NRES 488/688 Midterm Examination Solutions
1.a. We need to estimate annual survival from estimates of monthly survival using a
known fate analysis. PIMs for the analysis are shown below.
These PIMs allow for full interaction between areas and time (months). I assessed
models of variation in monthly survival using Design Matrices. The best performing
model included an effect of County on survival and a difference between survival during
October and other months. Two additional competitive models included an effect of
County and either an October harvest effect or a year+October effect on survival.
Models lacking a county effect or allowing for greater temporal variation in survival were
not competitive. Results table is shown below.
Design Matrix for the third best model is shown below. Note it is necessary to include a
beta that differentiates harvest in October from other months to correctly estimate
October survival with the covariate.
Monthly suirvival for months other than October for Elko County was 0.932 ± 0.008,
while October survival was estimated as 0.805 ± 0.030. Annual survival was thus,
(0.932)11(0.805) = 0.37. For White Pine County comparable estimates were 0.849 ±
0.016 and 0.627 ± 0.045. Annual survival for White Pine county was thus, 0.10.
Managers should be seriously concerned about viability of sage grouse populations in
both counties.
1b. We need two pieces of evidence for an effect of hunting on survival. Is survival
lower during the harvest period and is the beta relating harvest to survival negative?
Survival was lower during October, when hunting occurred but the beta for the
relationship between harvest and survival from the best model equalled -0.10 ± 0.16,
providing weak support for the hypothesis that hunting negatively affected survival.
Consequently, another factor (disease?) might explain the low survival in October.
Survival was sufficiently low in the nonharvest months that eliminating harvest is
unlikely to restore either popualiton to viability, but managers would certainly want to
eliminate harvest for both populations to reduce rate of popualiton decline.
2a. Based on our understanding of brant biology we expect that we need to model two
age classes for survival and three age classes for encounter probability. We need three
age classes for encounter probability because probability of breeding (which we expect to
increase for the first three years) affects probability of being present on the breeding
colony to be sampled. Pims for both survival and encounter probability models are
shown below.
Because young brant were only released during the first eight years of the study, we only
require parameter indices for young for the first eight years. Young graduate to adults for
the purposes of estimating survival after their first year. For the ninth through 13th years
of the study we have only adult survival estimates.
The PIM for encounter probabilities allows for three age classes, one-, two- and three
years old and older. Notice that there are only encounters for one year olds for the first
eight recapture occasions, and for two-year olds for the second through ninth recapture
occasions.
Design matrix for the best performing model is shown below. Because the
maximum PIM number exceeds the “normal situation” for non-age structured models,
MARK will not open the full design matrix and it is essential to open a reduced design
matrix and build the models from scratch.
I modeled survival with an intercept (1), age term (2), seven additional time
adjustments for first-year individuals (4 - 10) and the individual covariate, residual mass
(3). Encounter probabilities were modeled similarly, except there were three age classes
and I only included the covariate residual mass for the age classes capable of breeding.
Note that for both surival and encounter probability there is a one year delay before we
can generate estimates for the older age lcasses. The best model allowed for age + time
variation with an additive effect of residual mass on both first-year survival and
encounter probabilities for the two older age classes. I also constrained tha last two
encounter probabilities for each age class to be equal because of confounding between
survival and encounter probability for the last interval and sampling occaqssion. Results
table is shown below.
Models containing an effect of residual mass on first-year survival and encounter
probabilities at ages 2 and 3 performed substantially better tha other models considered
(Akaike weight = 0.95), providing strong support for an effect of residaul mass on both
first year survival and encounter probability. If encounter probability was correlated with
presence on the breeding colony (a reasonable assumption for this population), this model
provides suport for an effect of residual mass on breeding probability. Models containing
the effects of relative hatch date or date of peak of hatch received no support, indicating
that these variables had little influence on survival.
The beta estimate linking first-year survival to residual mass was  = 0.51 ± 0.09,
indicating that first-year survival increased significantly as residual mass increased.
That is, goslings that were larger than other goslings of the same age survived their first
year at higher rates. Similarly for the relationship between encounter probability and
residual mass,  = 0.25 ± 0.05, suggested that larger goslings were more likely to be
present on the breeding colony as two and three+-year-olds (assuming detection of
individuals that were actually present did not vary with size). I conclude that larger
goslings survived and eventually bred at higher rates.