J.C. Seijo Marist University of Merida. CLIFFMA Workshop Tromso, Norway November 27-28, 2012

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1 J.C. Seijo Marist University of Merida CLIFFMA Workshop Tromso, Norway November 27-28, 2012

2 From homogeneous to heterogeneous resource distribution S-G and B-H models are based on dynamic pool assumptions, which establish that: (i) (ii) (iii) (iv) the resource is homogeneously distributed in space; ages are perfectly mixed; and either fishing effort is applied uniformly over the range of resource distribution, or after fishing effort has been applied, the resource is able to redistribute itself according to (i) and (ii)..

3 Low mobility resources Not surprisingly, for sedentary and low mobility resources, models based on dynamic pool assumptions are inadequate and result in serious model error. Local habitats are unequal in quality and holding capacity throughout the stock range. The spatial distribution of these resources is patchy, in terms of size, density and age structure. As a result, fishing intensity is spatially heterogeneous. The principal consequence of this spatial heterogeneity is that under dynamic pool assumptions, the productive potential of the stock is overestimated, increasing the risk of over-exploitation and collapse of the fishery (Seijo and Caddy, 2008).

4 Two spatial situations Two situations are explored in this presentation: (i) (i) a spatially distributed population of a single stock. fisheries of metapopulations where sources are distinguished from sinks.

5 Procedure Recruit individuals in patches Calculate age specific biomass over space and time. Once spatial resource dynamics built in, we can then represent: i. the spatial behavior of fishers in response to heterogeneous resource abundance in space and time and, ii. the corresponding operating costs and revenues of fishing in alternative sites when departing from a specific port.

6 Spatial distribution of fishing intensity over time With the quasi-rent of the variable costs over space and time, the spatial distribution of fishing intensity can be calculated.

7 Recruitment over space The negative binomial distribution (e.g. Elliot 1977, Welch and Ishida 1993, Seijo et al. 2004) can be used to represent spatial heterogeneity in recruitment densities as follows: ( d 1)! P ( d) (1 ) ( ) d!( 1)! d (10.1)

8 Recruitment For a given maximum number of annual recruits, the number of individuals settling at geographic coordinates of site s in year t, is estimated by the following equation: SSBs, t s Rs, t P( s, d) SSB s s, t (10.2)

9 Recruits over space C25 C23 C21 C19 C17 C15 C13 Latitude C11 C9 C7 Recruits Longitude C5 C3 25 C

10 Population over space Population over space m,n: matrices of individuals age 1 to maximum age. m,n n 1 N i,11 N i,12 N i,13 N i,1n 2 N i,21 N i,22 N i,23 N i,2n 3 N i,31 N i,32 N i,33 N i,3n m N i,m1 N i,m2 N i,m3 N i,mn

11 Biomass over space m,n n 1 X i,11 X i,12 X i,13 X i,1n 2 X i,21 X i,22 X i,23 X i,2n 3 X i,31 X i,32 X i,33 X i,3n m X i,m1 X i,m2 X i,m3 X i,mn

12 Distance from ports to fishing sites To estimate distance from fishing port to alternative sites, each cell is specified a width and length. The distance to fishing sites from alternative locations of fishing port are estimated using the following equation. Ds ( LC( y m)) 2 ( WC( z n)) 2 (10.8) Where, LC = length of cell WC = width of cell m = 1,2,3,,RG and RG = rows of grid n = 1,2,3,,CG and CG = columns of grid y = RG/2 and z = CG/2

13 Distance from port

14 Spatial behavior of fishers Some spatial fisher behavior strategies documented in the literature include the following: Proportional distribution according to the spatial abundance of the resource (Caddy, 1975). Sequential distribution to those patches of greatest abundance (Hilborn and Walters, 1987). Random search (Hilborn and Walters, 1992). Free distribution of fishing intensity (Gillis et al., 1993) Proportional distribution to (Seijo et al. 1994, 1998): The quasi-rent of the variable costs (including transfer costs of traveling from port to alternative fishing sites). The friction of distance, i.e. non-monetary costs associated to vessel distance traveled to fishing sites. The probability of finding the target species in profitable levels at alternative sites.

15 Spatial behavior of fishing intensity In this presentation, the spatial behavior of fishing intensity (effort per unit area) over time, E st, is obtained by the following equation: E s, t1 quasi s s, t quasi s, t V t1 fd

16 Where fd are the average number of fishing days per vessel per year and, quasi are the quasi-profits of the s, t variable costs of a vessel from port A fishing in site s, calculated as follows: quasi ( py C E s, t st st st )

17 Variable costs per day of vessels fishing in site s over time (C st ), are estimated by (Anderson and Seijo, 2010): L c v D L c v D C s s st ) ] [ ] ([ 2 1

18 Where: D s = round trip distance between port of origin and fishing site s (km). = steaming speed of vessels (km/day). c 1 = cost per day of operating a vessel when steaming ($/day). c 2 = cost per day of operating a vessel when fishing ($/day). L= average length of trip (days).

