Ecological Applications, 16(1), 2006, pp. 213±224 q 2006 by the Ecological Society of America ELASTICITY ANALYSES OF SIZE-BASED RED AND WHITE ABALONE MATRIX MODELS: MANAGEMENT AND CONSERVATION LAURA ROGERS-BENNETT1,3 AND ROBERT T. L EAF2 1California Department of Fish and Game, University of California-Davis, Bodega Marine Laboratory, 2099 Westside Rd., Bodega Bay, California 94923-0247 USA 2Moss Landing Marine Laboratories, California State University, Moss Landing, California 95039-9647 USA Abstract. Prospective elasticity analyses have been used to aid in the management of ®shed species and the conservation of endangered species. Elasticities were examined for deterministic size-based matrix models of red abalone, Haliotis rufescens, and white ab- alone, H. sorenseni, to evaluate which size classes in¯uenced population growth (l) the most. In the red abalone matrix, growth transitions were determined from a tag recapture study and grouped into nine size classes. In the white abalone matrix, abalone growth was determined from a laboratory study and grouped into ®ve size classes. Survivorship was estimated from tag recapture data for red abalone using a Jolly-Seber model with size as a covariate and used for both red and white abalone. Reproduction estimates for both models used averages of the number of mature eggs produced by female red and white abalone in each size class from four-year reproduction studies. Population growth rate (l) was set to 1.0, and the ®rst-year survival (larval survival through to the ®rst size class) was estimated by iteration. Survival elasticities were higher than fecundity elasticities in both the red and white matrix models. The sizes classes with the greatest survival elasticities, and therefore the most in¯uence on population growth in the model, were the sublegal red abalone (150± 178 mm) and the largest white abalone size class (140±175 mm). For red abalone, the existing minimum legal size (178 mm) protects the size class the model suggests is critical to population growth. Implementation of education programs for novice divers coupled with renewed enforcement may serve to minimize incidental mortality of the critical size class. For white abalone, conservation efforts directed at restoring adults may have more of an impact on population growth than efforts focusing on juveniles. Our work is an example of how prospective elasticity analyses of size-structured matrix models can be used to quantitatively evaluate research priorities, ®shery management strategies, and con- servation options. Key words: deterministic matrix models; endangered species; growth transitions; marine con- servation; population growth; prospective elasticity analysis; sustainability. INTRODUCTION eggs in nests) toward the use of turtle exclusion devices Matrix models have been shown to be powerful tools in ®shing nets (reducing adult mortality) (Crouse et al. for addressing management and conservation issues 1987, Crowder et al. 1994, Heppell and Crowder 1996). (Crouse et al. 1987, Lande 1988, Heppell et al. 1994). Abalone are long-lived, slow-growing species with Quantitative vital rate information can be incorporated a poor track record for ®sheries sustainability world- into matrix models to explore the consequences of var- wide (Campbell 2000, Karpov et al. 2000, Shepherd et ious management and conservation options (Caswell al. 2001). Organisms with these life history traits may et al. 1998, Ebert 1999, Morris et al. 1999). Pertur- ®t into a suite of species that respond to perturbations bations of these models, by simulation, can systemat- in a predictable way with low fertility elasticities and ically compare which rates in¯uence the intrinsic rate high juvenile or adult survival elasticities (Heppell et of population growth the most (Benton and Grant 1999 al. 2000, Sñther and Bakke 2000, Gerber and Heppell and references therein). This type of ``forward look- 2004). To help guide management and conservation of ing'' or prospective sensitivity analysis (Caswell 2000) abalone populations it is important to examine the rel- has been used with far-reaching consequences. Pertur- ative importance of juvenile and adult elasticites. What bation analyses of loggerhead sea turtle matrix models we learn about the population dynamics of abalone may lead to a redirection of conservation efforts away from aid us in working with lesser known long-lived marine ``headstarting'' hatchlings (enhancing the survival of invertebrates which are being ®shed at an increasing pace in California (Rogers-Bennett 2001). Manuscript received 23 November 2004; revised 26 May Elasticity analysis can be used to support decisions 2005; accepted 23 June 2005. Corresponding Editor: P. K. Dayton. regarding the management of red