ages equally)

Mortality due to Mortality due to floods floods affects all affects all ages equally)ages equally)

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.

Determined only by direct observation of Determined only by direct observation of number of young produced by females.number of young produced by females.

Fecundity schedule: Fecundity schedule: Age-specify birth rates Age-specify birth rates across an entire lifetime.across an entire lifetime.

Interactions Between Interactions Between Survivorship and Birth RatesSurvivorship and Birth Rates

Net Reproductive Rate (RNet Reproductive Rate (R00))

Definition:Definition: The average number of The average number of offspring produced by an individual offspring produced by an individual organism organism during their entire lifetimeduring their entire lifetime..

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: The average time between The average time between when an organism is born and when it when an organism is born and when it reproduces.reproduces.

The average age of mothersThe 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 the + r means births exceed deaths, so the population size is increasing.population size is increasing.

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

Estimating r From the Life TableEstimating r From the 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

HomeworkHomeworkChapter 10 (Part 1)Chapter 10 (Part 1)

Question AQuestion AWhy must species very high reproductive Why must species very high reproductive rates have a Type III survivorship curve ?rates have a Type III survivorship curve ?

If these species didn’t have a Type III If these species didn’t have a Type III survivor-ship curve the Earth would be survivor-ship curve the Earth would be covered with their bodies.covered with their bodies.

Why must species low reproductive rates Why must species low reproductive rates have a Type I survivorship curve ?have a Type I survivorship curve ?

If these species didn’t have a Type I survivor-If these species didn’t have a Type I survivor-ship curve they would be extinct.ship curve they would be extinct.


What is the expected relationship b/t What is the expected relationship b/t reproductive rate and patterns of survival ?reproductive rate and patterns of survival ?

The greater the number offspring produced, The greater the number offspring produced, the less energy / care the parent can invest in the less energy / care the parent can invest in each offspring, the lower the survivorship of each offspring, the lower the survivorship of juveniles.juveniles.

Question BQuestion B

AgeAge ddxx nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 180180 660660 1.0001.000 00 00 00

11 240240 480480 0.7270.727 11 0.7270.727 0.7270.727

22 120120 240240 0.3640.364 22 0.7280.728 1.4561.456

33 6060 120120 0.1820.182 22 0.3640.364 1.0921.092

44 6060 6060 0.0910.091 00 00 00

TotalTotal 660660 RR00 = = 1.8191.819 3.2753.275

Problem B (continued)Problem B (continued)

Generation Time ( T )Generation Time ( T )T = Sum (X LT = Sum (X Lxx m mxx) / R) / R00 T = 3.275 / 1.819T = 3.275 / 1.819T = 1.80T = 1.80

Per Capita Rate of Increase ( r )Per Capita Rate of Increase ( r )r = Ln (Rr = Ln (R00) / T) / T

r = Ln (1.819) / 1.80r = Ln (1.819) / 1.80r = 0.332r = 0.332

Homework Question CHomework Question C

AgeAge nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 660660 1.0001.000 00

11 480480 0.7270.727 22

22 240240 0.3640.364 22

33 120120 0.1820.182 11

44 6060 0.0910.091 00

TotalTotal RR00 = =

Homework Question CHomework Question C

AgeAge nnxx LLxx mmxx LLxx m mxx X LX Lxx m mxx

00 660660 1.0001.000 00 00 00

11 480480 0.7270.727 22 1.4541.454 1.4541.454

22 240240 0.3640.364 22 0.7280.728 1.4561.456

33 120120 0.1820.182 11 0.1820.182 0.5460.546

44 6060 0.0910.091 00 00 00

TotalTotal RR00 = = 2.3642.364 3.4563.456

Problem C (continued)Problem C (continued)

Generation Time ( T )Generation Time ( T )T = Sum (X LT = Sum (X Lxx m mxx) / R) / R00 T = 3.456 / 2.364T = 3.456 / 2.364T = 1.46T = 1.46

Per Capita Rate of Increase ( r )Per Capita Rate of Increase ( r )r = Ln (Rr = Ln (R00) / T) / T

r = Ln (2.364) / 1.46r = Ln (2.364) / 1.46r = 0.589r = 0.589

Homework Question DHomework Question D

Effect of shifting reproduction to younger age Effect of shifting reproduction to younger age classes?classes?

Increased RIncreased R00 1.819 vs. 2.364 (30% increase)1.819 vs. 2.364 (30% increase)

Decreased TDecreased T 1.800 vs. 1.46 (19% decrease)1.800 vs. 1.46 (19% decrease)

Increased rIncreased r 0.332 vs. 0.589 (77% increase)0.332 vs. 0.589 (77% increase)

Should natural selection favor early Should natural selection favor early reproduction ?reproduction ?

If r = “fitness”, this analysis suggests YES.If r = “fitness”, this analysis suggests YES.

Question DQuestion DAny disadvantages to earlier reproduction?Any disadvantages to earlier reproduction?

Smaller mothers produce fewer, smaller, Smaller mothers produce fewer, smaller, and(or) less vigorous young.and(or) less vigorous young.

Smaller mothers at a disadvantage in Smaller mothers at a disadvantage in competition for resources, less able to competition for resources, less able to provide for young.provide for young.

Survivorship of small mothers and young Survivorship of small mothers and young lower.lower.

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 .

WHY ?

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

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

Question: Can an organism do both ???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 ?

Body Size and Generation Time

Larger species takelonger to grow to their

mature size.

Larger species oftenreproduce throughout

their 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. However:reproduce before they die. However:

– Small adults produce small offspring that Small adults produce small offspring that have lower Lhave lower Lxx than large offspring. 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 Lwith larger individuals (lower Lxx and m and mxx))

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

Age DistributionsAge Distributions

Reflect the PastReflect the Past

Predict the FuturePredict the Future

Age Distribution of a White Oak Population

Age Distribution of a Cottonwood Population

Age Distribution of a Cactus Finch Population(Variation of Lx and mx Over Time)

Age Distributions for Human Populations:

Predictors of Future Population Growth

Population SizeWill be Stable

Population SizeWill Decline

Population SizeWill IncreaseRapidly

Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.

Geometric rate of increaseFigure 10.10

10-9


Dispersal distances by collared dove fledglingsFigure 10.15

10-14 Source: Hengeveld 1988


Rates of expansion by animal populationsFigure 10.16

10-15 Source: Caughley 1977, Hengeveld 1988, Winston 1992


Dispersal/numerical response by predatorsFigure 10.18

10-17 Source: Korpimäki and Norrdahl 1991


Colonization cycle of stream invertebratesFigure 10.19

10-18


Variation in per capita rate of increaseFigure 10.21

10-19 Source: Soares, Baird, and Calow 1992


Effect of dichloroaniline concentrationFigure 10.22

10-20 Source: Baird, Barber, and Calow 1990

Survivorship: Cohort Lifetable

Survivorship of plant and rotifer populations

Chapter 10 Population Dynamics (Understanding How Populations Work)

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