(Understanding How Populations Work) Chapter 10 Population Dynamics (Understanding How Populations Work)

Homework Chapter 9

Question A Interactions that cause clumped dispersion? Patchy variation in habitat quality Physical environment Resource availability Limited dispersal of young from parents Social behavior (flock, school, herd), often as a predation avoidance adaptation.

Question A Interactions that cause regular dispersion? Competition for space or resources. Interactions that cause random dispersion? Neutral or NO interaction Interaction of limited dispersal of young (causing clumped dispersion) with competition among the young (causing mortality and shift to regular dispersion)

Question B How might variation in environment (soil type) affect dispersion in plants? Patchy variation of soil nutrients, water, or physical environment cause plants to occur in patches (clumped dispersion). How might interactions among plants affect dispersion? Competition for space & resources causes regular dispersion.

Question C (Part 1) What was the main finding of studies by Damuth (1981) & Peters & Wassenberg (1983)? Density of animal species decreases with increasing body size.

Question C (Part 2) Which of the 3 types of rarity described by (Rabinowitz 1981) is related to the findings of Damuth (1981), Peters & Wassenberg (1983)? Species with large body size have small local population size (within habitats).

Question C (Part 3) Example of endangered species affected by pattern described by (Damuth 1981), Peters & Wassenberg 1983)? Elephant Tiger Rhinoceros Mountain gorilla Panda Blue, Right whale

Question D Total of 30 whales photo “marked”. 50 whales observed later, of which 10 were photo “marked”. M = n = m = 30 50 10 Population = 30 (50 + 1) = 139 Size (N) (10 + 1)

Question E Total of 30 white oak in ten 0.05 ha plots. Density = Total oak / Total plot area = 30 / 0.5 = 60 white oak / ha Density = 60/10,000 = 0.006 white oak / m2 Which density value is better? Density per hectare is in whole numbers, rather than a small fraction of a tree.

Question F Average 64 zebra mussels / 0.01 m2 plot. Density = Avg Mussels / plot area = 64 / 0.01 m2 = 6400 zebra mussels / m2 Density = 6400 x 10,000 = 64,000,000 / ha Which density value is better? Density per m2 is a more manageable number than millions of mussels per ha.

Question G Average 12 velagers / 0.1 ml water. Density = Avg Velagers / Volume (liter) = 12 / 0.0001 liter = 120,000 velagers / liter

(Understanding How Populations Work) Chapter 10 Population Dynamics (Understanding How Populations Work)

What Processes Determine Current Population Size? Population size in earlier time period (Nt-1) Number of births (B) Number of deaths (D) Number of immigrants (I) Number that emigrate (E) Nt = Nt-1 + (B−D) + (I−E)

Dynamics of Death Survivorship

Age-Specific Survivorship (Lx) Def: The proportion of individuals born into a population that survive to a specified age x. Lx = nx / n0 x = age, nx = number of individuals surviving to age x. n0 = number of individuals born into population in a single time period (Cohort)

Cohort Survivorship Mark all individuals born in a single year (called a cohort). n0 Each year, count the number of surviving individuals in the cohort. nx Lx = proportion of original cohort still alive for each age class = x. = nx / n0

Example Calculations for Cohort Survivorship Age Class Number of Survivors ( nx ) Survivorship ( Lx ) 653 1.000 1 325 0.497 = 325 / 653 2 163 0.250 = 163 / 653 3 81 0.124 = 81 / 653 4 35 0.054 = 35 / 653

Survivorship From Age-at-Death Determine age-at-death for a sample of dead organisms. Often based on annual growth structures. Annual tree rings Annual layers in fish scales and ear bones Enamel layers in bear teeth Ridges on horns of Dall sheep

Computing Survivorship From Age-at-Death Class How Many Died at That Age Number of Survivors (nx) Survivor-ship (Lx) 223 530 1.000 1 145 307 = 530-223 0.579 2 89 162 = 307-145 0.306 3 58 73 = 162-89 0.138 4 15 15 = 73-58 0.028 Total

