Trends in policing effort and the number of confiscations for West Coast rock lobster A. Brandão, S. Johnston and D.S. Butterworth Marine Resource Assessment & Management Group (MARAM) Department of Mathematics and Applied Mathematics University of Cape Town Rondebosch 77, Cape Town July 26 Abstract GLM methods are applied to compliance data on confiscations (and abandonments) and on policing effort to estimate recent trends in the amount of rock lobster that is poached. Estimates for 26 are based on three months of data only; they are suggested by analysis not to be reliable, and hence recommended to be disregarded. A tentative suggestion for poaching trends relative to 28 for the northern region (Super-areas 3+4+5+6) is a decrease to.3 from 28 to 22, with a subsequent increase to.5 by 25. For the southern region (Super-area 8+) the corresponding rounded figures for the same periods (both increases) are 2. and 4.. There is room for alternative suggestions for these numbers, which are put forward primarily to serve as a basis from which to initiate discussions. Introduction To obtain overall annual rates of increase in number of confiscations (which throughout this paper include abandonments) and in policing effort in a manner that takes into account possible monthly effects and, in the case of policing effort, the fact that various types of policing exercises are carried out, Generalised Linear Models (GLMs) were applied to these data (either aggregated or disaggregated by Super-area) by Brandão et al. (2a, b and c). In this paper, the analyses of Brandão et al. (23) on a Super-area basis are updated to include the further data now available. Data Monthly data on confiscations and policing effort obtained from one of the Directorates within the CD (Directorate: Compliance) for the period of April 28 to March 26 are used in the present analyses. Data for the period April 23 to March 26 are new compared to those used for the analyses carried out by Brandão and Butterworth (23). These disaggregated data are reported in the Appendix.
The policing effort types included in the analyses were revised by scientists and compliance on the west coast rock lobster working group. The policing effort types selected as being those most likely to have resulted in rock lobster confiscations are: vehicles inspected, slipway inspections, coastal patrols, restaurant inspections, FPE inspections and sea patrols. The effort types of road blocks and permit checks used in previous analyses have consequently been omitted from the analyses presented in this paper. Methods Generalized linear models (GLMs) were used to investigate the variation of the number of confiscations of rock lobster as well as that of the policing effort that has occurred. Trends in the number of confiscations and in the policing effort are modelled in two ways; one by having the covariate year which is a factor which represents the year (i.e. a categorical nonlinear relationship is assumed between the number of confiscations/policing effort with the time period) and alternatively by having the covariate Time (essentially the date) which represents a continuous value for the year and month for which the data record applies (i.e. a linear relationship is assumed between the number of confiscations/policing effort with the date). (Note that year refers to a calendar year throughout this document.) The expected policing effort (assuming a linear relationship with time) is modelled as: P Time E exp month type () where P is the policing effort, assumed to have an overdispersed Poisson distribution, is the intercept, month