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The Causes and Quantification of Population Vulnerability

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Title: The Causes and Quantification of Population Vulnerability


1
The Causes and Quantification of Population
Vulnerability
2
Ecological and Genetic factors that threaten a
population(and may possible be mitigated through
proper management)
  • The life history of the species
  • The average environment conditions
  • The extrinsic variability in the biotic and
    abiotic factors influencing a population
  • The intrinsic variability caused by small
    population sizes

3
Exercise
  • Agree on a focal species
  • Identify the different factors influencing its
    population viability and their relationships
  • make a diagram summarizing the role of these
    variables
  • Important Do no consult the book

4
EnvironmentalStochasticity
Current population size
Density-dependence
Demographic stochasticity
Genetics
growth
survival
reproduction
Extinction risk
Population growth and decline
5
Vital rates
  • Components of individual performance
  • Birth rate
  • Death rate
  • Growth rate

www.owlsonline.org/babyanimals.html
6
R0 The net reproductive rate
Measures of population performance
  • It represents the average number of female
    offspring produced by a female over her entire
    life

7
The annual population growth rate
  • Defined by the equation
  • Nt1?tNt

8
Estimation of the annual population growth rate
from census data
  • ?t Nt1/ Nt

9
Temporal stochasticity
  • Environmental stochasticity
  • Catastrophes
  • Demographic stochasticity
  • Bonanzas

10
Environmental stochasticity
  • Erratic and unpredictable changes in the
    environment associated to the variation of biotic
    and abiotic forces
  • Does not include consistent trends in the
    environment
  • It is represented by a probabilistic distribution
  • It can imply temporal or spatial correlations

11
Catastrophes and Bonanzas
Extreme conditions that result in bimodal vital
rates
The normal annual mortality rates of the giant
columnar saguaro cacti in Southern Arizona is at
most 5, while rare freezing mortality can cause
much higher mortality (Steenbergh y Lowe 1983)
12
Demographic stochasticity
  • Temporal variation in population growth driven by
    chance variation in the actual fate of different
    individuals within a year
  • Its magnitude strongly depends on population size

13
The California condor
In the last years there have been over 89
releases of condors raised in captivity. The
individual annual survival rate of 28 birds
released in Arizona was estimated 0.85 (Meretsky
et al. 2000).
14
Possible outcomes of releasing a pair of condors,
each with a survival probability of 85. We would
expect 2 x 0.851.7 live condors
(2 x 0.72) (1 x 0.26) (0 x 0.02) 1.7
Probabilidad de fracaso 28
15
Consider multiple releases of two pairs
  • We expect that the number of survivors from each
    pair varies between 0, 1, y 2 even if the
    environmental conditions are constant

The expected value is calculated as Combinations
(n,r) pr x qn-r n total number of individuals
r number of survivors p probability of
survival q probability of dying
16
Percentage of populations expected to show
different observed survival rates under
demographic stochasticity
Population size
Rate
17
  • Demographic stochasticity can impact the future
    of populations.
  • However is only significant in small populations.
  • Bruce Kendall y Gordon Fox (2002) argue that it
    may less important than is usually predicted, due
    to the inherent differences in survival rates
    among individuals.

18
Temporal variability on the rate of population
growth
  • In the real world, population growth rates
    fluctuate over time
  • To simplify, we will assume that variation in
    vital rates is caused solely by run-of-the mill
    fluctuations in environmental conditions
  • Adding variation to population growth does not
    simply mean that growth is more variable it
    means that populations mostly do worse that they
    would without variation

19
We assume that
  • In the following equation during each interval
    lambda can take two values equally probable
  • Nt1?tNt
  • where
  • ?t 0.86 with p1/2 and
  • ?t 1.16 with p1/2

20
  • The arithmetic mean of these rates is 1.01. if
    the population rates always had this rate, the
    population will increase in size by 1 each
    interval
  • To compare this situation with the stochastic
    scenario we should consider that
  • N1?0N0, y N2?1N1 gt N2 ?1?0N0,
  • and more generally

Nt1 (?t?t-1 ?t-2... ?1? 0)N0
21
  • In the deterministic case, if N0100, and after
    100 years
  • N100 N0(1.01)100 1002.705270.5
  • For the stochastic case, we do not know exactly
    how many years ?1.16 and ?0.86, they are likely
    to be about equal (50 each). Therefore, the most
    likely outcome of the stochastic growth case is
  • N100 N0(1.16)50 (0.86)50
  • 1000.88788.7

