174
Lloyd Goldwasser, Scott Ferson, and Lev Ginzburg
One might assume that the number of available territories is fixed during the
foreseeable future, but such constancy is probably the least likely scenario. Because one of the primary effects of logging is to reduce the number of suitable
breeding habitats for the Spotted Owl, one might want to subtract sites to account
for future logging. Kenney (1994) estimated, however, that no additional owl sites
could fall below the 40% suitable habitat criterion (USFWS 1993), even assuming
that all privately held forest habitat was harvested. However, future growth of
young forest (representing sites that have already been harvested) may, over time,
acquire enough of the characteristics of old growth to provide breeding sites for
the Spotted Owl. The extent of this potential increase in terms of the number of
available breeding sites clearly depends on the future forest management practices, but it may be substantial. Calculations made by Robert Meier (personal
communication) suggest that the temporal increase in the number of territories
will be about 0.35% per year. This would amount to 35% over the next century.
Some other estimates suggest as much as a 50% increase in potential owl habitat
over this period from maturation of previously logged forests (e.g., USFS and
BLM 1994). We included this increase in habitats in our simulations, but to be
conservative, we used the lower value of 0.35% per year.
Demographic Stochasticity
Because populations consist of independent organisms, population sizes can take
on only whole number values, not fractional ones. For any finite population size,
survival rates cannot take on all values between 0 and 1 unless the rates are
regarded as probabilities of survival that are faced by each individual independently, rather than ratios of whole numbers. If the rates represent probabilities,
then the total number of survivors in the whole population is not a single deterministic value but is a random variate whose value comes from a distribution. It
may be a binomial distribution because the total corresponds to the outcome of an
independent “coin flip” by each member of the population. The term demographic
stochasticity refers to the uncertainty in total population numbers due to the
probabilistic nature of individual survival or reproduction. Even for a reasonably
high probability of survival, mere chance could occasionally result in very few
survivors in a given year. The smaller the population size, the larger the relative
uncertainty, so demographic stochasticity is of particular concern in populations
that are small enough already to be at risk of extinction (Burgman et al. 1993).
We could estimate the number of individuals who actually survive by drawing a
random number for each living individual and comparing it with the survival rate
and then tallying those whose random number is less than the rate as survivors.
This method is computationally intensive, however, and instead we included
demographic stochasticity in our simulations by using the methods described by
Ak¸ cakaya (1991). To simulate the number of survivors at each time step, we
generated a random variate from a binomial distribution with the survival rate as
the mean and the number of individuals as the number of trials. The binomial
Lloyd Goldwasser, Scott Ferson, and Lev Ginzburg
One might assume that the number of available territories is fixed during the
foreseeable future, but such constancy is probably the least likely scenario. Because one of the primary effects of logging is to reduce the number of suitable
breeding habitats for the Spotted Owl, one might want to subtract sites to account
for future logging. Kenney (1994) estimated, however, that no additional owl sites
could fall below the 40% suitable habitat criterion (USFWS 1993), even assuming
that all privately held forest habitat was harvested. However, future growth of
young forest (representing sites that have already been harvested) may, over time,
acquire enough of the characteristics of old growth to provide breeding sites for
the Spotted Owl. The extent of this potential increase in terms of the number of
available breeding sites clearly depends on the future forest management practices, but it may be substantial. Calculations made by Robert Meier (personal
communication) suggest that the temporal increase in the number of territories
will be about 0.35% per year. This would amount to 35% over the next century.
Some other estimates suggest as much as a 50% increase in potential owl habitat
over this period from maturation of previously logged forests (e.g., USFS and
BLM 1994). We included this increase in habitats in our simulations, but to be
conservative, we used the lower value of 0.35% per year.
Demographic Stochasticity
Because populations consist of independent organisms, population sizes can take
on only whole number values, not fractional ones. For any finite population size,
survival rates cannot take on all values between 0 and 1 unless the rates are
regarded as probabilities of survival that are faced by each individual independently, rather than ratios of whole numbers. If the rates represent probabilities,
then the total number of survivors in the whole population is not a single deterministic value but is a random variate whose value comes from a distribution. It
may be a binomial distribution because the total corresponds to the outcome of an
independent “coin flip” by each member of the population. The term demographic
stochasticity refers to the uncertainty in total population numbers due to the
probabilistic nature of individual survival or reproduction. Even for a reasonably
high probability of survival, mere chance could occasionally result in very few
survivors in a given year. The smaller the population size, the larger the relative
uncertainty, so demographic stochasticity is of particular concern in populations
that are small enough already to be at risk of extinction (Burgman et al. 1993).
We could estimate the number of individuals who actually survive by drawing a
random number for each living individual and comparing it with the survival rate
and then tallying those whose random number is less than the rate as survivors.
This method is computationally intensive, however, and instead we included
demographic stochasticity in our simulations by using the methods described by
Ak¸ cakaya (1991). To simulate the number of survivors at each time step, we
generated a random variate from a binomial distribution with the survival rate as
the mean and the number of individuals as the number of trials. The binomial