Population size and Conservation TEST 1 Mean = 83, Geometric mean - - PDF document

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Population size and Conservation TEST 1 Mean = 83, Geometric mean - - PDF document

Population size and Conservation TEST 1 Mean = 83, Geometric mean = 82, Harmonic mean = 81, Median = 85. I will add tonight the grades to Blackboard (and also add key on Tu/We) Determining whether a population is growing or shrinking To


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SLIDE 1

Mean = 83, Geometric mean = 82, Harmonic mean = 81, Median = 85.

TEST 1

I will add tonight the grades to Blackboard (and also add key on Tu/We) To get the test back you need to see me in my office DSL 150-T. I am in my office: Tu 10-12, 3-5:30

Population size and Conservation

Determining whether a population is growing or shrinking Predicting future population size Non-genetic risks of small populations

Population Viability Analysis (PVA)

Use of quantitative methods to evaluate and predict the likely future status of a population

Definitions

PVA = Use of quantitative methods to evaluate and predict the likely future status of a population Status = likelihood that a population will be above a minimum size Minimum size, quasi-extinction threshold = number below which extinction is very likely due to genetic or demographic risks

Uses of PVA

Assessment Assessing risk of a single population (for example Grizzly population) NPS Photo

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SLIDE 2

Grizzly population size in Yellowstone national park

Grizzlies are listed as threatened 1975; less than 200 bears left in Yellowstone 1983 Grizzly Bear recovery area (red) Increase of protection area discussed (blue)

Uses of PVA

Assessment Assessing risk of a single population (for example Grizzly population) Comparing risks between different populations

Sockeye and Steelhead catch 1866 1991

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SLIDE 3

Uses of PVA

Assessment Assessing risk of a single population (for example Grizzly population) Comparing risks between different populations Analyzing monitoring data – how many years of data are needed to determine extinction risk? Example: Gray Whale

Gray Whale

How many data points do we need?

5 years? 10 years? 15 years?

Gerber, Leah R., Douglas P. Demaster, and Peter M. Kareiva* 1999. Gray Whales and the Value of Monitoring Data in

Implementing the U.S. Endangered Species Act. Conservation Biology 13:1215-1219.

Uses of PVA

Assessment Identify best ways to manage. Example: loggerhead turtles

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SLIDE 4

Uses of PVA

Assessment Identify best ways to manage. Example: loggerhead turtles Determine necessary reserve size. Example: African elephants

PVA indicates minimum of 2,500 km2 needed to sustain population

Uses of PVA

Assessment Assisting management Identify best ways to manage. Example: loggerhead turtles Determine necessary reserve size. Example: African elephants Determine size of population to reintroduce Example: European beaver

Uses of PVA

Assessment Assisting management Identify best ways to manage. Example: loggerhead turtles Determine necessary reserve size. Example: African elephants Determine size of population to reintroduce Example: European beaver Set limit to harvest (intentional and unintentional)

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SLIDE 5

Uses of PVA

Assessment Assisting management Identify best ways to manage. Example: loggerhead turtles Determine necessary reserve size. Example: African elephants Determine size of population to reintroduce Example: European beaver Set limit to harvest (intentional and unintentional) Intentional Harvest and By-Catch Habitat degradation

Uses of PVA

Assessment Assisting management Identify best ways to manage. Example: loggerhead turtles Determine necessary reserve size. Example: African elephants Determine size of population to reintroduce Example: European beaver Set limit to harvest (intentional and unintentional) Intentional harvest Habitat degradation By-catch How many populations do we need to protect?

Dickey-Lincoln Dam was too laden with ecological and economic problems to ever be built, and the Furbish lousewort has held its

  • wn along the ice-scoured banks of the Saint
  • John. In 1989 the U.S. Fish and Wildlife Service

reported finding 6,889 flowering stems--far more than the 250 or so that were thought to exist earlier. Pedicularis furbishiae, a species with close relatives in Asia but nowhere else in North America, is still endangered, however. The current threats are new dam proposals, logging, and real-estate development The Saga of the Furbish Lousewort Kate Furbish was a woman who, a century ago, Discovered something growing, and she classified it so That botanists thereafter, in their reference volumes state, That the plant's a Furbish lousewort. See, they named it after Kate. There were other kinds of louseworts, but the Furbish one was rare. It was very near extinction when they found out it was there. And as the years went by, it seemed, with ravages of weather, The poor old Furbish lousewort simply vanished altogether. But then in 1976, our bicentennial year, Furbish lousewort fanciers had some good news they could cheer. For along the Saint John River, guess what somebody found? Two hundred fifty Furbish louseworts growing in the ground. Now, the place where they were growing, by the Saint John River banks, Is not a place where you or I would want to live, no thanks. For in that very area, there was a mightty plan, An engineering project for the benefit of

