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Department of Oceanography, Dalhousie University, Halifax, Nova Scotia B3H 4J1, Canada
* To whom correspondence should be addressed. E-mail: metaxas{at}dal.ca
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 TOP Abstract IntroductionParameterizationModel ValidationConclusionsLiterature cited |
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Abbreviations: PLD, planktonic larval duration
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Introduction |
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TOPAbstractIntroductionParameterizationModel ValidationConclusionsLiterature cited |
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Larval horizontal transport has been conventionally attributed to advection along the dominant direction of flow; recently, however, larval behavior (i.e., directional swimming in response to a cue) has emerged as a potentially significant factor influencing horizontal dispersal (Metaxas, 2001; Kingsford et al., 2002; Levin, 2006). For benthic invertebrates, adjustments in larval vertical position are possible because larval vertical swimming speeds are on the same order of magnitude as vertical flow speeds. In turn, these vertical adjustments can move larvae across water layers with different flow velocities, modifying larval direction and speed of transport. Measurements of the effect (and, consequently, relative importance) of larval behavior on larval transport are in their infancy.
Because of inherent difficulties in measuring larval dispersal in the field, biophysical models are increasingly being used to both quantify larval transport and assess its role in regulating population connectivity (e.g., Siegel et al., 2003; Aiken et al., 2007). These models can be either general circulation models (e.g., the Regional Ocean Modeling System) with particle-tracking subroutines (Baums et al., 2006; Edwards et al., 2007; Paris et al., 2007; Pfeiffer-Herbert et al., 2007; North et al., 2008) or simpler advection-diffusion models (Hill, 1990; Dekshenieks et al., 1996; Cowen et al., 2000; Gaylord and Gaines, 2000), and typically incorporate both physical and biological parameters. The physical parameters most frequently include mean velocity components and their variance, the circulation being driven by winds, tides, or density structure of the water column (Hare et al., 1999; Siegel et al., 2003; Aiken et al., 2007; Edwards et al., 2007). To date, the biological parameters have included planktonic larval duration (PLD; Siegel et al., 2003; Aiken et al., 2007; Edwards et al., 2007); diel and ontogenetic vertical migration—as differences in larval vertical position in response to light or related to larval age, respectively (Paris and Cowen, 2004; Pfeiffer-Herbert et al., 2007; Edwards et al., 2007); and timing of larval release (Baums et al., 2006; Edwards et al., 2007; Mitarai et al., 2008). In most instances, larvae are modeled as passive (non-swimming) particles (Siegel et al., 2003; Aiken et al., 2007). However, a few modeling studies have incorporated slightly more complex biological parameters, such as larval developmental rate given temperature and chorophyll regimes (Dekshenieks et al., 1996; Pfeiffer-Herbert et al., 2007), and larval swimming velocity (Dekshenieks et al., 1996) and depth distribution (North et al., 2008) in response to a salinity gradient.
The response variable of biophysical models is a dispersal kernel after a predetermined period of larval development (James et al., 2002; Baums et al., 2006; Aiken et al., 2007). It is estimated as the frequency distribution of settling larvae (number of propagules per unit area) at a series of settlement sites (or distances from the larval release site) normalized to the number of larvae produced at a release site (Siegel et al., 2003; Edwards et al., 2007). Other response variables include larval horizontal (Paris et al., 2005; Edwards et al., 2007; North et al., 2008) and vertical (Dekshenieks et al., 1996) distributions; larval trajectories, or "dispersal paths," (Baums et al., 2006; Pfeiffer-Herbert et al., 2007); mean dispersal distance (Edwards et al., 2007; North et al., 2008); and abundance of adults (Gaylord and Gaines, 2000).
The extent of validation of model predictions varies among studies. In most instances, models are used only to provide theoretical outcomes that quantify the effect of different factors (e.g., length of PLD, different flow scenarios, timing and location of larval release, larval behavior) on dispersal trajectories or dispersal kernels (e.g., Hill, 1990; James et al., 2002; Siegel et al., 2003; Aiken et al., 2007; Fiksen et al., 2007; North et al., 2008), and, consequently, are not validated. Alternatively, models have been validated by comparing predicted spatial patterns in dispersal destinations with spatial patterns in recruitment (e.g., Incze and Naimie, 2000; Pfeiffer-Herbert et al., 2007).
The predictive performance of biophysical models is constrained by two factors. First, the parameterization, and resolution, of the different components of the models can only be as accurate as our estimates of the parameters in the field. Second, validation of model outcomes must be done for the appropriate life-history stages. In this review, we discuss these two constraints. With respect to model parameterization, we address three biological parameters: larval growth rate, and by extension PLD; larval mortality rate; and larval behavior in response to cues in the water column during dispersal and on the benthos during settlement. For each parameter, we provide an overview of current knowledge, discuss its potential effect on the prediction of larval transport, and make suggestions on approaches for its parameterization. We also provide a perspective on suggested approaches to model validation.
