Male Breeding Pool: In many species, some adult males may be socially restricted
from breeding despite being physiologically capable. This can be modeled in
VORTEX specifying a portion of the total pool of adult males that may be
considered "available" for breeding each year. We assumed that each adult male is
equally capable of establishing a territory and, therefore, is equally capable of
breeding in a given year. This is not to say, however, that every male is actually
successful in that same year. Stochastic variation in the number of females that
breed, as well as the annual fluctuations in the total number of adults, may lead to
some males being unsuccessful.
Mortality: We developed the following simple age-sex specific mortality schedule,
based primarily on experience with other large felids (environmental variation (SD)
in parentheses):
Age %
Mortality
0-1
1-2
2-3
3-
50(15)
30(4)
10(3)
10(3)
Detailed field studies using radio-telemetry will be needed to determine
population-specific rates of mortality over a period of3-4 years. In addition, note
that we are assuming that these mortality rates apply to both males and females.
This may not be a valid assumption as males may experience higher mortality
through competition. This can be addressed in more detail in later modeling
efforts.
Inbreeding Depression: VORTEX includes the ability to model the detrimental
effects of inbreeding through reduced survival of jaguar cubs through their first
year. While we did not include these detrimental effects of inbreeding in our
baseline model, we did add it in subsequent model s in order to evaluate its impact
(see below).
Initial Population Size: For the purposes of this exercise, we arbitrarily set the
starting population size at 70 individuals. VORTEX then distributes the specified
initial population among age-sex classes according to a stable age distribution that
is characteristic of the mortality and reproductive schedule described previously.
Carrying Capacity: The carrying capacity, K, for a given habitat patch defines an
upper limit for the population size, above which additional mortality is imposed
randomly across all age classes in order to return the population to the value set
for K.
Once again, we arbitrarily set K to be 150 individuals in order to allow a
population to grow larger than its initial size if rates of birth and death rates
dictated. It is currently unclear if most isolated wild jaguar populations are at or
below carrying capacity.
Iterations and Years of Projection; All scenarios (defined as a single set of unique
input data) were repeated 100 times, with population projections extending to 50
years. All simulations were conducted using
VORTEX
version 8.41 (June 2000).
Features of the Model Not Included Here: In order to keep the demonstrations
simple at this workshop, a number of features within
VORTEXWQTQ
not included in
the process of developing population models. These features include:
• Density-dependent breeding;
• Catastrophes - natural or man-made - that can dramatically reduce birth and
death rates for brief periods of time;
• Age-specific reproductive rates among adult females;
• Time-specific changes in reproductive rates or habitat characteristics.
More detailed modeling efforts in the future may include these factors as
additional field data becomes available.
Results From Simulation Modeling
The input data described above constitutes what we call our baseline model. This
model serves as the foundation to which all other models are compared so that we
can determine the response of our simulated jaguar population to changes in one
or more input parameters.
The output from our baseline model is shown below in Figure 1. This plot shows
100 iterations (replicated simulations) as well as summary information about the
model above the graph. Note that, because of the addition to the model of annual
random variation in birth and death rates, no two individual replicate trajectories
are alike. As a result, it is important to run a number of simulations (e.g-, a
minimum of 100 is common) in order to evaluate both the most likely outcome as
well as the range of possible outcomes.
Figure 1. Population
trajectories from the
VORTEX
baseline
Mesoamerican jaguar
population model.
It is apparent from this graph that the population is able to grow in size over time;
the annual rate of growth (specified by r) is estimated to be more than 4%.
Moreover, none of the populations decline to extinction during the 100-year time
frame of the simulation. Therefore we can conclude that, under the specific
conditions that we assumed for this model, this simulated population has a high
probability of persistence through time. In order to investigate the impact that adult
mortality can have on overall population dynamics, we can develop a second model
in which the average rate of adult male and female mortality is increased from 10%
to 15%. Because all other input is unchanged, this particular model will allow us to
evaluate this parameter in detail.
^^o-ri
The results of this second model are shown in Figure 2. Immediately apparent from
this graph is the decreased rate of growth among replicate populations. Specifically,
the growth rate is reduced from 4% in the baseline model to just 1% in the model
with higher adult mortality. Perhaps more importantly, there is now a risk of
population extinction associated with this lower rate of population growth - six of
the 100 replicate population declined to zero within 70 years. Clearly, this reduced
rate of adult survival has a significant impact on the general health of a population
and its continued persistence. Using methods of analysis such as this, we can
identify those demographic parameters that play a major role in driving population
dynamics. Consequently, we can use this information to design detailed field
studies to provide researchers and managers with confident estimates of these
parameters for use in future population viability analyses.
Finally, we can investigate the impact that inbreeding and its detrimental effects on
cub survival can have on overall population viability. The results from this model
are shown in Figure 3. As is evident from the graph, the impact of inbreeding
depression is even more striking, leading to a strong decrease in population growth
rate and a large increase in population extinction probability. In fact, the average
population growth rate is now negative, indicating that the expected population
projection will show a gradual decline in population size over time. Clearly,
Figure 2. Population
trajectories from a
VORTEX
Mesoamerican jaguar
population model in which adult
mortality is increased from its
baseline value of 10% to 15%.
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