is the month effect, type is the type of policing effect, where the type factor is associated with the different types of policing such as coastal patrols, restaurant inspections, sea patrols, slipway inspections, FPE inspections and vehicles inspections, and Time is the time (date) representing the year and month to which the data applies, and is the associated coefficient. When a nonlinear relationship is assumed between policing effort and time, the expected policing effort is modelled as: where is the year effect (28 to 26). year P E exp month type year (2) A weight is applied to each of the GLMs above to account for different levels of variance (beyond Poisson) in the data for the different measures of policing. The weight applied to the data is given by 2
the inverse of the estimated overdispersion parameter obtained by fitting the GLM of Equation () (without the type factor) to each separate data set for the different types of policing employed. The same procedure as for policing effort is applied to the number of confiscations. The one difference in the GLMs is that the effect does not apply in this case. There is no weighting of the data in this case. type Results Tables -5 shows the parameter estimates for the GLMs fitted to the policing effort data and to the number of confiscations for Super-areas 3+4, 5+6, 8+, 3+4+5+6 and 3+4+5+6+8+ respectively. For policing effort, whether a linear or nonlinear function is assumed over time, a slight positive trend is evident (Table ) for Super-area 3+4, but a slight decreasing trend in Super-areas 5+6, 3+4+5+6 and 3+4+5+6+8+ if a linear function is assumed over time (Tables 2, 4 and 5) and no trend for Super-area 8+ (Table 3). For a nonlinear function over time, slight downward to stable trends for Super-areas 8+, 3+4+5+6 and 3+4+5+6+8+ (Figures to 3) and a continuing downward trend for Super-area 5+6. For the number of confiscations, whether a linear or nonlinear function is assumed over time, a downward trend is evident for Super-areas 3+4, 5+6 and 3+4+5+6. A downward trend since 23 is evident for Super-area 3+4+5+6+8+. For Super-area 8+, a non-linear function assumed over time shows a downward trend since 23 but a positive trend is evident if a linear function over time is assumed (Table 3 and Figure ). Thus, the instantaneous annual rates of increase obtained from the linear GLM for Super-area 3+4 are: : -23.8% (s.e. = 7.5%) :.9% (s.e. =.6%) Together these suggested that removals from poaching have been decreasing at an instantaneous rate of 34.7% p.a. (s.e.=7.6%) over the last seven years. This corresponds to a net decrease of 29.3% over one year, or 5% over two. For Super-area 5+6 these are: : -2.6% (s.e. = 7.%) : -9.% (s.e. =.%) Together these suggested that removals from poaching have been decreasing at an instantaneous rate of.5% p.a. (s.e.=7.2%) over the last seven years. This corresponds to a net decrease of.9% over one year, or 2.5% over two. For Super-area 8+ these are: : 4.4% (s.e. = 5.6%) :.2% (s.e. =.9%) 3
Together these suggested that removals from poaching have been increasing at an instantaneous rate of 4.2% p.a. (s.e.=5.7%) over the last eight years. This corresponds to a net increase of 5.3% over one year, or 32.8% over two. For combined Super-area 3-6 these are: : -2.4% (s.e. = 5.4%) : -2.2% (s.e. =.4%) Together these suggested that removals from poaching have been decreasing at an instantaneous rate of 9.2% p.a. (s.e.=5.6%) over the last seven years. This corresponds to a net decrease of 7.5% over one year, or 3.9% over two. For combined Super-area 3-8+ these are: : -3.5% (s.e. = 4.