1. A Population Viability Analysis Model of Polioptila californica californica inOrange
County
Jacob Grisham, December 5, 2015
Abstract
I constructed a breeding-pair stage-structured matrix for environmentally
stochastic model of Polioptila californica californica (California Gnatcatcher)
subpopulation decline from 1993 to 2040 in Orange County (Figure 1). From the
simulations that were run in the model, I calculated the proportion of extinctions at each
year to create a graph of probability of extinction (Figure 2). In 10 to 20 years, the
species should be in danger of rapid decline to extinction because the model predicts that
each subpopulation contains 60 individuals as of now. The model’s predictive power is
not useful for accurately projecting population dynamics. The model needs to be refined
using less assumptions and a greater quantity of reliable data.
Introduction
The California Gnatcatcher, listed as threatened by the U.S. Fish and Wildlife
Service since 1993, inhabits California Coastal Sage Scrub (CSS); a community that
contributes to the California Floristic Province’s designation as a biodiversity hotspot
with high endemism. CSS itself is an “endangered” ecosystem. Scientists estimate CSS
habitat has declined by 90% as a result of development, agriculture, and land-use
practices. This has left the remaining habitat fragmented with increased wilderness to
urban interface and increasingly threatened by invasive species, anthropogenic fires, and
urban expansion (Westman 1981; Tippets et al. 1995; Kristan III et al 2003). These
threats have direct influence on the California Gnatcatcher population dynamics. Indeed
these threats were the likely cause the regional population decline. A population viability
analysis model of this umbrella/indicator species would be useful for managers working
within the framework of the State of California’s Natural Community Conservation
Planning Program (NCCP) to estimate effects of management decisions on population
dynamics. Ultimately, it is the hope that managers can use this species to conserve CSS
biodiversity and gauge habitat quality for CSS dependent species.
Methods
I sourced the data of initial population size, vital rates, vital rate standard
deviations from H. Reşít Akçakaya and Jonathon L. Atwood’s “A Habitat-Based
Metapopulation Model of the California Gnatchatcher”. Initial population size is a
function of carrying capacity. Akçakaya and Atwood calculated carrying capacity as a
function of patch size and quality using the RAMAS program. Vital rate data and
standard deviations are summarized in Table 1.

2. Grisham California Gnatcatcher PVA 2
Table 1: Stage matrix parameters: maternity (number of fledgling per breeder) (M),
juveniles survival rate (SJ), proportion of juveniles that become breeders (PJB),
juvenile fecundity (FJ=PJB*M), adult survival rate (SA), and adult fecundity
(FA=SA*M)
(H. Reşít Akçakaya and Jonathon L. Atwood, 1997)
Vital rate means and standard deviations were restricted to years 1993 and 1995 because
Akçakaya and Atwood noted 1994 was an exceptionally cold and wet winter, and
therefore was not representative of median environmental conditions. I also sourced the
corresponding matrix to which these data most appropriately fit:
.
I randomly populated the matrix with vital rates at the start of each simulation. To
generate a distribution of vital rates from which to randomly sample, I used a lognormal
distribution fitted with means and standard deviations for each vital rate. Using RStudio
programming language requires the input of the additional variable “observations” in the
“rlnorm()” function. I arbitrarily chose 200 to ensure variability within the hundredths-
place of vital rates. To randomly sample from each vital rate distribution I used the
“sample()” function, which required me to define an “x”. I set “x” equal to 100 to also
ensure variability within the hundredths-place of vital rates.
To project population decline from one year to the next, I performed matrix
multiplication of the stage matrix by the subpopulation size of the previous year. I
assumed the subpopulation initial size was always at a stable stage distribution among
503 individuals at the beginning of every simulation. I also assumed the subpopulation
remains at stable stage distribution throughout the projection into the future. I
incorporated a quasi extinction threshold, below which the population size declined
immediately to zero. Using variables from Akçakaya and Atwood, I set the quasi
extinction subpopulation size as 2% of the initial subpopulation size.
Results

3. Grisham California Gnatcatcher PVA 3
Figure 1: Number of individuals from 0 to 553 versus time projected from 1993 to
2040. The subpopulation size is assumed to decline to zero whenever the size reaches
10 individuals.
Figure 2: Probability of extinction from 0% to 100% versus time projected from
1993 to 2040. There is a 0% chance of subpopulation extinction until about 2026.
Subsequently, in the following 10 years, the probability of extinction increases
dramatically to 100%.
As of now, all subpopulations of the California Gnatcatcher should have about 60
individuals. In 10 to 20 years, the species should be in danger of rapid decline to
extinction.
Discussion