Although biophysical models have been used to quantify larval transport in both benthic invertebrates and fish, we have focused our review on the former, and provide only a few key examples for the latter. A number of recent reviews have evaluated the utility and applicability of these models either mainly or exclusively for larval fish (e.g., Werner et al., 2001, 2007; Fiksen et al., 2007; Leis, 2007), but ours is the first comprehensive treatment for larval benthic invertebrates. In many instances, models have represented "larvae" as passive particles that could fall under any taxon; however, it is the taxon-specific behaviors that may generate differences in model performance between taxa. By limiting this review to benthic invertebrates, we attempt to describe these behaviors in detail for this group. Although similar processes operate on the two taxa, the scales over which a particular process becomes relevant may differ between larval fish and benthic invertebrates (Bradbury and Snelgrove, 2001). In particular, the stronger swimming ability of larval fish allows for greater potential dispersal distances (Gaines et al., 2007), but also a higher probability of retention or of a successful response to a cue, than for benthic invertebrates (Cowen and Sponaugle, 2009). A relatively small number of studies (tens) have used biophysical models to quantify larval transport in marine benthic invertebrates; however, the majority has been published in the last 5 years, suggesting that the use of the approach is accelerating and making our review very timely.
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Parameterization |
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TOPAbstractIntroductionParameterizationModel ValidationConclusionsLiterature cited |
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Several environmental factors can affect larval growth rates, but temperature is the most important; warmer temperatures result in faster growth rates and shorter development times (Hart and Scheibling, 1988; Hoegh-Guldberg and Pearse, 1995). However, at temperatures much warmer than typically experienced in the field, development and survival are reduced (e.g., Chen and Chen, 1992). In a modeling study, Reitzel et al. (2004) demonstrated that the shape of the functional relationship with temperature could have significant implications for the development times of marine invertebrates, depending on the timing of spawning. O’Connor et al. (2007) determined that the functional relationship between PLD and temperature was the same for 72 species of invertebrate and fish. Variations among species existed in the magnitude of PLD at a given temperature, but not in the relationship between PLD and temperature, which was mainly influenced by developmental mode (lecitrophic vs. planktotrophic), size, and geographic region (global scale) (O’Connor et al., 2007). In the laboratory, larval growth rate and development time are measured at a range of fixed temperatures, and most studies use mean temperature to predict larval development period. However, for ectothermic organisms, the thermal integral, or growing-degree-day (GDD), is a much better predictor of growth than is mean temperature (Neuheimer and Taggart, 2007) because it incorporates the variability in temperature, as well as the thermal history the organism experienced in the past. Thermal time has been used extensively to predict growth in insects and plants (Trudgill et al., 2005), and recently, size-at-age of fish (Neuheimer and Taggart, 2007) and settlement in marine invertebrates (Saunders and Metaxas, 2007). The metric is particularly relevant for the accurate prediction of development time of larvae in the water column, where they can spend up to several weeks experiencing fluctuating temperatures. For example, the size-at-age of a larval species could be determined using either a number of relationships at different temperatures or a single relationship for GDD (see Neuheimer and Taggart, 2007, for examples using fish).
Food availability can limit development (Lucas, 1982; Paulay et al., 1985; Olson and Olson, 1989) of planktotrophic larvae, but its effect is considered less important than that of temperature (Hoegh-Guldberg and Pearse, 1995). Larval natural diets are presumably quite diverse and may include bacteria, microalgae, and possibly dissolved organic matter (Boidron-Métairon, 1995). Consequently, larvae may be able to avoid food limitation by taking advantage of patches of different types of food (Boidron-Métairon, 1995; Metaxas and Young, 1998a). The combined effects of temperature and food availability on larval development can have a significant impact on transport distances and connectivity, since longer development time can result in longer dispersal distances (Shanks et al., 2003). If PLD is strongly dependent on food, the patchiness of food in the field will need to be resolved (e.g., Pepin et al., 2003, for fish).