%) : -3.9% (s.e. =.%) Together these suggested that removals from poaching have been increasing at an instantaneous rate of.5% p.a. (s.e.=4.2%) over the last eight years. This corresponds to a net increase of.5% over one year, or.9% over two. Figure 4 shows the ratio of confiscations (plus abandonments) to policing effort type for the different Super-areas, corresponding to indices of the amount of rock lobster poached by policing effort type. Discussion In 23 when such analyses were last considered to inform on poaching trends, summary views were developed for northern (Super-areas 3+4+5+6) and southern (Super-area 8+) regions. Since it seems likely that a similar approach might be followed now, the discussion below focuses on Figure 2 for the northern, and Figure for the southern region. Visual impressions of overall poaching trends (the ratios of confiscations plus abandonments to policing effort) in these two Figures are dominated by the very low values for 26. Results for 26 are, however, based on data for January-March only, rather than for all twelve months as for the other years. Although in principle the GLM standardisation removes the month effect, and accordingly renders the 26 values comparable with those for the earlier years, questions of reliability do arise given the smaller sample sizes involved. In 23, results were summarised as a decrease in poaching from 28 to 22 of between and 5% for the northern region, and an increase between 25 and 25% for the southern region. As a first suggestion only, based on Figures 2 and respectively (and recognising the existence considerable room for discussion), we tentatively put forward the following rounded best estimates (relative to 28) with ranges in square brackets for relative changes in the extent of poaching: Northern region (Super-areas 3+4+5+6): 28-22 Decrease to.3 [.;.6] 4
22-25 Increase to.5 [.3;.7] Southern region (Super-areas 8+): 28-22 Increase to 2. [.; 3.] 22-25 Increase to 4. [2.; 6.] References Brandão, A., Johnston, S.J. and Butterworth, D.S. 2a. Trends in policing effort and the number of confiscations for West Coast rock lobster. Fisheries/2/JUN/SWG-WCRL/32. Brandão, A., Johnston, S.J. and Butterworth, D.S. 2b. Trends in policing effort and the number of confiscations for West Coast rock lobster on a Super-area basis. Fisheries/2/AUG/SWG- WCRL/46. Brandão, A., Johnston, S.J. and Butterworth, D.S. 2c. Further trends in policing effort and the number of confiscations for West Coast rock lobster on a Super-area basis. Fisheries/2/AUG/SWG-WCRL/48. Brandão, A., Johnston, S.J. and Butterworth, D.S. 23. Updated trends in policing effort and the number of confiscations for West Coast rock lobster. Fisheries/23/AUG/SWG-WCRL/8. 5
Table. GLM parameter/coefficient (and standard error) estimates for Super-area 3+4. January. (.45 ).62 (.43 ) -.662 (.54 ) -.73 (.665 ) February -.253 (.55 ) -. (.52 ) -.7 (.446 ) -.66 (.547 ) March -.228 (.54 ) -.94 (.5 ).948 (.368 ).99 (.449 ) April -.24 (.56 ) -.4 (.58 ).27 (.49 ).58 (.58 ) May -.9 (.5 ) -.27 (.52 ) -.45 (.64 ) -.284 (.763 ) June -. (.52 ) -.56 (.53 ) -4.5 ( 2.32 ) -4.7 ( 2.88 ) July -.4 (.49 ).4 (.5 ) -2.255 (.987 ) -2.35 (.22 ) August -.2 (.48 ).6 (.5 ) -.2 (.635 ) -.29 (.786 ) September -.284 (.59 ) -.257 (.6 ) -2.96 (.36 ) -3.2 (.69 ) October.58 (.45 ).77 (.47 ) -3.38 (.68 ) -3.42 ( 2.7 ) November.5 (.45 ).6 (.47 ) -.749 (.537 ) -.769 (.663 ) December Time (yr - ).9 (. ) -.2 (.6 ) 28 29 -.23 (.54 ) -.424 (.542 ) 2. (. ). (. ) 2.346 (.23 ) -.367 (.37 ) 22.244 (.25 ) -2.95 (.528 ) 23.8 (.27 ) -3.2 (.769 ) 24.378 (.22 ) -.978 (.32 ) 25.585 (.7 ) -.297 (.36 ) 26.855 (.68 ) -3. (. ) coastal.938 (.36 ).938 (.37 ) FPE -3.98 (.25 ) -3.98 (.27 ) restaurant -3.73 (.97 ) -3.73 (.99 ) sea -4.79 (.235 ) -4.79 (.237 ) slipway.988 (.36 ).988 (.37 ) vehicles 6
