30 landings
time series used only intervention terms in classical Box‐Jenkins time series methodologies.
The overall model can be written as
t i
i t
t
z B
B I
B c
Eq.
2 where
c is the catch, Θ is a constant, B is the backshift operator, ω is an estimated parameter
related to the impact of the intervention I which is a 0,1 variable whose value is
1 for years after the intervention and 0 in prior years, and θ and φ are polynomial parameters
related to a moving average and autoregressive time series model that result
from the model fitting so that the residuals from the model z are a pure white noise
process. The approach to fitting was to first check the raw landings time series for stationarity.
Where necessary the time series was differenced or otherwise filtered to achieve
stationarity. The appropriate order of the moving average and autoregressive terms
was then determined by using the auto.arima function in R v.2.11.1, which uses the
Akaike’s Information Criterion AIC to determine the order for the two polynomial parameters
that will give the best model fit and have residuals that do not significantly differ
from a pure white noise process. The estimated regression parameters ω, θ, ϕ from
the model fitting were sequentially tested to determine if the magnitude of the effect
was significantly different from zero using a t‐test. If the effect was significant it was
included and the ARIMA model rerun. In the case that an intervention was found to be
significantly different from zero, the portion of the time series that occurred prior to the
intervention was adjusted based on the most recent period of the time series. This assumes
that current management strategies for reporting in each state are the most accurate
and therefore the landings from this period are the most reliable. Assessment
of stationarity and the intervention analyses were conducted in R v. 2.11.1.Appendix
II ‐‐ R Core Development Team 2007. Both Virginia and Maryland time
series had to be 1
st
order differenced in order to achieve stationarity and significant
interventions were found for both states. Details of the results of the reconstructed
landings are presented in section 5.3.
5.3. Reconstructed Commercial Landings
We only reconstructed landings for Virginia and Maryland as these were the only
jurisdictions that had reporting changes during the time series considered.
5.3.1. Virginia
Virginia commercial landings data were provided by Robert O’Reilly and Hershel
Shackelford VMRC, Newport News, VA. Raw monthly data, summarized by market
category, gear type and water code were available for the period 1973 – 2009. Only
annual totals were available for the period prior to 1973. The response variable in all
31 analyses
was the total annual landings of blue crab by weight metric tonnes, MT for the
period considered Table 5.1, Fig. 5.1. The
average annual commercial landings in Virginia over the period 1950‐2009 was
16,394 4,953MT =36.14 x 10
6
Lbs. Virginia commercial blue crab landings varied from
7,791 MT 17.18 x 10
6
Lbs in 1958 to 29,374 MT 64.77 x 10
6
Lbs in 1966. Although,
highly variable, there is no global trend evident in the time series Fig 5.1. There
is some indication of cycles in the time series of annual landings, with peaks in landings
in 1950, 1966, 1984 and 1993. A rapid drop in landings, followed by an equally abrupt
increase is apparent in 1992‐93. When the first differenced i.e., L
t+1
– L
t
time series
is examined, the landings anomalies for 1992‐1993 become more evident Fig. 5.2.
As discussed above see Section 5.1.1, VMRC has concerns regarding the validity of
reported landings in these two years. However, similar abrupt changes are evident in the
winter dredge survey time series Fig. 3.17 and in the Maryland commercial landings
reported below. Accordingly, we conducted all time series modeling with the raw
data as reported rather than leaving out the 1993 estimate as had been done previously
Miller et al. 2005. Time series analyses indicated the presence of a significant
reporting change intervention in 1993, which marked a switch from a dealer‐ based
reporting system to a mandatory fisher‐based reporting system Table 5.2. The inclusion
of the 1993 intervention suggests that under the dealer‐based reporting system
pre‐1993 landings were underestimated Fig. 5.3. Neither polynomial parameter
from the ARIMA model was found to be significant so they were excluded from
the model. The
reconstructed time series is shown in Table 5.1 and Figure 5.3. The average of
the reconstructed 1950‐2009 landings was 25,757 9,155 MT. This represents a
57.11 increase from the unadjusted values. The lowest adjusted landing was 20,856
MT 1958, and the highest adjusted landing was 42,440 MT 1966. The average
landings in the most recent five years 9,541 MT indicates that landings are near a time
series minimum. The period of decline apparent in the recent years in Figure 5.3 is of a
similar magnitude to the declines that occurred in the 1950’s.