4. Grisham California Gnatcatcher PVA 4
Obviously the species is not at 60 individuals for each subpopulation. The species
was listed as threatened in 1993 and has maintained this status suggesting the meta-
population has maintained a somewhat stable size. The model’s predictive power is not
useful for accurately projecting population dynamics. The model lacks quantity of
reliable data and employs an overwhelming number of assumptions and simplifications.
Simulations are entirely dependent on inputted data. Using surrogate data from
published scientific literature as inputs for demographic models exposes users to
inferential errors (Etterson and Bennett 2006). Propagation of error decreases the
predictive power any simulation.
Regarding variables I used, if initial population size was 100% of carrying
capacity, then unpaired birds are included in the model. Therefore population size of
interest is clearly less than 100%. The designation of 80% is arbitrary. Similarly, the
designation of quasi extinction as 2% of the initial population size is meant to account for
allee effects, which are not well studied enough for this species to warrant a more
complex equation. 2% is an arbitrary value.
I used the lognormal distribution because I was unable to obtain raw data and fit
an appropriate distribution.
Structuring the matrix by breeding pairs results in exclusion of unpaired birds.
This is a reasonable assumption because these are the individuals that contribute to
population growth, the species is monogamous, and they have equal sex ratios at birth.
Additionally, Akçakaya and Atwood don’t define stages so it’s unclear whether stages
are based on age or some other biological indicator. A priori, since the matrix is stage
based, there is no information about any differences within states. Implied in the matrix, I
assume all reproduction occurs during a short breeding season (birth-pulse population),
the subpopulation is censused immediately after breeding season, all adults breed, and the
maternity rate, number of fledglings per breeder, is same for experienced and
inexperienced parents. Overall, these assumptions imply process error (compared to
observer error).
I was unable to successfully incorporate vital rate data from 1994-1995 to
incorporate the catastrophe of extreme wet and cold winter. Implied due absence from
simulations, are the assumptions that vital rates are uncorrelated; that there is no temporal
autocorrelation, no density dependence, and that there is homogeneous spatial
distribution and size of subpopulations. Subsequently, this assumes that vital rates are
equal despite local environmental conditions and demography.
For a long term model, beyond 50 years, changes to the landscape and the climate
should be accounted for. Development in southern California counties is the greatest
threat (Rodrigue et al.) Climate change will increase the frequency and severity of fire,
and of extreme weather. In particular, lower minimums and higher maximums. Invasive
annual European grasses pose a serious threat to CSS habitat quantity and quality.
Compounding this threat is the process of type-conversion of CSS to annual grassland if
fire frequency is too high. With increased density and range of human populations comes
increased probability of anthropogenic fires.
The NCCP is a private-public cooperative program for planning to preserve
biodiversity on an ecosystem scale while allowing economic development. Ultimately, I
want to create models that display relative effects on extinction as a result of various
NCCP planning options. To prevent the extinction of this species, models could be used

5. Grisham California Gnatcatcher PVA 5
to target management of nest predators such as invasive ants and rodents. To preserve the
CSS animal community, pairing population simulation models with GIS could lead to
novel insights on areas of key conservation concern. For example, maintaining/creating
habitat corridors among certain subpopulations or maintaining the size of certain habitat
patches by stalling development and restoring degraded habitat. Indeed, the NCCP often
redirects development to sites with low habitat quality in order to preserve higher quality
patches.
Beyond the model is the assumption that the California Gnatcatcher is an
adequate indicator and umbrella species for CSS. There is currently much debate of the
efficacy of this single species to accomplish conservation goals (Daniel Rubinoff 2001;
Chase et al., 2000). Currently, contemporary models incorporate spatially explicit multi-
species to examine the effects of threats to preservation (Conlisk et al. 2015). In the
future, models should be constructed to more intimately connect space and to more
closely examine specific effects.
Literature Cited
Akcakaya, H. Resit and Jonathan L. Atwood. (1997) A Habitat-Based Metapopulation
Model of the California Gnatcatcher. Conservation Biology, 11(2), 422-434.
Daniel Rubinoff. (2001) Evaluating the California Gnatcatcher as an Umbrella
Species for Southern California Coastal Sage Scrub, Conservation Biology,
15(5), 1374-1383.
Chase, Mary K., William B. Kristan III, Anthony J. Lynam, Mary V. Price, and John T.
Rotenberry. (2000) Single Species as Inicators of Species Richness and
Composition in California Coastal Sage Scrub Birds and Small Mammals.
Conservation Biology, 14(2), 474-487.
Conlisk, Erin, Alexandra D. Syphard, Janet Franklin, Helen M. Regan (2015) Predicting
the impact of fire on vulnerable multi-species community using a dynamic
vegetation model. Ecological Modeling, 301, 27-39.
Etterson, Matthew A., and Richard S. Bennett (2006) On the Use of Published
Demographic Data for Population-Level Risk Assessment in Birds. Human
and Ecological Risk Assessment, 12(6), 1074-1093.
Kristan III, William B., Antony J. Lynam, Mary V. Price and John T. Rotenberry.
(2003) Alternative causes of edge-abundance relationships in birds and small
mammals of California coastal sage scrub. Ecography, 26(1), 29-44.
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Walter E. Westman. (1981) Diversity Relations and Succession in Californian Coastal
Sage Scrub. Journal of Ecology, 62, 170-184.
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