Biological component

Tiger and endeavour prawn dynamics

The bio-economic model includes explicit population dynamics of grooved and brown tiger and blue endeavour prawns based on a multi-species weekly time-step, sex-structured population model as described in chapter 4. Abundance dynamics of grooved (s= 1) and brown (s=2) tiger prawns are based on size-structured models and the dynamics of blue endeavour prawn (s= 3) is based on an aggregated population model as expressed by:

           ~ Ns(t+1)= f t, ~Ns(t), ~Fs(t) , s=1,2 N3(t+1)=g t,N3(t),F3(t) . (5.1)

whereN~s(t) is the vector of abundance Ns,x,l(t) of prawns of species s = 1,2 of sex x(with x = ♂

for male and_♀for female) in size-classl(1-mm size-classes between lengths of 15 to 55 mm) alive at the start of timetwhich corresponds to one time step (i.e. one week), and N3,x(t) is the abundance

of blue endeavour prawn of sexxat timet. F~s(t) is the vector of fishing mortalityFs,l(t) of animals

of speciess= 1,2 and size-classl, andF3(t) the fishing mortality of blue endeavour prawn at time

and g accounts for the species recruitment and mortality mechanisms as detailed respectively in sections 4.5.1 and 4.2.1 of chapter 4.

Recruits are assumed to be related to the spawning stock size index Ss for species s = 1,2,3

according to a Ricker stock-recruitment relationship fitted assuming temporally correlated environ- mental variability and down-weighting recruitments, as described in chapter 4 section 4.5.2.

The annual spawning stock size indices of the grooved and brown tiger and blue endeavour prawns for the yeary(t) are given by:

Ss y(t)= 1 52 52y(t) X t=52 y(t)−1+1 βs(t) X l γs,l 1−exp −Zs,l(t) Zs,l(t) Ns,♀,l(t), s=1,2. (5.2) S3 y(t)= 1 52 52y(t) X t=52 y(t)−1+1 β3(t)1−exp (−Z3(t)) Z3(t) N3,♀(t). (5.3)

wherey(t) is the year corresponding to the timet,βs(t) measures the relative amount of spawn-

ing of species sduring the timet, andγs,l corresponds to the proportion of females of species sin

size-classlthat are mature. Zs,l(t) is the total mortality on animals of speciessin size-classlduring

timetand is defined by:

Zs,l(t)= Ms+Fs,l(t). (5.4)

withMsthe natural mortality of animals of speciess.

White banana prawn: an uncertain resource

Abundance of white banana prawns (species s = 4) appears to be more heavily influenced by the environment than by fishing pressure (Die and Ellis, 1999;Venables et al., 2011) and its year to year availability is highly variable. More specifically, stocks are strongly influenced by weather patterns, generally peaking in years in which there has been high rainfall. In the present study, white banana prawn annual biomass is modelled as a uniform i.i.d. random variable:

B4 y(t);U(B−4,B+4), (5.5)

withB4 y(t)the stochastic biomass of white banana prawn for the yeary(t), andB−₄ andB+₄ the uniform law bounds given in appendix 4.6 of chapter 4.

5.2. Material and Methods S. Gourguet

Sea snakes: impacted species

Assessing the performance of the NPF also requires that its impacts on marine biodiversity be considered. Dichmont et al. (2008) studied the effects of trawling in the NPF on benthic com- munities using a benthic impact model. The spatially explicit model estimates the primary effects of repeated trawling on the biomass of benthic organisms, but is focused on the tiger prawn sub- fishery. Their study demonstrates that effects of trawling on benthos are dependent on the aggre- gation of effort, suggesting that global effects are very small compared to local effects. Thus, the effects of trawling on benthos communities would only adequately capture the biodiversity impacts of trawling in a spatial analysis.

NPF operations also interact with several groups of threatened, endangered and protected (TEP) species including sea snakes, turtles, elasmobranchs (as sawfishes, sharks and ray), syngnathids (seahorses and pipe fishes) (AFMA, 2012). Interactions with these TEP species are required to be recorded on catch and effort logsheets and by crew member observers (CMO) and scientific observers. Reported interactions with sea snakes are generally an order of magnitude higher than reported interactions with other species (e.g., 4.1 sea snake interactions per day versus 0.056 turtle, 0.021 syngnathid and 0.6 sawfish interactions per day as reported by scientific observers during the tiger prawn season in 2010; c.f.Barwick,2011). Many of these species are already managed under various plans of action (Recovery Plan for Marine Turtles in Australia, National Plan of Action and Conservation and Management of Sharks, and National Recovery Plan for Whales Sharks). Furthermore, the amount of by-catch species caught in prawn trawl nets has been significantly reduced since 2000 through the mandatory introduction of Turtle Excluder Devices (TEDs) and By-catch Reduction Devices (BRDs). Nets with TEDs are particularly effective at reducing catches of larger animals such as turtles (by 99%), large rays and sharks (>1m wide and long, by 94% and 86%, respectively); in contrast, BRDs are more effective at excluding small fishes (Brewer et al., 2006). However, Brewer et al. (2006) estimate that nets with a combination of a TED and BRD reduced the catches of sea snakes (Hydrophiidae) by only 5%.