Computing Survivorship From Age-at-Death Class How Many Died at That Age Number of Survivors (nx) Survivor-ship (Lx) 223 530 1.000 1 145 307 = 530-223 0.579 2 89 162 = 307-145 0.306 3 58 73 = 162-89 0.138 4 15 15 = 73-58 0.028 Total

Three Types of Survivorship Curves Logarithmic Scale

Mortality due to predation affects old more than young)

Type 2 Survivorship Curve: Constant Mortality Rate Winter mortality due to freezing affects all ages equally) Mortality due to floods affects all ages equally)

Type 3 Survivorship Curve: Perennial Plant Species Mortality due to predation affects seeds and seedlings more than mature plants

Dynamics of Birth

Age-Specific Birth Rate (mx) Definition: The average number of young born to female organisms of a specific age x. Determined only by direct observation of number of young produced by females. Fecundity schedule: Age-specify birth rates across an entire lifetime.

Interactions Between Survivorship and Birth Rates

Net Reproductive Rate (R0) Definition: The average number of offspring produced by an individual organism during their entire lifetime. R0 = Sum for all age classes {Lx mx} WHERE: x = age and Lx and mx are age-specific survivorship and birth rates.

Computing Net Reproductive Rate (R0) Age Class Survivorship Lx Birth Rate mx Lx mx 1.000 1 0.579 5 2.95 2 0.306 10 3.06 3 0.138 11 1.52 4 0.028 9 0.26 Total R0 = 7.79

Generation Time ( T ) Definition: The average time between when an organism is born and when it reproduces. The average age of mothers T = Sum (Age)(Lx)(mx) / R0

Computing Generation Time (T) Age (X) Survivorship Lx Birth Rate mx Lx mx X Lx mx 1.000 1 0.579 5 2.95 2 0.306 10 3.06 6.12 3 0.138 11 1.52 4.56 4 0.028 9 0.26 1.04 Total R0 = 7.79 14.67 T = 14.67 / 7.79 = 1.88

Per Capita Rate of Increase (r) The difference Birth Rate − Death Rate + r means births exceed deaths, so the population size is increasing. − r means births are less than deaths, and the population size is decreasing.

Estimating r From the Life Table r = Ln (R0) / T “Ln” indicates the natural logarithm function. Generation Time Net Reproductive Rate

End of Part 1: Population Dynamics

Homework Chapter 10 (Part 1)

Question A Why must species very high reproductive rates have a Type III survivorship curve ? If these species didn’t have a Type III survivor-ship curve the Earth would be covered with their bodies. Why must species low reproductive rates have a Type I survivorship curve ? If these species didn’t have a Type I survivor-ship curve they would be extinct.

Question A What is the expected relationship b/t reproductive rate and patterns of survival ? The greater the number offspring produced, the less energy / care the parent can invest in each offspring, the lower the survivorship of juveniles.

Question B Age dx nx Lx mx Lx mx X Lx mx 180 660 1.000 1 240 480 0.727 180 660 1.000 1 240 480 0.727 2 120 0.364 0.728 1.456 3 60 0.182 1.092 4 0.091 Total R0 = 1.819 3.275

Problem B (continued) Generation Time ( T ) T = Sum (X Lx mx) / R0 T = 3.275 / 1.819 T = 1.80 Per Capita Rate of Increase ( r ) r = Ln (R0) / T r = Ln (1.819) / 1.80 r = 0.332

Homework Question C Age nx Lx mx Lx mx X Lx mx 660 1.000 1 480 0.727 2 660 1.000 1 480 0.727 2 240 0.364 3 120 0.182 4 60 0.091 Total R0 =

Homework Question C Age nx Lx mx Lx mx X Lx mx 660 1.000 1 480 0.727 2 660 1.000 1 480 0.727 2 1.454 240 0.364 0.728 1.456 3 120 0.182 0.546 4 60 0.091 Total R0 = 2.364 3.456

Problem C (continued) Generation Time ( T ) T = Sum (X Lx mx) / R0 T = 3.456 / 2.364 T = 1.46 Per Capita Rate of Increase ( r ) r = Ln (R0) / T r = Ln (2.364) / 1.46 r = 0.589

Homework Question D Effect of shifting reproduction to younger age classes? Increased R0 1.819 vs. 2.364 (30% increase) Decreased T 1.800 vs. 1.46 (19% decrease) Increased r 0.332 vs. 0.589 (77% increase) Should natural selection favor early reproduction ? If r = “fitness”, this analysis suggests YES.

