Transcript The Causes and Quantification of Population Vulnerability

The Causes and Quantification
of Population Vulnerability
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
Exercise
1. Agree on a focal species
2. Identify the different factors influencing
its population viability and their
relationships
3. make a diagram summarizing the role of
these variables
Important: Do no consult the book
Current population size
Densitydependence
survival
Demographic
stochasticity
growth
Population growth and
decline
Environmental
Stochasticity
Genetics
reproduction
Extinction
risk
Vital rates
• Components of
individual
performance:
Birth rate
Death rate
Growth rate
www.owlsonline.org/babyanimals.html
Measures of population performance
R0
The net reproductive rate
• It represents the average number of
female offspring produced by a female
over her entire life

The annual population growth rate
• Defined by the equation:
Nt+1=tNt
Estimation of the annual
population growth rate from
census data
t = Nt+1/ Nt
Temporal stochasticity
•
•
•
•
Environmental stochasticity
Catastrophes
Demographic stochasticity
Bonanzas
Environmental stochasticity
1. Erratic and unpredictable changes in the
environment associated to the variation of
biotic and abiotic forces
2. Does not include consistent trends in the
environment
3. It is represented by a probabilistic distribution
4. It can imply temporal or spatial correlations
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)
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
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).
Possible outcomes of releasing a pair of condors, each with
a survival probability of 85%. We would expect 2 x 0.85=1.7
live condors
Event
Fate of the
female
Fate of the
male
Probability
Both survive
Live (p=0.85)
Live (p=0.85)
0.85 x 0.85=
0.7225
One bird
survives
Live (p=0.85)
Die (p=0.15)
0.85 x 0.15=
0.1275
One bird
survives
Live (p=0.15)
Die (p=0.85)
0.85 x 0.15=
0.1275
Neither
suvives
Die (p=0.15)
Die (p=0.15)
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 %
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
Percentage of populations expected to show different observed
survival rates under demographic stochasticity
Rate
0
0-0.1
0.1-0.2
0.2-0.3
0.3-0.4
0.4-0.5
0.5-0.6
0.6-0.7
0.7-0.8
0.8-0.9
0.9-1
1
2
2
0
0
0
0
26
0
0
0
0
0
72
Population size
16
8
4
0
0
0
0
0
0
0
0
0
0
0
1
0
0
0
0
0
10
2
2
0
6
8
0
13
24
37
51
38
0
21
0
0
7
27
52
32
0
0
0
0
0
0
0
2
18
53
27
1
64
0
0
0
0
0
0
0
0
15
71
14
0
128
0
0
0
0
0
0
0
0
6
89
4
0
• 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.
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
We assume that
• In the following equation during each interval
lambda can take two values equally probable
Nt+1=tNt
where
t= 0.86 with p=1/2 and
t= 1.16 with p=1/2
• 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 => N2= 10N0,
and more generally:
Nt+1= (tt-1 t-2... 1 0)N0
• In the deterministic case, if N0=100, and after
100 years:
N100 = N0(1.01)100 =100*2.705=270.5
• 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 =
100*0.887=88.7
• 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
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
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
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.
Density Dependence
• Change in individual
performance, and hence
population growth rate, as
the size or the density of
a population changes
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
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
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
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
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
individual’s two copies of a gene are “identical
by descent”
Genetic Factors
Indicators
• Inbreeding depression is commonly estimated
as a certain percentage reduction in some vital
rate with a given increase in inbreeding level
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.html
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
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?
Probabilidad acumulada de cuasiextincion
Cumulative extinction
probability of the Grizzly
bears at Yellowstone. The xaxes indicates the time
required for a population of
99 females to decrease to 20
0.0020
0.0018
0.0016
0.0014
0.0012
0.0010
0.0008
0.0006
0.0004
0.0002
0.0000
0
10
20
30
40
Años en el futuro
50
60
Tasa estocastica de crecimiento
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)
1.2
1
1.05
0.95
0.8
0.6
0
0.2
0.4
0.6
0.8
Desviacion estandar de lambda
1
1.2
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