Table 2. GLM parameter/coefficient (and standard error) estimates for Super-area 5+6. January.498 (.23 ).46 (.22 ).637 (.52 ).33 (.53 ) February.283 (.28 ).254 (.28 ).389 (.55 ).99 (.532 ) March.258 (.29 ).236 (.29 ).573 (.528 ).3 (.5 ) April.44 (.2 ).38 (.23 ).263 (.53 ).26 (.5 ) May.535 (.9 ).482 (.2 ).77 (.523 ).57 (.52 ) June.344 (.24 ).299 (.25 ) -3.6 (.82 ) -3.6 (.8 ) July.499 (.2 ).46 (.2 ) -4.4 ( 2.95 ) -4.3 ( 2.93 ) August.53 (.9 ).5 (.2 ) -2.89 (.69 ) -2.96 (.67 ) September.232 (.27 ).2 (.28 ) -.326 (.842 ) -.377 (.836 ) October.67 (.7 ).62 (.9 ) -.78 (.2 ) -.82 (. ) November.567 (.8 ).559 (.2 ) -.6 (.747 ) -.23 (.74 ) December Time (yr - ) -.8 (. ) -.7 (.6 ) 28 29 -.6 (.84 ).373 (.47 ) 2 2 -.8 (.75 ) -.48 (.446 ) 22 -.48 (.77 ) -.937 (.528 ) 23 -.333 (.8 ) -.68 (.485 ) 24 -.486 (.84 ) -.687 (.486 ) 25 -.63 (.88 ) -.639 (.478 ) 26 -.489 (.53 ) -2.86 (.63 ) coastal -.947 (.96 ) -.947 (.97 ) FPE -2.99 (.99 ) -2.99 (. ) restaurant -3.74 (.23 ) -3.74 (.25 ) sea -5.58 (.4 ) -5.58 (.42 ) slipway -.723 (. ) -.722 (. ) vehicles 7
Table 3. GLM parameter/coefficient (and standard error) estimates for Super-area 8+. January.98 (.8 ).94 (.8 ) -.34 (.59 ) -.66 (.636 ) February.29 (.8 ).25 (.7 ).77 (.473 ).33 (.59 ) March.39 (. ).35 (.9 ) -.32 (.896 ) -.358 (.967 ) April.57 (. ).59 (.2 ).953 (.483 ).49 (.523 ) May.26 (.9 ).27 (. ) -.46 (.587 ).38 (.636 ) June.9 (.7 ).92 (.8 ) -.36 (.586 ).36 (.634 ) July.288 (.5 ).288 (.6 ) -.25 (.793 ) -.966 (.863 ) August.243 (.6 ).243 (.7 ) -2.24 (.32 ) -2.9 (.43 ) September -.43 (.3 ) -.43 (.4 ).87 (.568 ).22 (.64 ) October.98 (.9 ).98 (. ) -.9 (.594 ) -.66 (.642 ) November.77 (. ).77 (. ) -.73 (.73 ) -.69 (.77 ) December Time (yr - ). (. ).2 (.5 ) 28 -.4 (.96 ) -.647 (.75 ) 29 -. (.88 ) -.75 (.654 ) 2 2.25 (.83 ).452 (.482 ) 22.47 (.85 ) -.43 (.595 ) 23.4 (.87 ).3 (.433 ) 24 -.65 (.89 ).396 (.487 ) 25.3 (.85 ).726 (.459 ) 26 -.48 (.43 ) -.9 (.23 ) coastal.567 (.8 ).567 (.8 ) FPE -2.247 (.95 ) -2.247 (.96 ) restaurant -2.85 (.88 ) -2.85 (.89 ) sea -4.544 (.46 ) -4.544 (.47 ) slipway.28 (.77 ).28 (.77 ) vehicles 8
Table 4. GLM parameter/coefficient (and standard error) estimates for Super-areas 3+4+5+6. January.37 (.43 ).338 (.4 ).37 (.398 ).25 (.397 ) February.74 (.5 ).6 (.48 ).282 (.46 ).55 (.46 ) March.68 (.5 ).2 (.48 ).724 (.37 ).56 (.368 ) April.96 (.44 ).8 (.45 ).25 (.377 ).8 (.386 ) May.299 (.4 ).286 (.42 ) -.56 (.45 ) -.8 (.44 ) June.64 (.46 ).53 (.46 ) -3.25 (.45 ) -3.36 (.49 ) July.29 (.42 ).28 (.42 ) -3.6 (.4 ) -3.25 (.44 ) August.38 (.4 ).3 (.4 ) -2.86 (.85 ) -2.58 (.87 ) September.32 (.5 ).26 (.5 ) -.583 (.674 ) -.637 (.692 ) October.43 (.38 ).399 (.39 ) -2.4 (.834 ) -2.76 (.852 ) November.366 (.39 ).365 (.4 ) -.926 (.53 ) -.944 (.542 ) December Time (yr - ) -.2 (. ) -.8 (.5 ) 28 29 -.77 (.3 ) -.43 (.356 ) 2. (. ) 2.38 (.98 ) -.75 (.324 ) 22 -.4 (. ) -.282 (.399 ) 23 -.87 (.3 ) -.39 (.379 ) 24 -.26 (.4 ) -.796 (.335 ) 25 -.79 (.3 ) -.858 (.342 ) 26.2 (.67 ) -2.95 (.4 ) coastal.249 (.2 ).249 (.2 ) FPE -2.73 (.29 ) -2.73 (.3 ) restaurant -2.959 (.59 ) -2.959 (.59 ) sea -4.575 (.84 ) -4.575 (.84 ) slipway.39 (.22 ).39 (.22 ) vehicles 9