Question D Any disadvantages to earlier reproduction? Smaller mothers produce fewer, smaller, and(or) less vigorous young. Smaller mothers at a disadvantage in competition for resources, less able to provide for young. Survivorship of small mothers and young lower.

Population Dynamics Part 2

Understanding Population Growth Rate Ln (R0) r = _____ T High net reproductive rate results in high r (rapid population growth) Small generation time results in high r . WHY ?

Effect of Generation Time 20 yrs 20 yrs 20 yrs 60 yrs

Effect of Generation Time 30 yrs 30 yrs 60 yrs

Effect of Net Reproductive Rate

How to Increase R0 = Sum Lx mx? Increase suvivorship: Longer-lived individuals have more opportunities for reproduction during their life time. Increase birth rates: Increase the number of offspring produced by individuals in each age class. Question: Can an organism do both ???

How to Decrease T ? Rapid Growth Rate: Organisms reach sexually mature body size sooner. Question: What is required to do this ? Reproduce at a smaller body size: Less time required to reach sexual maturity. Any disadvantages to this ?

Body Size and Generation Time Larger species take longer to grow to their mature size. Larger species often reproduce throughout their long life span. Higher average age of reproducing individuals

Trade – Offs (Assuming Limited Resources) Allocating resources to reproduction reduces resources available for adult survivorship (immune system, fat reserve). mx Lx

Trade - Offs Reproducing at an earlier age (smaller body size) means more individuals reproduce before they die. However: Small adults produce small offspring that have lower Lx than large offspring. Smaller parents and offspring at disadvantage in competition for resources with larger individuals (lower Lx and mx)

r - vs K - Selected Life History r - selected traits Short generation time Small adult body size Short life span High birth rates Small offspring Low survivorship of offspring Low Parental Care Type III Survivorship K - selected traits Long generation time Large adult body size Long life span Low birth rates Large offspring High survivorship of offspring High Parental Care Type I Survivorship

Dispersal (Immigration and Emigration) Causes of Dispersal Over-population and depletion of resources Environmental change alters habitat quality Organisms carried by wind or water currents Spatial/Temporal variation in resources Human transport

Importance of Dispersal Gene flow among separate populations Re-colonization of empty habitats Enhances utilization of shifting or ephemeral resources PROBLEM: Exotic species

Dispersing/sedentary stages of organisms

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

Invasion of Africanized Honeybees Exotic Species: Invasion of Africanized Honeybees

Expansion of Collared Doves into Europe Due to occasional long-distance dispersal of young doves in search of new territories. Why did the collared dove not occur in Europe before ???

The End

Reflect the Past Predict the Future Age Distributions Reflect the Past Predict 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 Size Will be Stable Population Size Will Decline Population Size Will Increase Rapidly

Geometric rate of increase Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Geometric rate of increase Figure 10.10 10-9    

Dispersal distances by collared dove fledglings Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Dispersal distances by collared dove fledglings Figure 10.15 10-14     Source: Hengeveld 1988

Rates of expansion by animal populations Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Rates of expansion by animal populations Figure 10.16 10-15     Source: Caughley 1977, Hengeveld 1988, Winston 1992

Dispersal/numerical response by predators Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Dispersal/numerical response by predators Figure 10.18 10-17     Source: Korpimäki and Norrdahl 1991

Colonization cycle of stream invertebrates Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Colonization cycle of stream invertebrates Figure 10.19 10-18    

Variation in per capita rate of increase Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Variation in per capita rate of increase Figure 10.21 10-19     Source: Soares, Baird, and Calow 1992

Effect of dichloroaniline concentration Copyright © The McGraw-Hill Companies, Inc. Permission required for reproduction or display. Effect of dichloroaniline concentration Figure 10.22 10-20     Source: Baird, Barber, and Calow 1990

Survivorship: Cohort Lifetable

Survivorship of plant and rotifer populations