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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.
Question AQuestion A
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.
Question C (Part 2)Question C (Part 2)
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).
Question C (Part 3)Question C (Part 3)
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
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.
Question AQuestion A
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
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Dispersal distances by collared dove fledglingsFigure 10.15
10-14 Source: Hengeveld 1988
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Rates of expansion by animal populationsFigure 10.16
10-15 Source: Caughley 1977, Hengeveld 1988, Winston 1992
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Dispersal/numerical response by predatorsFigure 10.18
10-17 Source: Korpimäki and Norrdahl 1991
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Colonization cycle of stream invertebratesFigure 10.19
10-18
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Variation in per capita rate of increaseFigure 10.21
10-19 Source: Soares, Baird, and Calow 1992
Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display.
Effect of dichloroaniline concentrationFigure 10.22
10-20 Source: Baird, Barber, and Calow 1990
Survivorship: Cohort Lifetable
Survivorship of plant and rotifer populations