Larvae must be competent to settle before they can move from the pelagic to the benthic habitat. For some invertebrate species, including corals (Wilson and Harrison, 1998), asteroids (Hoegh-Guldberg and Pearse, 1995), and molluscs (Pechenik and Lima, 1984; Coon et al., 1990), larvae can prolong the period of settlement competence for days or weeks. The ability to maintain competence for a period of time increases the probability that larvae will encounter appropriate settlement substrata. However, larvae that delay settlement will have an increased probability of planktonic mortality and may have reduced post-settlement growth or survival (Pechenik et al., 1993; Maldonado and Young, 1999). Delayed competence is more prevalent among invertebrates than among fish, probably because, in contrast to fish, most adult invertebrates have limited or no ability to move to preferable habitat (Bradbury and Snelgrove, 2001). For some species (e.g., gastropods; Pechenik and Lima, 1984), the ability to delay settlement after competence is related to temperature, with a longer delay being associated with slower growth rates in colder temperatures. If warmer temperatures cause both shorter larval durations (thus, shorter dispersal distance) and shorter periods of delayed competence (thus, lower probability of encountering suitable settlement substrate), increases in temperature can have significant impacts on larval transport.
In biophysical models, PLD usually ranges from a few days to weeks and is parameterized to broadly reflect development periods from the literature (e.g., Siegel et al., 2003; Ellien et al., 2004; Paris and Cowen, 2004; Aiken et al., 2007). To our knowledge, PLDs longer than 100 days have not been included in any models, even though they are common for many species (Shanks and Eckert, 2005; Graham et al., 2008). In a few studies, functions describing growth and development in terms of the temperature or food regime encountered during dispersal have been included in models of larval lobsters, oysters, and barnacles (Incze and Naimie, 2000; Dekshenieks et al., 1996, 1997; Pfeiffer-Herbert et al., 2007). These functions were based on laboratory experiments and on the temperature or phytoplankton concentration corresponding to each time step of the model. Coupled bio-physical models of invertebrate larval transport that incorporate rate-dependent processes, such as stage development, ingestion, and excretion, are less developed for benthic invertebrates than for fish (Daewel et al., 2008) and copepods (e.g., Lynch et al., 1998; Tittensor et al., 2003). While Nutrients-Phytoplankton-Zooplankton-Detritus (NPZD) models have been coupled to physical models (e.g., Franks and Chen, 2001), they do not typically incorporate or examine the transport of individual larvae (but see Daewel et al., 2008).
Judging from the outcomes of the few biophysical models that have tested for it, the length of PLD can have significant effects on larval transport (Edwards et al., 2007). For example, a reduction in the PLD of scallop larvae on the Scotian Shelf substantially decreased their displacement distance (Tremblay et al., 1994). Rates of larval retention in the natal region and of colonization of distant populations decreased with increasing PLD for populations of the brittle star Ophiothrix fragilis in the English Channel (Lefebvre et al., 2003). Importantly, when examining the effect of PLD on dispersal, mortality (M) must be incorporated into models (see below), because increasing PLD significantly increases the probability of mortality and decreases the number of larvae settling at distant sites (Lefebvre et al., 2003; for fish, Paris et al., 2007). Shanks (2009) found a bimodal relationship between PLD and dispersal distance. A third of the species with long PLD (>1 day and <1 month) dispersed less than 1 km, the same distance as those with short (e.g., <1 h) PLD (Shanks, 2009). To date, most efforts to model invertebrate larval transport have used a fixed PLD (e.g., Barnay et al., 2003) and have not accounted for variability in the periods of pre-competency and competency. Given the potentially significant effect of PLD (including prolonged competency) on dispersal distance, it is important that the estimates used in the models are robust. To achieve this, temperature- or food-dependent (rather than mean) larval growth rates should be used (e.g., Incze and Naimie, 2000), because the amount of variation in these two environmental parameters can have pronounced effects on PLD and, consequently, on larval trajectories (Pfeiffer-Herbert et al., 2007). The resolution of the temperature and phytoplankton distributions in the model domains is typically high enough to allow for a linked function that adjusts growth rate on the basis of the regime encountered at the end of each time step. Additionally, because the development rate can vary even among larvae that have experienced the same temperature and food regime (Pechenik and Lima, 1984), variability in the duration of pre- and post-competency periods should also be included in the models. This could be accomplished by assigning different development periods to different individuals in the population in individual-based models. Delayed competence can be incorporated into models by allowing larvae to settle at any point within the competency window during which they encounter suitable substrate (as for corals: Baums et al., 2006; and larval fish: Mitarai et al., 2008, Siegel et al., 2008). Given (1) the extensive information on the effects of different factors on larval growth, development, and competency period that has been collected in laboratory studies, and (2) the high resolution of those factors in the physical models, the use of accurate estimates of PLD in the biophysical models should be within reach.