Sea snake catches appear to be significantly correlated to fishing effort in the fishery. Although the tiger and banana prawn sub-fisheries both use gear that can be broadly classified as demersal otter trawls, the method of gear deployment varies. In the tiger prawn sub-fishery, the trawl is

generally lowered over suitable prawn habitat to fish as close as possible to the seabed, and is towed for three to four hours. In contrast, in the banana prawn sub-fishery the trawl gear is deployed for less than an hour on a prawn aggregation (or ‘boil’) in the water column identified using an echo sounder (Griffiths et al., 2007). The amount of by-catch thus varies by sub-fishery, making it important to consider their effects separately.

Linear regressions, between historical sea snake catches Ysnake,f(y(t)) by sub-fishery f = 1+2,3

(with f = 1+2 corresponding to the tiger prawn sub-fishery and f = 3 to the banana prawn sub- fishery) and the associated annual fishing effort Ef(y(t)), are displayed in appendix B (figure 5.6).

Table 5.1 displays the statistics of these regressions.

Table 5.1: Statistics of the linear regression between annual sea snake catches by tiger and banana prawn sub-fisheries and annual effort associated (intercept at 0).

sub-fishery

tiger (f =1+2) banana (f =3)

Adjusted R Square 0.785 0.778

Residual Varianceσ2_f 938.98 274.25

P-value 8.843.10−6 _{2.687. 10}−5

Coefficient valuesareg_f 1.1883 0.5235

Estimation of total annual sea snake catches Ysnake,f(y(t)) from tiger and banana prawn sub-

fisheries are calculated separately:            Ysnake,1+2(y(t))=a reg 1+2E1+2 y(t) +ξ 1+2 y(t), Ysnake,3(y(t))=a reg 3 E3 y(t) +ξ 3 y(t). (5.6) with            ξ1+2 y(t) ;N(0, σ2₁₊₂), ξ3 y(t);N(0, σ2₃). (5.7)

where E1+2 y(t)and E3 y(t)are respectively the annual effort of tiger and banana prawn sub- fisheries during the yeary(t). areg₁₊₂andareg₃ are the coefficient values from the linear regressions by sub-fishery f =1+2,3 given in table 5.1.ξ1+2 y(t)andξ3 y(t)are the residual terms for the year

y(t) and are assumed to be independent normally distributed random variables with mean equal to zero and varianceσ₁₊₂andσ3, respectively.

5.2. Material and Methods S. Gourguet

Economic component

The economic component of the model estimates the flow of costs and revenues from fishing over time.

Gross income for grooved (f = 1) and brown (f = 2) tiger prawn fishing strategies are calcu- lated from catches of tiger and blue endeavour prawns (s = 1,2,3) and gross income for banana prawn sub-fishery (f = 3) from catches of white banana prawn (s = 4), as described in chapter 4 section 4.2.3.

Total annual profit of the whole fisheryπ y(t)

for yeary(t) is then expressed by: π y(t)= 3 X f=1 52y(t) X t=52 y(t)−1+1 Incf t,Ef(t)−cvarf Ef(t) −cvf ixK y(t) . (5.8)

where Incf t,Ef(t) is the annual gross income of fishing strategy f for the timetand related

to Ef(t), the fishing effort (expressed in days at sea) of the fishing strategy f during time t, cvar_f

corresponds to the variable cost for one unit of fishing effort of fishing strategy f, and cvf ix is the

annual fixed cost by vessel. Details on costs are given in section 4.2.3 in the chapter 4. K y(t) is the number of vessels involved in the NPF during the yeary(t).

The net present value (NPV) of the flow of profits over the simulation time is calculated as in Punt et al.(2010): NPV= T−1 X y(t)=1 π y(t) (1+δ)y(t)−1 + [π(T)/δ] (1+δ)T−1. (5.9)

whereδis the discount rate andπ(T) is the level of profit during the terminal year of the simulation.

Major components and interactions that characterise the NPF and described earlier are repre- sented in figure 5.1. This figure displays also the fact that weekly effort of tiger and banana prawn sub-fisheries are dependent, as explained in chapter 4 section 4.2.5.

Figure 5.1: Stylized representation of the Northern Prawn Fishery used as a basis to develop the bio- economic model. The width of the arrows between the fishing strategies and prawn species are proportional to the proportion of catch by species by fishing strategies (grooved and brown tiger prawn and banana prawn sub-fisheries) compared to the total catch of the fishery in 2010. The width of the blue arrows towards the sea snake species are proportional to the sea snake catches by tiger and banana prawn sub-fisheries in 2010. The dashed arrow between tiger and banana prawn sub-fisheries illustrates the influence of the banana prawn season on the tiger prawn effort.