  • man. The Dickey-Lincoln Dam it's called,

hydroelectric power. Energy, in other words, the issue of the

  • hour. Make way, make way for progress now,

man's ever-constant urge. And where those Furbish louseworts were, the dam would just submerge. The plants can't be transplanted; they simply wouldn't grow. Conditions for the Furbish louseworts have to be just so. And for reasons far too deep for me to know to explain, The only place they can survive is in that part of

  • Maine. So, obviously it was clear that something had to

give, And giant dams do not make way so that a plant can live. But hold the phone, for yes, they do. Indeed they must in fact. There is a law, the Federal Endangered Species Act, And any project such as this, though mighty and exalted, If it wipes out threatened animals or plants, it must be halted. And since the Furbish lousewort is endangered as can be, They had to call the dam off, couln't build it, don't you see. For to flood that louseworth haven, where the Furbishes were at, Would be to take away their only extant habitat. And the only way to save the day, to end this awful stall, Would be to find some other louseworts, anywhere at all. And sure enough, as luck would have it, strange though it may seem, They found some other Furbish louseworts growing just downstream. Four tiny little colonies, one with just a single plant.

Types of PVA

Count based PVA: simple -- uses census data (head counts) Structured PVA: uses demographic models (age structure)

PVM: Count based model

Nt = λNt−1

population size at time t population size at time t-1 ‘lambda’ = growth rate

includes birth and death does not include gene flow (movement among different populations)

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SLIDE 6

What does mean

λ Nt = λNt−1 Population is shrinking Population is stable Population is growing λ < 1 λ = 1 λ > 1

Predicting future population sizes

N1 = λN0 N2 = λN1 = λ(λN0) = λ2N1 Nt = λtN0

Example

For some insect, =1.2 and N0 = 150 How many insects will we have in 10 years? N10 = 150*1.2*1.2*1.2*1.2*1.2*1.2*1.2*1.2*1.2*1.2 = 150 * 1.210 = 150 * 6.19 = 929

Nt = λtN0

Measuring from data

λ = Nt Nt−1

If we known the population size in two generations we are able to calculate the growth rate

Incorporating stochasticity into model

For some insect, good = 1.3, bad = 1.1 and N0 = 150 Assume good/bad years alternate. How many insects will we have in 10 years? N10 = 150*1.1*1.3*1.1*1.3*1.1*1.3*1.1*1.3*1.1*1.3 = 897

  • Cyclical example

Stochasticity

With no variability of (= 1.2) With variability of (good = 1.3, bad = 1.1) N10= 929 N10= 897

Influence of small is larger

Cyclical example

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SLIDE 7

Stochasticity

N0 = 150 λ =

  • 1.3

with p = 0.5 1.1 with p = 0.5

N10 = 150 × 1.1 × 1.1 × 1.3 × 1.3 × 1.1 × 1.1 × 1.3 × 1.1 × 1.3 × 1.3 = 897 N10 = 150 × 1.1 × 1.1 × 1.3 × 1.3 × 1.1 × 1.1 × 1.1 × 1.1 × 1.1 × 1.3 = 642

Stochasticity

N0 = 150 λ =

  • 1.3

with p = 0.5 1.1 with p = 0.5

N10 = 150 × 1.1 × 1.1 × 1.3 × 1.3 × 1.1 × 1.1 × 1.3 × 1.1 × 1.3 × 1.3 = 897 N10 = 150 × 1.1 × 1.1 × 1.3 × 1.3 × 1.1 × 1.1 × 1.1 × 1.1 × 1.1 × 1.3 = 642 TIME Population Density (Ln)

Mean = 1

Stochasticity

Models without a stochastic component produce ONE population size Models with a stochastic component produce a distribution

  • f possible population sizes

50 100 150 200 250 300 350 400 0 1 2 3 4 5 6 7 8 9 10

Population size Population size frequency

Distribution of population sizes Measuring from data

λ = Nt Nt−1

If we known the population size in two generations we are able to calculate the growth rate

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SLIDE 8

Estimation of growth rate with more than two time points

λt

G = λtλt−1λt−2...λ0

λG = (λtλt−1λt−2...λ0)1/t = (ln(λt) + ln(λt−1) + ln(λt−2)...ln(λ0) t µ = ln(λG) λ = Nt Nt−1 Nt = λtN0

Estimation of average growth rate

µ = (ln(λt) + ln(λt−1) + ln(λt−2)...ln(λ0) t

µ      > 0 then λG > 1and population is mostly growing ∼ 0 then λG ∼ 1 and population size is constant < 0 then λG < 1 and population is mostly shrinking

is the average over all ln()

NPS Photo

Example: Grizzly bears in Yellowstone park Grizzly population size in Yellowstone national park Grizzly population size in Yellowstone national park