abalone, Haliotis ru- 3 E-mail: [email protected] fescens (see Plate 1), and the conservation of the en- 213 214 LAURA ROGERS-BENNETT AND ROBERT T. LEAF Ecological Applications Vol. 16, No. 1 PLATE 1. Large red abalone are susceptible to multiple sources of mortality, including ®shing, predation, disease, wave dislodgement, and boring clams and sponges that compromise the integrity of the shell. Photo credit: L. Rogers-Bennett. dangered white abalone, H. sorenseni, in California. have been hindered by a lack of vital rate information The recreational red abalone ®shery in northern Cali- for red abalone in northern California. fornia is now the only abalone ®shery open in the state. Quantitative analyses of white abalone populations Recreational and commercial abalone ®sheries in are also lacking as little is known about their vital rates southern California have been closed since 1997 (Cal- (Hobday et al. 2001). White abalone are a deep-water ifornia Senate Bill 463). Failure to manage individual species and today only remnant populations exist at species masked serial depletion of the species complex depths below 40 m on remote offshore banks in south- by the ®shery (Dugan and Davis 1993, Karpov et al. ern California (Lafferty et al. 2004; J. Butler, personal 2000). Predatory sea otters also expanded their range communication). White abalone were highly prized by south toward Point Conception (Wendell 1994, Vogel the ®shery and, in just ®ve years (1971±1976), popu- 2000). In addition, the warm water regime in the 1980s lations were reduced to ,10% of their pre®shing bio- and 1990s may have been unfavorable for red abalone mass (Hobday et al. 2001, Rogers-Bennett et al. 2002). productivity (Hobday and Tegner 2002) as con®rmed The absence of evidence for successful recruitment in by the lack of juveniles signaling recruitment collapse areas which once produced .80% of the total ®shery in southern California (Rogers-Bennett et al. 2004a). landings has increased the concern for the recovery of In contrast, estimates of landings from the recreational white abalone (National Marine Fisheries Service, free-diving ®shery for red abalone in the north appear White Abalone Recovery Team, personal communi- to be stable (California Department of Fish and Game, cation). Quantitative evaluations are needed to aid the unpublished data). Concerns however, about the con- White Abalone Recovery Team (NOAA Fisheries) in tinued sustainability of the northern red abalone ®shery drafting a recovery plan that addresses restoration op- precipitated reductions in the daily and yearly bag lim- tions and potential threats (M. Neuman, personal com- its in 2001 leading the California Department of Fish munication). and Game Commission to decrease the total allowable We determined vital rate information for red and catch by an estimated 20%. To date, there have been white abalone to construct deterministic size-based ma- few quantitative evaluations of the ef®cacy of the cur- trix models (Lefkovitch 1965) for elasticity analyses rent size limits and the other management strategies in (Caswell 1978, de Kroon et al. 1986). We determined the ®shery (but see Tegner et al. 1989). Assessments which size classes of abalone had the greatest in¯uence February 2006 ABALONE MATRIX MODELS 215 FIG. 1. Map showing red abalone tag and recapture sites in northern California and white abalone reproduction site in southern California, USA. on the intrinsic rate of population increase in the mod- changes in vital rates changed population growth (Mor- els. For red abalone in northern California, we used ris and Doak 2003). demographic data from a large tag recapture study to METHODS generate growth transition probabilities and survival probabilities as well as a four-year reproduction study Red abalone mark and recapture ®eld study quantifying egg abundance to estimate size-speci®c fe- Red abalone were tagged at ®ve sites in northern cundities. For white abalone, we used growth data from California (Fig. 1). This tagging program was initiated a one-year laboratory growth experiment in conjunc- in 1971 and recaptures were conducted at approxi- tion with estimates of survival from a congener and a mately annual frequencies. Red abalone were collected four-year reproduction study (Tutschulte 1976). Since by divers, brought to the boat, measured for maximum survival in the plankton through to the ®rst year is shell length (SL), and tagged with individually labeled unknown for abalone (and many other invertebrates), stainless steel disc tags. Tags were attached with stain- we set population growth to 1.0 (dominant eigenvalue less wires inserted into the ®rst two open respiratory of the matrix) and solved for ®rst-year survival by it- pores and then twist tied. Red