19 Costs of steaming and fishing From equation we have two variable costs associated to the spatial behavior of fishing intensity: the costs of steaming to the fishing site: D s [ ] c v 1 and the cost of fishing: Ds [ L ] c v 2

20 Spatial behavior of fishing intensity over time m,n n m,n n 1 q i,11 q i,12 q i,13 q i,1n 2 q i,21 q i,22 q i,23 qi,2n 3 q i,31 q i,32 q i,33 qi,3n m q i,m1 q i,m2 q i,m3 q i,mn 1 E i,11 E i,12 E i,13 E i,1n 2 E i,21 E i,22 E i,23 E i,2n 3 E i,31 E i,32 E i,33 E i,3n m E i,m1 E i,m2 E i,m3 E i,mn (a) Quasi rent of variable (b) Fishing intensity over costs in time t. space in time t+1.

21 Number vessels over time The number of vessels over time active in the fishery (V t ) is calculated by numerically integrating (using Euler numerical integration with DT= 1) the spatially adapted Vernon Smith (1969) function, as follows: V t1 V t [ ( p Y C st ) FC V s st t ]

22 Yield over space and time Yield from site s, in time period t, is given by the spatially-specified age-specific catch equation: Y st i X ist ( F ist F ist M (1 e ( ( F ist M )) ))

23 Bioeconomic performance variables over space and time

24 Profits (000' US$) Y (ton) X (ton) Bioeconomic variables over time Bioeconomic variables over space Time (years) Port Longitude C25 C23 C21 C19 C17 C15 C13 C11 C9 C7 C5 C3 C1 Latitude Biomass (ton) Time (years) Port Time (years) Port Longitude C25 C23 C21 C19 C17 C15 C13 C11 C9 C7 C5 C3 25 C1 Latitude Profits ($)

25 A spatial management question Where to locate an MPA to manage a fishery targeting a sedentary species?

26 Spatial management: MPA near port C25 C23 C21 C19 C17 Port MPA C15 C13 Latitude C11 C9 C7 Effort (days at sea) C C Longitude 25 C

27 Spatial management: MPA far from port C25 C23 C21 MPA C19 C17 Port C15 C13 Latitude C11 C9 C7 Effort (days at sea) C C Longitude 25 C

28 X (ton) X (ton) Effect of a MPA and its location under open access OA & MPA near port OA & MPA away from port OA without MPA OA & MPA near port OA & MPA away from port OA without MPA Time (years) Effort (000 fishing days)

29 An additional question What is the bioeconomic effect of port location when managing a metapopulation with a source-sink configuration changing with climate?

30 Metapopulations with s-s configurations A metapopulation is a set of local populations connected among them by a large number of individuals migrating in different stages of the life cycle. For metapopulations with a source sink configuration, in addition to the size of the MPA, its location is mainly relevant with respect to source areas and position of fishing ports.

31 Some contributions Sumaila (1998) determined the bioeconomically optimal size of a marine reserve for Barents Sea cod fishery as a function of transfer rates between protected and unprotected areas, Sanchirico and Wilen (2001) developed a biomass dynamic model for exploited metapopulations to explore impacts of biological and economic factors on the evolution of exploitation patterns over space and time. Anderson (2002) used a biomass dynamic approach for a two-patch stock to derive spatial bioeconomic equilibrium conditions with alternative migration assumptions. Hannesson (2008) three stock migration model.

32 Contributions Beattie et al. (2002) applied game theory within a spatial biomass dynamic model to evaluate the efficiency of marine protected areas in the North Sea both in ecological and economic terms. Models have also been applied to site selection for MPAs (Crowder et al. 2000).

33 Changing source areas with climate change

34 Simulation experiment 1

35 Spatial distribution of resource biomass Latitude N Biomass (ton) Longitude W

36 Biomass (ton) LE & M P A in so urce area LE & M P A in sink area OA & M P A in so urce area OA & M P A in sink area Time (years)

37 Some findings Location of inshore ports close to an unprotected source area is a recipe for stock collapse Closing at least half the source area to fishing, substantially mitigates the effect of port location and improves all performance variables, regardless of port location. MPA s established outside a source area may even accentuate the risk of stock collapse if fishing intensity is diverted to the open access source area. Even with effort control, fishing intensity (effort per unit of area) is increased when closing an area.

38 Some additional questions How are costs and benefits distributed in shared stock fisheries of metapopulations with source sink configurations? Can positive externalities of responsible management of transboundary metapopulations with s-s configurations be internalized through cooperation? What is the spatial bioeconomic effect of ocean acidification on bivalve molluscs and gastropods?

39 Gracias

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