Population Viability Analysis

Conservation Planning

• U.S. Endangered Species Act mandates two processes– Habitat Conservation Plans– Recovery Plans

• Quantitative methods are needed to assess viability of threatened and endangered populations in these plans

• Population viability analysis is a set of tools for quantifying the current and future status of population of conservation interest

Population Viability Analysis

• Differ significantly from traditional fisheries populations models

• Prediction of population growth or decline• Quantitative methods to predict probability or time

to extinction • Predict which life stages contribute most to

population growth• Assess affects of variation in vital rates on

prediction capabilities• Determining which additional data are most

needed to improve future population estimate

Population Viability Analysis

• Prediction of time to extinction given current status

• Predict how different management strategies will affect extinction probability

• Predict how many individuals would be needed to establish a new population

• Predict what harvest limits would still permit population growth (or stability)

• Predict how many populations are needed to prevent global extinction

Analyzing Monitoring Data

• PVAs can be used to integrate and analyze monitoring data– Recovery plans specify that survival, growth and

reproduction of populations be monitored– Habitat conservation plans also require monitoring of

populations at some level, although requirements vary

• Often the use of these data is not specified and data are not always used to aid recovery or evaluate HCPs

Vital Rates• Like most demographic analyses, PVAs focus on key

birth and death processes• Simpler models ignore immigration and emigration

(although more complicated ones can include multiple populations with migration)

• Survival– Typically refers to remaining in an stage class (age class)

• Growth– Typically refers to going from one stage class (age class) to

another

• Reproduction– Typically refers to number of offspring per individual (usually

female)

Estimating Population Growth

• Vital rates determine rate of population growth• Population size at time “t” is Nt

• Population size at some later time interval (the next year) “t+1” is Nt+1

• Thus the relationship (growth or decline) of the population is expressed Nt+1=λtNt

• λ describes the annual population growth rate (from one year to next)

• If λ > 1, the population is growing, if λ < 1 the population is declining, λ = 1 stable

• For some species, estimate λt = Nt+1/Nt

• More than just estimating change over time

Sources of Variation in Population Growth

• Population growth λ can be influenced by a number of factors that can influence predictions of future population size– Environmental stochasticity (random

fluctuations)– Environmental catastrophes and bonanzas

(large perturbations)– Demographic stochasticity (change variation

in vital rates)

Variation in Population Growth

• If population growth λ was the same every year, prediction of population growth would be easy

• Spatial variation among populations is also present

• Many factors both spatial and temporal result in changes in population growth

• Increased variation in growth among years, even if the long term average is the same has detrimental effects

Variation in Population Growth

• One of the key results of population models is that variation in population growth reduces

• Even if the average growth rate (arithmetic mean) is the same, increase variation results in smaller (geometric mean) growth rate

Arithmetic vs. Geometric Mean in Growth

• Imagine a population where Nt+1=λtNt

where λt = {0.86 with prob ½, 1.16 with prob ½

• Arithmetic mean of the two λ’s is 1.01 which would be the case for deterministic (nonrandom) growth

• If you start with 100 individuals and the population grows for 500 generations then N500 = N0 (1.01)500 = 14,477

Arithmetic vs. Geometric Mean in Growth

• But population growth is subject to stochasticity or random variation

• Now imagine same population (100 individuals growing for 500 generations) but grow rate varies stochastically (randomly) either 1.16 or 0.86

• So with both growth rates about equally likely (about 250 generations with high and with low growth rates then population size after 500 is N500 ~ N0 (1.16)250 x (0.86)250 = 54.8

• Adding variation to population growth λ usually reduces population growth

Figure of Population Growth Rate

From Morris and Doak (2002)

Variation in Population Growth Rate

• Addition of variation to population growth rate will have additional consequences

• This will make future predictions of population growth less certain

• It also means that there will be an increasing probability of extinction (or also of high population abundance)

Population Growth and Prediction

Populations of Clapper Rails

From Harding et al. 2001

Other Sources of Variability

• Spatial variability in demographic rates also has significant consequences for population survival

