Lecture Outline

1. Quick re-cap:COHORT vs. STATIC life tables

2. Case study: Sea turtle conservation-AKA Why we care about these calculations

3. The special problem of small populationsWhy they are more vulnerable to extinction?

1. Quick re-cap of COHORT vs. STATIC life tables

Cohort: Follow the fate of one cohort through the lifespan (Cascade frog, Cactus finch)

Static: Estimate birth and death rates of each stage over several surveys (Desert tortoise)

Cohort – share a year of birth

Number surviving each yearà lx (proportion living at age x)

Combine with births at each age bx

à Calculate net reproductive rate (is the population )R0 = Σ lx bx

Calculate generation timeG= (Σ x lx bx)/ R0

Calculate the intrinsic rate of increase ra = Ln(R0) / G

Estimate lambdara = Ln(𝜆) an approximation

Static – share a year or time period of death

Number surviving a time periodà Sx survival from x to next period

Combine S0 S1 S2 etc (multiply)à estimate lx

Aren’t these just theoretical examples?!

Case study: Sea turtle population declines

Loggerhead sea turtle, Caretta caretta

Kemp’s ridley sea turtle, Lepidochelys kempii 1948: 42,000 females were filmed nesting in one day in Rancho Nuevo1985: 740 nesting at Rancho Nuevo

Anecdotal evidence of unbelievable #’s 200 years agoQuantitative evidence—

dramatic pop’n declines in 1970’s & 1980’s

Today:

(AKA Why should I care?)

Why??Poaching/HarvestEgg predatorsBeach developmentCollision with shipsFishing bycatch

Southeastern US:

Conventional wisdom for reversing declines

Extensive protection programs at nesting beaches for ~15 years

Captive rearing of eggs

Duke grad student (Deborah Crouse) notices that population trends for loggerheads don’t seem to change after all this effort

Analyzes a stage-structured dataset….and spent 3 years collecting dead adults washed up on beaches

Eggs/hatch1yr

Sm juveniles7yrs

Lg. juveniles8yrs

Subadults6yrs

Adults>32yrs

Norbert Wu

Crouse builds a model based on life-table (matrix model) Crouse et al. 1987 Ecology

61.9

.675 .047 .019 .061

.703 .657 .682 .809

4.7

Norbert Wu

She systematically changed the survival (up to 100%) and fecundity rates (up to +50%)…..

-projected the population growth rate into the future (r)

-which one results in the biggest change in r

-determines the most “sensitive” life-stage for population growth—focus protection efforts

• Where should we invest conservation efforts to reverse population decline?

• Even 100% survival of eggs/hatchlings doesn’t reverse decline!

Shrimp trawling inefficiency….. for every 1lb shrimp --12 lbs of other species are caught (150)

Norbert Wu

136,000 metric tons of shrimp worth over $700 million (2000)

136,000 metric tons x 12 = >1.6 million tons of bycatch!!

5,000 Kemp’s ridley50,000 Loggerhead turtles caught per yr

Biggest source of human-caused turtle mortality

Turtle excluder devices (TED’s)Federally mandated on most shrimp trawls by 1991

Crouse et al. 1984 pivotal in passing legislation

70-90% effective at eliminating turtle bycatch

How to increase large juvenile survival?

Reduce bycatch in shrimp trawls!

TED effects on loggerheads

ProjectedCrowder et al. 1991 Ecol Appl

A – seasonal use of TEDsB – all waters, all seasonsC – observed reduction in mortality on local beaches

TED effects on loggerheads (?)Index beaches in FloridaNational Save the Sea Turtle Foundation

Kemp’s Ridley TurtleCaillouet et al. (2018)

Problems with this modelling approach

• Demographic rates are fixed– Models (e.g. geometric, exponential, logistic) are DETERMINISTIC– r, λ don’t change

• But small populations are vulnerable to stochastic processes– we can add variation in rates to models– but, it makes them more complex

• Stochastic = random processes are especially important for accurately predicting the dynamics of small populations

Three reasons why populations may fail to increase from low density:

1. r < 0 : Deterministic decline at all population densities

2. Depensation: individual performance declines at low population size (deterministic decline at low densities)

3. Below “Minimum Viable Population” size: when population is small, more susceptible to random (stochastic) events (3 typesà demographic, environmental, genetic)

2. Depensation

• Positive density dependence-- individuals do worse at low population size– Resources are not limiting, but…– Mates difficult to find (“Allee effect”)– Lack of neighbors may reduce foraging or

breeding success, vulnerability to predators (flocking, schooling)

– Note: don’t have a model (equation) for this, but know how to add it to a figure like above!

2. Depensation

• Positive density dependence- individuals do worse at low population size– Resources are not limiting, but…– Mates difficult to find (“Allee effect”)– Small numbers may reduce foraging success,

or vulnerability to predators

– Note: don’t have a model (equation) for this, but know how to add it to a figure like above!

Mechanism of depensation…

At low densities successful spawning declines….mates too far away

Consequence of depensation…

Population growth rate is LOWER with fewer individuals

Red abalone

Depensation Example: Red Abalone

Millions to billions in N. America before colonization (most common bird in N.Am.)

1896: 250,000 in one flock

Probably required large flocks for successful reproduction

1900: last record of pigeons in wild

1914: “Martha” dies Cincinnati zoo

Example: Deterministic extinction from low population size

Passenger Pigeon, Ectopistes migratorius

1. r < 0, Deterministic decline

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons

Population density (N)

Birth

s/in

divi

dual

/yea

r

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons

Scenario 1: If not density dependent

Population density (N)

Birth

s/in

divi

dual

/yea

r

N

dNdt

As would be the case for density-independent population growth(geometric/exponential)

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons

Population density (N)

Birth

s/in

divi

dual

/yea

r

Carrying capacity (K) when dN/dt/N=0

N

dNdt

Decreasing births per individual with increasing population (logistic)

Scenario 2: If density dependent

Draw a hypothetical graph of fecundity as a function of population size for passenger pigeons

Population density (N)

Birth

s/in

divi

dual

/yea

r

Scenario 3: Depensation

N

dNdt

Density dependent population regulation at BOTH high and low population sizes(not logistic!)

Carrying capacity (K) when dN/dt/N=0

1st Exam

Need to know how to calculate: R0GraNt+1 for Geometric growthNt for Exponential growthdN/dt for Logistic growth

N from Mark-Recapture data