February 1997
This document describes the parameters of the Marbled Murrelet models that will be discussed at a workshop on 4 March 1997. The list of parameters and their possible ranges described below are based on discussions in the previous workshop, on 22-23 November 1996 at Lewis and Clark College in Portland, Oregon. All parameters mentioned below will be discussed and may be subject to change as a result of these discussions. However, particular attention should be given to those for which we did not have any ranges discussed in the November workshop, including
Using the population modeling program RAMAS GIS (Akcakaya 1995), we will
develop three stage-structured, stochastic population models:
(1) metapopulation model of all Marbled Murrelets in CA, OR, and WA (about 6
populations),
(2) metapopulation model of Marbled Murrelets in CA (about 3 populations),
(3) single population or metapopulation model of Marbled Murrelets in the
"bioregion".
The workshop on March 4th will concentrate on (1) and (2) only.
The within-population dynamics of the models will be described by a stage
matrix (Caswell 1989), whose elements are the vital rates (survival rates and
fecundity) of juveniles (0-12 months), subadults (12-24 months) and adults (24+
months). The vital rates estimated by Beissinger (1995) provide a good
starting point for the stage matrix.
The stage matrix (survival rates and fecundity) must be considered in
conjunction with density dependence. Three combinations of stage matrix and
density dependence were considered at the November workshop:
(1) Ceiling-type of density dependence with the following stage matrix based on
Beissinger (1995):
Juv. SubAd. Adult
Juv: 0.0000 0.0000 0.1050
SubAd: 0.6125 0.0000 0.0000
Adult: 0.0000 0.7770 0.8750
This model results in an average decline of 7% per year. The decline may be
faster, especially at the beginning of the simulated time period, depending
on the variation and the carrying capacity (see below).
(2) Ceiling-type of density dependence with the following stage matrix:
Juv. SubAd. Adult
Juv: 0.0000 0.0000 0.1620
SubAd: 0.6300 0.0000 0.0000
Adult: 0.0000 0.7992 0.9000
This model results in a deterministically stationary population (i.e.,
average growth rate 0% per year). However, because of the ceiling-type of
density dependence imposed, the predicted abundance may decline, depending
on the variation and the carrying capacity (see below).
(3) Contest (Beverton-Holt) type of density dependence with a stable carrying
capacity. In this case, the maximum rate of population growth at low
densities (when there are no density effects) must also be specified, and
was estimated as 1.06 (6% growth per year) based on an assumption of a
maximum of 1 chick fledged per nest.
The contest (Beverton-Holt) type density dependence may arise when the
limitation ("ceiling") acts only on the breeding population, and the adults
in excess of this ceiling become non-breeders, decreasing the average number
of chicks per adult in the population. In contrast, the ceiling model
assumes that all stages are limited; individuals in excess of the ceiling
are assumed to be dead.
The parameters (vital rates) in the stage matrix may be modified according to
the trend in abundance (growth or decline rate) predicted from an analysis of
off-shore count and in-land detection data.
The population growth of Marbled Murrelets may be limited by food and/or nesting sites. The observed population changes may reflect a deterministic decline to extinction (systemic pressure), a decline to an equilibrium abundance (carrying capacity) or to a ceiling that is lower than the current abundance, or fluctuations without a significant trend. Density dependence should be modeled with several models (see above). These require a carrying capacity estimate for each population in a metapopulation. In the November workshop, we modeled a single population, and assumed that carrying capacity was equal to initial abundance (see below).
Another type of density dependence involves Allee effects which may arise from the negative effects of low abundances on the genetics and social structure of the population. Such effects may be modeled by a local (population-specific) extinction threshold, below which the population is assumed to be extinct. The value of such a threshold may be set as a fixed number (such as 2, 4 or 6 individuals), or as a percentage of the carrying capacity (e.g., 1%, 2% or 3%).
The initial abundance of each population in a metapopulation model may be based on data from off-shore counts and in-land detections. In the November workshop, we modeled a single (bioregion) population and used a total of 1,700 birds as the initial size of this population. For the two metapopulation models that will be considered at the March workshop, the range of abundances of each population will be determined by the discussion among the workshop participants. The initial distribution of individuals to stages (juvenile, subadult, adult) probably will not affect the results very much. A low proportion (e.g., 6%) may be used for juveniles to reflect the off-shore counts. In the November workshop, we used 6%, 12% and 82% juveniles, subadults, and adults, respectively.
