The Causes and Quantification of Population Vulnerability

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The Causes and Quantification of Population
Vulnerability
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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

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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

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EnvironmentalStochasticity
Current population size
Density-dependence
Demographic stochasticity
Genetics
growth
survival
reproduction
Extinction risk
Population growth and decline
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Vital rates

• Components of individual performance
• Birth rate
• Death rate
• Growth rate

www.owlsonline.org/babyanimals.html
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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

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The annual population growth rate

• Defined by the equation
• Nt1?tNt

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Estimation of the annual population growth rate
from census data

• ?t Nt1/ Nt

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Temporal stochasticity

• Environmental stochasticity
• Catastrophes
• Demographic stochasticity
• Bonanzas

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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

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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)
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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
  

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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).
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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
Event Fate of the female Fate of the male Probability
Both survive Live (p0.85) Live (p0.85) 0.85 x 0.85 0.7225
One bird survives Live (p0.85) Die (p0.15) 0.85 x 0.15 0.1275
One bird survives Live (p0.15) Die (p0.85) 0.85 x 0.15 0.1275
Neither suvives Die (p0.15) Die (p0.15) 0.15 x 0.15 0.0225
(2 x 0.72) (1 x 0.26) (0 x 0.02) 1.7
Probabilidad de fracaso 28
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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
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Percentage of populations expected to show
different observed survival rates under
demographic stochasticity
Population size
Rate
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• 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.

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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

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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

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• 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
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• 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

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• 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

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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

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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

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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.

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Density Dependence

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

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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

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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
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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
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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

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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

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Genetic FactorsIndicators

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

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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
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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

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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?
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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
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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)
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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