Figure 1.
Fraction of lifetime egg production (FLEP, i.e., per recruit egg production/natural per recruit egg production) ((a)) and harvest-per-recruit over maximum harvest-per-recruit (h/hmax) in function of harvest mortality over fishing mortality ((b)) when lifetime egg production is at 25% of its unfished value (f/f25) for the three species studied in the present study.
The dashed lines represent the harvest mortality above which the studied species collapse in the absence of reserves (i.e., the harvest mortality for which lifetime egg production is at 35% of its unfished value in the context of this paper).
Table 1.
Non-movement parameter estimates for the long-lived (canary rockfish - Sebastes pinniger), harvest-first (yellowfin tuna - Thunnus albacares) and spawn-first (skipjack tuna - Katsuwonus pelamis) species.
Figure 2.
Per recruit egg production as a function of harvest mortality rate for the long-lived species (red curve).
Immediately after reserve implementation, changing the fraction of habitat in reserves moves the average reproductive capacity on the blue line for a population with dispersing larvae and sedentary adults. For a population with adults moving within a home range and non-dispersing larvae, changing the fraction in reserves moves the reproductive capacity on the red curve. Consequently, when lifetime egg production is a decreasing, convex function of harvest mortality, adult movement leads to lower egg production immediately after reserve implementation than larval dispersal. Per recruit egg production functions are, respectively, more and less convex for the harvest-first and spawn-first species, but similar qualitative results are obtained for these species.
Figure 3.
Border between persistence and collapse in the adult movement case (black curves) versus the larval dispersal case (red curves) as a function of reserve width (in units of the dispersal distance or home-range size) and fraction of habitat in reserves.
In all cases, collapse occurs for very small reserves covering a small fraction of habitat (lower, left corner of panels). Harvest effort is uniformly distributed outside reserves. (a,d) are for the long-lived species, (b,e) for the harvest-first species and (c,f) for the spawn-first species. For (a,b,c), it is assumed that the effort that had previously been in the reserves disappears at the time of reserve creation, while for (d,e,f) it is assumed that the total effort does not change before and after reserve creation. Per recruit egg production is 25% of its unfished value in harvested areas, and three different values of the critical per recruit egg production below which collapse occurs in the absence of reserves are shown (27, 35 and 45% of the natural per recruit egg production).
Figure 4.
Minimum reserve width (in units of the dispersal distance or home-range size) required for persistence of an isolated reserve as a function of critical per recruit egg production and per recruit egg production in harvested areas for the long-lived species.
(a) is for larval dispersal alone, (b) is for adult movement alone, and (c) gives the ratio of these two quantities, with values greater than one indicating larger reserves are needed to ensure persistence for the larval dispersal case than for adult movement. Here harvest effort is assumed uniformly distributed outside reserves and the effort that had previously been in the reserves disappears at the time of reserve creation. Note that similar qualitative results are obtained for the harvest-first and spawn-first species.
Figure 5.
Equilibrium harvest as a function of reserve width (in units of the dispersal distance or home-range size) and fraction of habitat in reserves for the long-lived species.
Panels to the left are for populations with sedentary adults and dispersing larvae, while panels to the right are for populations with mobile adults and non-dispersing larvae. For (a,b,c,d), it is assumed that the effort that had previously been in the reserves disappears at the time of reserve creation, while for (e,f,g,h) it is assumed that the total effort does not change before and after reserve creation. For (a,b,e,f), harvest effort distribution is uniform outside reserves, while for (c,d,g,h), it depends on local expected harvests and the value of γ is 1.2. The light blue area represents reserve configurations leading to a collapsed population and for (b,c,d,e,f,g,h) the dash-dotted grey line represents the border between persistence and collapse when harvester behavior and effort redistribution after reserve creation are both ignored. Harvest values shown are relative to the maximum value for the adult movement case when harvester behavior and effort redistribution after reserve creation are ignored.
Figure 6.
Equilibrium harvest as a function of reserve width (in units of home-range size) and fraction of habitat in reserves for populations with mobile adults and non-dispersing larvae.
(a) is for the harvest-first species and (b) for the spawn-first species. Here it is assumed that the total effort does not change before and after reserve creation and that harvest effort distribution depends on local expected harvests, and the value of γ is 1.2. The light blue area represents reserve configurations leading to a collapsed population the grey line represents the border between persistence and collapse when harvester behavior and effort redistribution after reserve creation are both ignored. Harvest values shown are relative to the maximum value for the adult movement case when harvester behavior and effort redistribution after reserve creation are ignored.
Figure 7.
Spatial patterns of (a,b) recruitment, (c,d) real harvest mortality rate (f), and (e) effective harvest mortality rate (feff) for a system of periodically-spaced, uniformly-sized reserves (grey areas) at equilibrium for the long-lived species.
(a,c) are for populations possessing only larval dispersal, whereas (b,d,e) are for populations that only have adult movement in a home range. The effective mortality rate is not shown for the larval dispersal case as it is identical to the real harvest mortality rate. Harvest effort is uniform outside reserves for red curves. For the green and blue curves, the harvest effort distribution in the non-protected areas depends on local expected harvests, with the value of γ being 1.2 for green curves and 2.4 for blue curves. The units of recruitment are arbitrary, but consistent between simulations. The dashed black line on (c) and (d) represents the harvest mortality rate above which the population collapses in the absence of reserves.
Figure 8.
Border between persistence and collapse as a function of reserve width (in units of the ‘total movement scale’) and the fraction of habitat in reserves for the long-lived species.
The ‘total movement scale’ is the sum of the larval dispersal distance and the adult home-range size. Blue to red curves are for different fractions of the total movement scale in adult home-range movement, ranging from larval dispersal only (0) to adult home-range movement only (1). In all cases, harvest effort is uniform outside reserves. In (a), there is no harvest effort redistribution after reserve creation, whereas in (b) total harvest effort is conserved before and after reserve implementation. Per recruit egg production is 25% of its unfished value in harvested areas.