• Variation in vital rates usually vary from site to site

• Degree of correlation among sites (spatio-temporal variability) substantially affects outcome

• If a bad year in one population coincides with a bad year in another population then this reduces population viability

• If a bad year in one population coincides with good years in other populations, this improves viability

Observation Error or Lack of Data

• Observation error – Make measurements in better habitats– Easier to find and mark healthiest plants (easier to

find) or less healthy animals (easier to catch)– Difficulty finding/seeing organisms– Estimates will be more variable thus more pessimistic

• Density dependence– Negative density dependence (reduced growth rates

with increasing density)– Positive density dependence (Allee effects,

decreased growth with decreased density)

Measuring Population Viability

• Very small populations (<100) are subject to additional processes (inbreeding, demographic stochasticity) that complicate simple population projections

• Conservation biologist typically estimate time to a “quasi-extinction” threshold

• Metrics often calculated – Probability of quasi-extinction in a given time– Probability of quasi-extinction ever occurring– Mean time to extinction

Probability of Extinction

Viability Based on

Population Growth

• Growth rates may be more useful for populations where short-term extinction probabilities are low but population is vulnerable

• Atlantic right whales are currently at a population size of a bit less than 150 and declining

• The probability of extinction in the next 100 years is nearly zero, but is almost a certainty within 300 years

Viability Based on Population Growth

• Managers must increase the population growth rate above the current rate of λ = 0.976 to make population viable

• Higher growth rates obviously reduce probability of extinction (similar answers)

• Population growth is better estimated with limited data

• Stochastic growth is influenced less by temporal variability than is risk of extinction

Assumptions with Simple PVA Models

• No density dependence

• No demographic stochasticity

• No trends or correlation in environmental variation

• Environmental variation is moderate

• Census counts represent entire population

Demographic PVAs

• Particularly with long-lived organisms all individuals are not equal

• Need to explicitly account for differences in growth, survival and reproduction with age

• Use matrix population models to project future population growth

• Based on survival, growth and reproduction of different individuals in population

Demographic PVAs

• Conduct study using marked individuals and measure growth, survival and reproduction over several years

• Classify individuals into stages like size or age (unknown for many species)

• Stages dependent on species (e.g. young juvenile, old juvenile, young adult, reproductive adult, old reproductive adult)

• Estimate vital rates for each stage

Matrix Population Model

Elasticity Analysis

• Elasticity analysis is a method determining the “sensitivity” of population growth (λ) to scaled changes in vital rates (growth, survival, reproduction)

• The analysis looks at this sensitivity of growth to change in each element in the matrix (for each stage)

• Based on this, we can conclude which elements (which stages and rates) will have the greatest influence on population survival

Identifying Key Life Stages

• Management actions can be determined based on information about which life stages are most important for population growth

• Crouse et al. (1987) and Crowder et al. (1994) used PVAs to assist with management of threatened logger head turtles in southeastern U.S.

• Need to detemine which of two major threats to logger head turtles is most important– Trampling of eggs and hatchlings on beaches– Drowning of adult turtles in fishing nets

Loggerhead Turtle PVA

From Crouse et al. 1987

Identifying Key Life Stages

• They use PVAs on population data to measure the contributions of different life stages to population growth

• They found that reproductive adults were the most important stage

• Efforts aimed at saving eggs and hatchlings would not reverse population declines even if they were 100% effective

• Putting TED (turtle excluder devices) in fishing nets to prevent drowning would produce recovery even if didn’t eliminate all mortality

Analyzing Monitoring Data

• Gerber et al. (1999) used monitoring data for eastern Northern Pacific Gray Whales

• They asked how many years of data would be needed to determine if these whales should be delisted (reach population target)

• Population increased to mid 1990s and was delisted in 1994 but with no quantitative basis

• They found the delisting was warranted, but also this could have been done several years earlier

Consequences of Elasticity Analysis

• Determine which stages contribute most to population growth

• Management can focus on most important life stages

• Reserves can be created to accommodate most important life stages for organisms with complex life histories, migration