Dependence of settlement rate on suitable substrate area

Several recent ®eld studies have found disproportionately high barnacle settlement rates (expressed on a per-area basis) in situations where the amount of suitable substrate is reduced, either due to occupation by other individuals or to physical processes. We call this phenomenon the intensi®cation e€ect; it is not included in many models of benthic populations, which assume that the per-area settlement rate is a constant, or in ®eld larval-collector studies, where number of larvae caught is assumed to be a function only of larval supply. In this paper we derive a simple Markov chain model that generates the intensi®cation e€ect. It describes the fate of a settling larva, which may be washed out of the system or may attempt to settle in suitable or unsuitable substrate. If it lands on unsuitable substrate, it returns to the water column to try again. At low values of the washout rate, the per-area settlement rate decreases with increasing substrate area. At high values of the washout rate, per-area settlement rate is constant. We conducted a set of laboratory experiments in March through April 1995 with barnacle larvae (Semibalanus balanoides Linnaeus) to illustrate the predictions of the model. Substrate area was manipulated by varying the number of settling panels available, and the larval loss rate was adjusted by manipulating the residence time of larvae in the experimental units (1.5 h or 12 h). As predicted by the model, in the 12-h treatment settlement per area decreased nonlinearly as the amount of substrate increased, whereas in the 1.5-h treatment no di€erences were found. These results explain and predict the intensi®cation e€ect, and suggest that variability in the proportion of suitable substrate may be an important factor in determining variability in settlement rate. Introduction The larval phase of marine species critically in ̄uences such population phenomena as age-class strength (Hjort 1926), population ̄uctuations correlated with life history (Thorson 1950; Coe 1956), and uncorrelated densities of recruits and adults (Loosano€ 1964). Settlement and recruitment estimates have been used to compare larval input from the plankton, in spatial data or temporal series. Studies of ̄uctuations in settlement have focused on biological and physical factors in ̄uencing the settling larva. For example, Connell (1985) recognized three factors in ̄uencing invertebrate settlement rate: the number of propagules arriving, the site-speci®c hydrodynamic conditions, and behavioral factors. The resident assemblage of species can also in ̄uence settlement (e.g. Strathmann et al. 1981; Young 1988; Osman et al. 1989; Osman and Whitlatch 1995). Larvae of sessile species in hard-surface communities require space to settle. Their impact on population dynamics will depend on how settlement is a€ected by availability of free space. Many studies of barnacle settlement have documented the in ̄uence of substrate characteristics on the choice of alternative substrates and settlement [presumably related to behavior of the cyprid stage; Pye®nch (1948); Connell (1961); LeTourneaux and Bourget (1988)]. We are not concerned here with these di€erences, but with the e€ect of the amount of suitable substrate, de®ned here as free space upon which larvae will settle. Few studies have examined this e€ect; those that have, draw di€ering conclusions. Gaines and Roughgarden (1985), Navarrete and Castilla (1990), and Minchinton and Scheibling (1993) observed in the ®eld that settlement was proportional to suitable substrate: the more substrate, the more total settlement. Other ®eld studies suggest, however, that as suitable substrate becomes scarce, settlement per unit area intensi®es. Bertness et al. (1992) found that the settlement per unit area of Semibalanus balanoides increased late in the season, Marine Biology (1997) 129: 541±548 Ó Springer-Verlag 1997 Communicated by J.P. Grassle, New Brunswick J. Pineda (&) á H. Caswell Biology Department, Woods Hole Oceanographic Institution, Woods Hole, Massachusetts 02543, USA E-mail: [email protected] apparently as a result of favorable sites being ®lled by settlers early in the season. Pineda (1994b) found that settlement per unit area of the barnacles, Chthamalus spp., was consistently higher at the edges of a rocky shore, where suitable settlement area was scarce, than at the middle of the rocky beach, where suitable substrate was abundant, suggesting higher settlement per unit area in areas with less suitable substrate. At another rocky shore, some areas of the intertidal zone were seasonally inundated by sand, an unsuitable substrate for barnacle settlement. Areas with more sand ± less suitable substrate ± received predictably higher settlement per unit area than areas not invaded by sand. This ranking disappeared when the sand was not present, suggesting that the ranking was maintained by di€erences in the amount of suitable substrate. These observations resulted in the development of the ``decreased-substrate settlement-intensi®cation hypothesis'' (Pineda 1994b) according to which the per-area settlement rate is a decreasing function of available substrate. Hunt and Scheibling (1996) observed enhanced mussel settlement in settlement collectors relative to ice-scoured emergent rocks, and suggested that settlement intensi®cation could be related to unsuitability of ice-scoured surfaces. Osman and Whitlatch (1995) compared settlement panels with high, low, and no adult cover. They observed that settlement density of several sessile taxa was often higher in treatments with the highest density of adults, and suggested that settlement could be intensi®ed in these panels due to larvae rejecting adults as substrate, and then swimming a short distance to settle on open substrates; this would result in a settlement intensi®cation e€ect. They created a model incorporating larval discrimination, probability of settlement on adults, on free substratum, and probability of larvae being removed from the substratum. Their model predicts that the pattern of intensi®cation is determined ``by the mobility of the larvae that fail to attach''. Settlement rate can be measured in various ways (Table 1), and for the present study we are careful to specify which rates we are talking about. These are made clear in the population models of Roughgarden et al. (1985) and Roughgarden and Iwasa (1986), which identify an important set of hypotheses about the relationship between settlement and suitable substrate (free space, in their notation). Let B(t), L(t), and F(t) be the numbers of adults, larvae, and the suitable substrate within the region under consideration. Then