22
  • To better appreciate the stochastic process we
    can rewrite the equation and use the most-likely
    value to estimate a most likely stochastic
    population growth rate
  • (N100 /N0)(1/100) (88.7/100) (1/100)
  • 0.9888
  • This is a constant annual growth rate that would
    give the same final population size as does the
    most-likely outcome of the stochastic growth
    process. This is also the so-called geometric
    mean of the lambda values ?
  • ?G (0.86)1/2(1.16)1/2 0.9988

23
Spatial variability
  • The means and variances of the vital rates, and
    hence of population growth rates, will usually
    not be equal across all sites and habitats.
  • The most serious complication in a multi-site
    situation arises due to correlations in the
    temporal variation across sites.
  • Movement of individuals between populations

24
Observation Error
  • Both vital rates and population counts will
    usually reflect the influence of population error
  • It merely reflect our inability to measure vital
    rates or population growth size with absolute
    precision, and so has no effect on viability
  • Nevertheless, introduce biases and uncertainty
    into our estimates of population viability

25
The importance of the sampling design
  • Some examples
  • Do sampling in what we think is the best habitat.
  • There is a bias to the most robust plants or less
    fit animals.

26
Density Dependence
  • Change in individual performance, and hence
    population growth rate, as the size or the
    density of a population changes

27
Negative density dependence
  • It is a decline in average vital rates as
    population size increases
  • It is typically caused by intraspecific
    competition for limited resources or by
    interacting species whose impacts increase
    proportionally as the density of the focal
    organism increases

28
Positive density dependence or Alee effect
  • It is an increase in the population growth rate
    as population size increases
  • It may result from improvements in mating
    success, group defense, or group foraging as
    density increases
  • we do not have a good sense of the strength of
    such effects or the population sizes at which
    they will start to operate.

www.saskschools.ca/gregory/arctic/Amuskox.html
29
Martha Groom
  • She documented null or low reproduction rates in
    patches with few individuals of Clarkia concinna
    and suggested that they lacked effective pollen
    transfer
  • In contrasts patches with many individuals
    attracted enough pollinators independently of
    their degree of isolation

Martha Groom 1998
30
Some considerations about density dependence
  • Generally we lack information on its
    manifestation
  • Due to the sensibility of the models to these
    factors and the data limitations, it is
    reasonable to define
  • 1. higher thresholds beyond which the population
    does not growth
  • 2. Quasi-extinction thresholds high enough to
    avoid that Alee effects are significant

31
Genetic factors Concepts
  • Heterozygosity It is an indicator of genetic
    diversity the probability that, for the average
    locus, there will be two different alleles
  • Inbreeding the average probability that an
    individuals two copies of a gene are identical
    by descent

32
Genetic FactorsIndicators
  • Inbreeding depression is commonly estimated as a
    certain percentage reduction in some vital rate
    with a given increase in inbreeding level

33
Quantifying Population Viability
  • Viable populations are those that have a suitable
    low chance of going extinct before a specified
    future time.
  • Quasi-extinction thresholds
  • (Ginzburg et al. 1982)

Lev Ginzburg
http//life.bio.sunysb.edu/ee/people/ginzbgindex.h
tml
34
The measurement of extinction risk
  • Probability density function for the time
    required to first hit the quasi-extinction
    threshold, given the current population size
  • The cumulative distribution function of
    extinction times

35
Viability metrics
  • The probability of extinction by a given time
  • The ultimate probability of extinction
  • Mean, median and mode of the predicted extinction
    times (given that it occurs eventually)

Which one?
36
Cumulative extinction probability of the Grizzly
bears at Yellowstone. The x-axes indicates the
time required for a population of 99 females to
decrease to 20
37
Si la distribución probabilística de ?t se
aproxima a la lognormal, la magnitud de la
depresión en la tasa estocástica se puede
calcular como
?G ?A/?(1??2/ ?A2)
38
Caughley dichotomy
  • Small population paradigm emphasizing the role
    of stochastic factors
  • Decline population paradigm focused on the
    deterministic factors that lead to positive or
    negative population growth rates

www.science.org.au/academy/memoirs/caughley.htm
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