1960 1970 1980 1990 20 40 60 80 100

Female grizzly bears Census year

Grizzly population size in Yellowstone national park

1960 1970 1980 1990 2000 0.75 1 1.25 Growth rate Census year

λt = Nt Nt−1

Change of growth rate

  • ver time
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SLIDE 9

Grizzly population size in Yellowstone national park

Ln(Growth rate ) Census year

ln(λt) = ln( Nt Nt−1 )

1960 1970 1980 1990 2000 0.25 0.25 0.5

Change of ln(growth rate) over time

Average growth curve

Ln(Growth rate ) Census year

ln(λt) = ln( Nt Nt−1 )

1960 1970 1980 1990 2000 0.25 0.25 0.5

average growth Change of ln(growth rate) over time

Grizzly population size in Yellowstone national park

ˆ σ2 = 1 T − 1

T

  • t=1

(ln( Nt Nt−1 ) − ˆ µ)2

σ2 = 0.0130509 µ = 0.0213403

ˆ µ = 1 T

T

  • t=1

ln( Nt Nt−1 )

The average growth rate is positive, so Grizzlies survive in Yellowstone park, right?

Confidence intervals

0.4 0.2 0.2 0.4 0.5 1 1.5 2 2.5 3 3.5 0.4 0.2 0.2 0.4 0.5 1 1.5 2 2.5 3 3.5

ˆ µ µ σ2 = 0.0130509 ˆ µ + σ ˆ µ − σ ˆ µ = 0.0213403

Freq. 95% of all values 2.5% 2.5%

ˆ µ − 2σ ˆ µ + 2σ

σ = 0.114

Extinction probability

One does not try to predict when the last individual is gone but when the population size goes below a threshold, the quasi-extinction threshold, under which the population is critically and immediately imperiled (Ginzburg et al. 1982) A value of 20 reproductive individuals is often used for practical purposes. Genetic arguments would ask for 100 or more reproductive individuals

Relationship between the probability of extinction and the parameters and 2

A population goes extinct when its size falls below the quasi-extinction threshold. if is negative, eventually the population goes extinct, independent of the variance of the growth rate 2. if is positive, there is still a risk to fall under the quasi- extinction threshold, depending on the magnitude of the variance of the growth rate, with high variance, the risk is higher to go extinct than with low variance. Extinction risk depends on the average growth rate , the variance of the growth rate, and time.

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SLIDE 10

Cumulative risk of extinction

σ2 = 0.04 µ = −0.01 µ = −0.01 σ2 = 0.12

Years from now Extinction probability

20 40 60 80 100 120 0.1 0.2 0.3 0.4 0.5 0.6

Nthreshold = 1 Ncensus = 10

Cumulative risk of extinction

20 40 60 80 100 120 0.1 0.2 0.3 0.4 0.5 0.6

σ2 = 0.04 µ = −0.01 µ = −0.01 σ2 = 0.12 σ2 = 0.12 µ = 0.01 µ = 0.01 σ2 = 0.04

Years from now Extinction probability

Nthreshold = 1 Ncensus = 10

Extinction risk for Grizzlies

25 50 75 100 125 150 175 200 25 20 15 10 5

[Log10 ]

Extinction Probability Years from now

25 50 75 100 125 150 175 200 0.0000001 0.00001 0.001 0.01

[Blow-up of top part of graph]

Confidence interval

}

Using Extinction time estimates for conservation planning

460 400 60 30 Adult birds: NORTH CAROLINA Adult birds: FLORIDA 1980 1980 1990 1990 Year Year

1 0.5 0.1 100 300 Year Extinction probability

When to use count-based PVMs ?

When only “few” data is available, we still need about 10 years

  • f census data to get usable extinction risk estimates.

This method is useful to compare multiple populations; to give a relative population health (in comparison to these

  • ther populations).

Simplicity [there are many assumption]

Key assumptions of count based PVAs

The parameters and 2 are constant over time. No density dependence: growth rate is independent of population size. Small populations might enjoy more

  • resources. Pessimistic estimates of extinction risk. [but

density dependence of finding mates: Allee effect] Demographic stochasticity is ignored for derivation of extinction probability formula: 2 is considered to be constant over time and independent of the population size (Remedy is to set quasi-extinction threshold sufficiently high) Environmental trends are ignored.

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SLIDE 11

Key assumptions of count based PVAs

The parameters and 2 are constant over time. No environmental autocorrelation: No catastrophes or bonanzas The extinction probability calculations was derived by assuming only small changes of the population size over time: Catastrophes, such as ice storms, wild fires, droughts,

  • etc. will reduce numbers fast, and are not taken into

account [too positive view]; bonanzas (good years) are also not taken into account [too pessimistic view] No observation error, the numbers are treated as true population sizes. (only one population: no population structure) Individuals are all treated all the same λt−1 ∼ λt

NO