Table 5. GLM parameter/coefficient (and standard error) estimates for Super-areas 3+4+5+6+8+. January.34 (.2 ).276 (.9 ).46 (.363 ).58 (.37 ) February.88 (.23 ).63 (.22 ).654 (.326 ).569 (.333 ) March.46 (.25 ).24 (.24 ).29 (.357 ).37 (.364 ) April.34 (.22 ).8 (.23 ).549 (.325 ).526 (.335 ) May.222 (.2 ).99 (.2 ) -.52 (.37 ) -.73 (.38 ) June.77 (.2 ).57 (.22 ) -.37 (.55 ) -.54 (.52 ) July.289 (.8 ).273 (.9 ) -.896 (.77 ) -.9 (.733 ) August.284 (.8 ).27 (.9 ) -2.35 (.797 ) -2.47 (.88 ) September -.3 (.26 ) -.2 (.27 ) -.679 (.442 ) -.688 (.456 ) October.272 (.8 ).266 (.9 ) -.923 (.484 ) -.929 (.498 ) November.242 (.9 ).239 (.2 ) -.844 (.472 ) -.847 (.485 ) December Time (yr - ) -.3 (. ) -.3 (.3 ) 28.738 (.36 ) -.958 (.723 ) 29 -.8 (.96 ) -.448 (.336 ) 2 2.4 (.86 ) -.326 (.289 ) 22.34 (.88 ) -.22 (.363 ) 23 -. (.9 ) -.97 (.27 ) 24 -.5 (.92 ) -.4 (.295 ) 25 -.64 (.9 ) -.26 (.283 ) 26 -.47 (.48 ) -2.279 (.93 ) coastal.2 (.94 ).5 (.94 ) FPE -2.39 (.5 ) -2.43 (.5 ) restaurant -2.59 (.3 ) -2.596 (.3 ) sea -4.73 (.56 ) -4.743 (.57 ) slipway.245 (.94 ).24 (.94 ) vehicles
Table 6. Summary of change in poaching levels from 29 to 25 (and 95% confidence intervals) for the continuous log-linear model and the percentage change from average of 29 and 2 to the average of 25 and 26 for the poaching indices for the discrete year factor model. Area Continuous linear trend Discrete year factor Super-area 3+4-9.2% (-96.8%; -75.4%) -86.8% Super-area 5+6-55.3% (-83.3%; 9.6%) -6.5% Super-area8+ 7.% (24.3%; 487.%) 46.% Super-area 3+4+5+6-73.9% (-87.9%; -43.7%) -73.9% Super-area 3+4+5+6+8+ -3.3% (-42.%; 83.8%) -43.7%
.6.4.2.8.99...23.6..94..95.6.4.2 28 29 2 2 22 23 24 25 26 8 7 6 5 4 3 2 3. 2.7.57.49.52.49..67.3 28 29 2 2 22 23 24 25 26 3.5 3 3.9 2.5 2.5..28.59.86.5.53.49.58.32 28 29 2 2 22 23 24 25 26 Figure. effect (together with 95% confidence limits) for policing effort (top), the number of confiscations plus abandonments (middle) and the ratio of the number of confiscations plus abandonments to policing effort for Super-area 8+. 2
.6.4.2.8.84..4.96.83.8.84.2.6.4.2 28 29 2 2 22 23 24 25 26 2.5 2.5.96..5.2.49.28.32.45.42.5 28 29 2 2 22 23 24 25 26.4..8.6.4.2.48.29.39.55.5 28 29 2 2 22 23 24 25 26.5 Figure 2. effect (together with 95% confidence limits) for policing effort (top), the number of confiscations plus abandonments (middle) and the ratio of the number of confiscations plus abandonments to policing effort for Super-areas 3+4+5+6. 3
2.5 2 2.9.5.98...3.9.86.94.95.5 28 29 2 2 22 23 24 25 26.8.6.4.2.8.6.64..72.9.67.77.4.2.38.36. 28 29 2 2 22 23 24 25 26.2...8.78.82.6.65.65.4.2.35.8. 28 29 2 2 22 23 24 25 26 Figure 3. effect (together with 95% confidence limits) for policing effort (top), the number of confiscations plus abandonments (middle) and the ratio of the number of confiscations plus abandonments to policing effort for Super-areas 3+4+5+6+8+. 4
Area 3+4 2.5.5 28 29 2 2 22 23 24 25 26 Vehicles slipway coastal sea restaurant FPE Area 5+6 4 3.5 3 2.5 2.5.5 28 29 2 2 22 23 24 25 26 vehicles slipway coastal sea restaurant FPE Area 8+ 8 6 4 2 28 29 2 2 22 23 24 25 26 vehicles slipway coastal sea restaurant FPE Figure 4. The ratio of the number of confiscations plus abandonments to policing effort type for Super-areas 3+4, 5+6 and 8+. 5
Appendix : West Coast rock lobster confiscations and policing effort data by month and Superarea. NOTE: For reasons of confidentiality, the data in these tables have been excluded from this publically available version of this document. Table A.. (confiscations+abandonments) by month and Super-area. Table A.2. by vehicles inspected by month and Super-area. Table A.3. by slipway inspections by month and Super-area. Table A.4. by coastal patrols by month and Super-area. Table A.5. by sea patrols by month and Super-area. Table A.6. by restaurant inspections by month and Super-area. Table A.7. by sea FPE inspections by month and Super-area. 6