5.3.2. Maryland
The raw landings time series for Maryland is provided in Table 5.1 and shown in
Fig 5.4. The abrupt increase in reported landings that occurred in 1981 is clear in this
figure. Landings prior to 1981 averaged 11,188
2,330 MT ~25x10
6
Lbs. In 1981, landings
jumped substantially to 26,150 MT. After a period of relatively stable landings until
the early 1990’s landings have declined such that they are now equivalent to landings
observed prior to 1981. It
is important to determine the contribution to the observed increase in landings
throughout the 1980s and early 1990s of changes in underlying abundance
32 during
this period that are evident in the survey data see Section 3.2.7 and of changes that
reflect the contribution of the reporting change. In the 1997 assessment, Rugolo et al.
1997 assumed that all of the change was the result of changes in underlying abundance.
In their assessment, Miller and Houde 1999 assumed the contrary, that all of
the change resulted from the reporting change. Fogarty and Miller 2004 concluded that
both a change in underlying in abundance and the reporting change contributed to the
change in abundance. When
Fogarty and Miller 2004 analyzed the Maryland commercial landings data
they initially determined that the data for the period 1929 – 1980 were stationary and
that the 1981‐1994 data were similarly stationary. Since their analysis, data from subsequent
years have been added to the time series. These new data have caused the recent
time series to become non‐stationary. Stationarity is a principal assumption of time
series analysis and a breach of this assumption has serious consequences. For example,
if we fit an intervention model to a decaying time series, the intervention term will
be significant because of the pattern of decay, not because of some underlying shift. Accordingly,
the analysis was conducted on a differenced time series Fig. 5.5. Differencing
removed the impact of the recent decline in landings. However, differencing
still allows the potential impact of the 1981 and 1993 reporting changes to be
examined. For example, first differenced estimates for these two years are both 10,
whereas the remainder of the data fall between –7.5 d 7 Fig. 5.5. We
tested both the 1980‐1981 and the 1993‐1994 reporting changes to determine
if either had a significant effect on the reported landings. We did not attempt
to adjust for the 2008 reporting change given how recently it occurred. Only the
1981 intervention was found to be significant p0.05; Table 5.3. The adjusted time series
suggested that landings were underreported during the years of self‐reporting, which
occurred prior to 1981. A moving average polynomial parameter was included in the
model as the parameter was significantly different from zero Table 5.3. We
used the estimated intervention term parameter to reconstruct the Maryland
commercial landings. The reconstructed Maryland landings are shown in Table
5.1 and in Figure 5.6. The mean of the adjusted annual 1950 –2009 landings time series
was 20,444 ± 5,017 MT. This represents a 45.72 increase in the estimated average
annual landings with the landings of years prior to 1981 increasing 110.94 on average.
The lowest adjusted landing was 9,180 MT 2000, and the highest adjusted landing
was 27,610 MT 1965. The landings over the last decade have remained fairly stable
at an average of about 12,000 MT, indicating a cause for concern because this represents
an extended period of time series lows when compared to the rest of the adjusted
time series. 5.3.3.
Baywide
33 We
present the combined, adjusted baywide landings for 1950‐2009 in Table 5.1 and
Figure 5.7. The average baywide annual landings for this period was 47,523
13,304 MT. The reconstructed landings indicate that removals have been 49.7 higher
over the period 1950‐2009 than previously reported. The highest recorded baywide
harvest was 70,574 MT 155.6 Million Lbs in 1966. The lowest recorded baywide
harvest was 20,207 MT 44.5 Million Lbs that occurred in 2007.
5.4. Estimates of Fishing Exploitation and Mortality