There are no data on the temporal (year-to-year) variation in survival rates or fecundities of Marbled Murrelet populations. If such data can be found for other alcids, they could be analyzed to estimate the coefficients of variation in vital rates. A better alternative is to use the temporal variation in off-shore counts (or in-land detections) to estimate the variation in vital rates. This may be done by progressively increasing the variation in model parameters until the temporal variation in predicted abundance matches the temporal variation observed in the data. This iterative process necessarily results in a crude and approximate estimate, but will be preferable to data from other species. In the November workshop, we used the following two sets: CV of fecundity (F) and juvenile survival (Sj): 15%, 30% CV of subadult survival (Ss) and adult survival (Sa): 5%, 10% In addition to environmental variations, the model will incorporate demographic stochasticity in survival, reproduction and dispersal (Akcakaya 1991).
Rare and extreme changes in vital rates ("catastrophes") may occur due to fires
on land, oil spills off-shore, and other marine events. The frequency of such
events should be calculated from historical data on frequency and impact of oil
spills, frequency and size of fires, and marine cycles.
Modeling catastrophes requires two types of information: The probability of
the catastrophes (e.g., 0.01 for 1 in 100 years), and the effect of
catastrophes (e.g., 50% additional juvenile mortality, or 10% decline in
carrying capacity).
In the November workshop we assumed no catastrophes.
The degree of similarity among the year-to-year fluctuations of different populations may have important effects on metapopulation viability. In the November workshop we did not have to consider this, because we were focusing on a single population model. Time series data on in-land detections or off-shore counts form several locations (preferably far-away from each other) will give clues about the possible range of these parameters. However, such data are unlikely to become available in the short-run. Instead, we may simply consider the extremes of no correlation and full correlation.
Another set of metapopulation-level parameters that we did not have to consider in the November workshop involve dispersal among populations. Here dispersal refers to the movement of individuals from one population to another at the annual time scale. It is very unlikely that there will be any data on this. At the March workshop, we will have to come up with a maximum possible rate of dispersal, and use it, together with a zero dispersal rate, as a wide range of possible parameter values.
The PVA model will be used to analyze the viability of the Marbled Murrelet
under three options:
(1) logging in all Pacific Lumber Company land ("full logging"),
(2) logging in part of the Pacific Lumber Company land as specified in a
proposed agreement ("partial logging"), and
(3) no logging.
In all three cases, the effect of logging will be modeled as a decrease in the
carrying capacity (or ceiling) of the model, in proportion to the decrease in
total habitat suitability (i.e., decrease in available habitat, weighted by the
suitability of the habitat).
This effect should be quantified with an analysis of the GIS data on the
habitat characteristics. However, such data is not likely to become available
soon. In the absence of such data, we will use approximate ranges suggested by
workshop participants.
In the November workshop, where we considered only the local ("bioregion")
population, we made the following assumptions:
Habitat in currently protected areas: 7,000 to 21,000 acres.
Total habitat in Pacific Lumber land: 7,000 acres.
Habitat in P.L. land to be preserved: 3,500 acres.
Total habitat in the bioregion: 14,000 to 28,000 acres
Option 3 (no logging): 0% decrease in carrying capacity (K)
Option 2 (partial logging): 3,500 of 14,000-28,000 acres logged, i.e., 3.5/14
to 3.5/28, or 25% to 12% decrease in K.
Option 1 (full logging): 7,000 of 14,000-28,000 acres logged, i.e., 7/14 to
7/28, or 50% to 25% decrease in K.
Logging may also effect the vital rates, for example, through increased edge
effects that may cause an increase in predator densities. This effect could be
studied with data from an experimental study in Washington that uses artificial
nests to measure predator pressure in different habitat types and
configurations. This effect may be especially important in the full logging
option, but may be unimportant or negligible in the partial logging case. This
is because the partial logging will target small fragments of suitable habitat,
and leave larger patches relatively unimpacted.
The effect of the three options should be considered within the context of similar impacts on Marbled Murrelet habitat in other parts of the bioregion, as well as in other regions in California, Oregon and Washington. These cumulative effects should be characterized by discussion among the participants of the March workshop.
The results of the PVA will be expressed as increases in the risk of decline with partial or full logging, from the risk of decline with no logging. Two parameters must be specified for the presentation of these results: the decline threshold (amount of decline) and a time horizon (number of years for which to make the prediction). Results should be presented for two different numerical values of each of these parameters. One numerical value should be fixed (such as 50 years for the time horizon, and 90% decline for the amount of decline). The other numerical value should be specific to the comparison, giving the result for the threshold and time horizon for which the change in risk was maximum. This is necessary because it may be impossible to find the amount of decline and time horizon appropriate for all cases; case-specific time horizons and decline thresholds, in addition to fixed ones, will allow the selection of the appropriate criteria for assessment.
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