Population size and Conservation. Definitions. Population Viability Analysis (PVA) Uses of PVA TEST 1

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1 TEST 1 Mean = 83, Geometric mean = 82, Harmonic mean = 81, Median = 85. Population size and Conservation 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 Determining whether a population is growing or shrinking Predicting future population size Non-genetic risks of small populations Population Viability Analysis (PVA) Definitions Use of quantitative methods to evaluate and predict the likely future status of a population 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 Assessing risk of a single population (for example Grizzly population) NPS Photo

2 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) Assessing risk of a single population (for example Grizzly population) Comparing risks between different populations Sockeye and Steelhead catch

3 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* Gray Whales and the Value of Monitoring Data in Implementing the U.S. Endangered Species Act. Conservation Biology 13:

4 Determine necessary reserve size. Example: African elephants Assisting management Determine necessary reserve size. Example: African elephants Determine size of population to reintroduce Example: European beaver Assisting management Determine necessary reserve size. Example: African elephants Determine size of population to reintroduce Example: European beaver Set limit to harvest (intentional and unintentional) PVA indicates minimum of 2,500 km2 needed to sustain population

5 Assisting management 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 Assisting management 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? 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. Dickey-Lincoln Dam was too laden with ecological and economic problems to ever be built, and the Furbish lousewort has held its own 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 Types of PVA Count based PVA: simple -- uses census data (head counts) Structured PVA: uses demographic models (age structure) PVM: Count based model N t = λ 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)

6 What does λ mean N t = λ Predicting future population sizes λ < 1 λ = 1 λ > 1 Population is shrinking Population is stable Population is growing N 1 = λn 0 N 2 = λn 1 = λ(λn 0 ) = λ 2 N 1 N t = λ t N 0 Example N t = λ t N 0 Measuring! from data For some insect,!=1.2 and N 0 = 150 How many insects will we have in 10 years? If we known the population size in two generations we are able to calculate the growth rate N 10! =! 150*1.2*1.2*1.2*1.2*1.2*1.2*1.2*1.2*1.2*1.2!!!!!!! =! 150 * !!!!!!! =! 150 * 6.19!!!!!!! =!! 929 λ = N t Incorporating stochasticity into model Cyclical example For some insect,! good = 1.3,! bad = 1.1 and N 0 = 150 Stochasticity Cyclical example Assume good/bad years alternate. How many insects will we have in 10 years? N 10 = 150*1.1*1.3*1.1*1.3*1.1*1.3*1.1*1.3*1.1*1.3!!!!!! = 897 With no variability of! (= 1.2) With variability of! (! good = 1.3,! bad = 1.1) N 10 = 929 N 10 = 897 Influence of small! is larger

7 Stochasticity N 0 = 150 { 1.3 with p = λ = 1.1 with p = N 10 = = 642 N 10 = = 897 Stochasticity N 0 = 150 { 1.3 with p = λ = 1.1 with p = N 10 = = 642 N 10 = = 897 Mean! = 1 Stochasticity Population Density (Ln) Models without a stochastic component produce ONE population size Models with a stochastic component produce a distribution of possible population sizes TIME Distribution of population sizes Measuring! from data Population size Population size frequency If we known the population size in two generations we are able to calculate the growth rate λ = N t

8 Estimation of growth rate with more than two time points λ t G = λ t λ t 1 λ t 2...λ 0 λ G = (λ t λ t 1 λ t 2...λ 0 ) 1/t µ = ln(λ G ) N t = λ t N 0 λ = N t = (ln(λ t) + ln(λ t 1 ) + ln(λ t 2 )...ln(λ 0 ) t Estimation of average growth rate µ = (ln(λ t) + ln(λ t 1 ) + ln(λ t 2 )...ln(λ 0 ) t " is the average over all ln(!) > 0 then λ G > 1and population is mostly growing µ 0 then λ G 1 and population size is constant < 0 then λ G < 1 and population is mostly shrinking Example: Grizzly bears in Yellowstone park NPS Photo Female grizzly bears Census year Growth rate! λ t = N t Change of growth rate over time Census year

9 Ln(Growth rate!) Change of ln(growth rate) over time ln(λ t ) = ln( N t ) Ln(Growth rate!) Average growth curve Change of ln(growth rate) over time ln(λ t ) = ln( N t ) average growth Census year Census year ˆµ = 1 T T t=1 ln( N t ) µ = ˆσ 2 = 1 T 1 T (ln( N t ) ˆµ) 2 t=1 σ 2 = The average growth rate is positive, so Grizzlies survive in Yellowstone park, right? Freq ˆµ = % ˆµ 2σ Confidence intervals ˆµ σ µ ˆµ σ 2 = σ = ˆµ + σ 95% of all values 2.5% ˆµ + 2σ 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 quasiextinction 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.

10 Cumulative risk of extinction Cumulative risk of extinction Extinction probability µ = 0.01 σ 2 = µ = 0.01 σ 2 = 0.04 Extinction probability µ = 0.01 σ 2 = µ = 0.01 σ 2 = 0.04 µ = 0.01 σ 2 = 0.12 µ = 0.01 σ 2 = 0.04 N threshold = 1 N census = 10 Years from now N threshold = 1 N census = 10 Years from now Extinction Probability Extinction risk for Grizzlies [Log 10 ] Years from now Confidence }interval Using Extinction time estimates for conservation planning Adult birds: NORTH CAROLINA Year Adult birds: FLORIDA Extinction probability [Blow-up of top part of graph] 1980 Year Year When to use count-based PVMs? Key assumptions of count based PVAs The parameters " and # 2 are constant over time. When only few data is available, we still need about 10 years of 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 other populations). Simplicity [there are many assumption] 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.

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 NO λ t 1 λ t