Larval mortality
The magnitude of larval natural mortality in the plankton is not well-quantified for benthic invertebrates, although it is presumed to be great (>90%; Rumrill, 1990). Different approaches have been used or proposed to quantify mortality in the laboratory and in the field, but only a few studies have directly addressed this difficult problem. The main source of mortality is assumed to be predation (Young and Chia, 1987; Rumrill, 1990; Morgan, 1995), but other factors include starvation and physiological stress due to temperature or salinity (Young and Chia, 1987; Morgan, 1995). The relative importance of each of these factors also is not known (Morgan, 1995; Pechenik, 1999). Additionally, mortality can vary with developmental stage or size (Pennington et al., 1986).
Larval predators can be both planktonic and benthic suspension-feeders from a wide range of taxa, such as cnidarians, ctenophores, polychaetes, chaetoganths, and crustaceans, including decapod larvae and megalopae (Young and Chia, 1987), but studies that have quantified predation rates are limited. In the laboratory, experiments have mostly measured survival rates (expressed as percentage of introduced larvae) of echinoderms, bivalves, polychaetes, and crustaceans, using small containers (125-ml to 19-l containers) and concentrations of prey much higher than those found in the field (Cowden et al., 1984; Pennington et al., 1986; Morgan, 1992; Johnson and Brink, 1998). Some experiments have examined ingestion, rejection, and excretion rates of prey items by the predators (Mileikovski, 1974; Purcell et al., 1991). Measurements of predation rates in the field are even more limited, and they range in approach from tracking individual ascidian tadpoles (Olson and McPherson, 1987) and tethering of lobster postlarvae (Acosta and Butler, 1999) and crab megalopae (Allen and McAlister, 2007) to using large enclosures (123 liter) with natural concentrations of echinoplutei and snail veligers, as well as other plankton (Johnson and Shanks, 2003). Predation rates in the field appear to be much lower than those measured in the laboratory, most likely because both predators and prey are less abundant (Johnson and Shanks, 1997) and the container effects are smaller (in the case of enclosures) or nonexistent.
Rates of larval mortality (including, but not limited to, that from predation) can be estimatedin situ if cohorts or patches of larvae can be identified and tracked. However, because spawning events that can produce large enough numbers of larvae over short periods of time are generally unpredictable for most benthic invertebrates, measures of mortality rates are sorely lacking. When larval cohorts can be tracked, mortality is estimated using changes in larval abundance (total or stage-specific) between temporally consecutive data points or by comparing larval production at spawning with post-settlement recruitment (Rumrill, 1990). A mass spawning event of the sea urchin Evechinus chloroticus in a New Zealand fjord provided a unique opportunity to track a single larval cohort for 7 weeks (Lamare and Barker, 1999). In that study, mortality estimates were similar when using changes in two measures of abundance (total: 0.164 per day, stage-specific: 0.173 per day), but much lower when using the relationship of production to recruitment (0.092 per day). In general, estimates of mortality that are based on the difference between production and recruitment tend to be lower than those based on changes in larval abundance in the plankton, because the former combine periods of potentially different levels of mortality (higher in the plankton than during and after settlement) (Rumrill, 1990). It must be noted that a number of cohorts or spawning events would be required to generate statistically meaningful estimates of mortality. Interestingly, biophysical transport models have been used to estimate larval mortality in the field. Pepin et al. (2003) tracked a water parcel using a biophysical model with a particle-tracking subroutine (no mortality included), and sampled a group of larval fish within the parcel at consecutive times. They then estimated mortality in the larval patch by comparing the larval abundance as predicted by the model to that sampled in the field.
The main assumption in the analyses described above is that the same group of larvae is being tracked over the study period (e.g., Natunewicz et al., 2001). However, larvae that are lost from or added to the patch from other populations between consecutive points also contribute to the estimates of "mortality" in the patch. Concurrent measures of the flow regime and the size/age structure of the larval population within the sampling domain may minimize under- or over-estimation of mortality. Aksnes and Ohman (1996) proposed an alternative approach, which uses the relative abundance of all developmental stages at one point in time to calculate mortality. Tapia and Pineda (2007) used this approach by sampling multiple cohorts of the barnacles Balanus glandula and Chthamalus spp. in the nearshore waters at La Jolla, California, over 7 days during the reproductive period of this species. Mortality rates varied between days by up to an order of magnitude, ranging from 0.043 to 0.693 per day.
Mortality is not explicitly included in all biophysical models, despite its potentially significant role in limiting larval dispersal at different times during the planktonic periods (different locations or at different developmental stages). By definition, advection-diffusion-mortality models incorporate mortality as a term (Jackson and Strathmann, 1981; Hill, 1990; Cowen et al., 2000; Lefebvre et al., 2003; Ellien et al., 2004). These studies have shown that larval mortality in the plankton can have a pronounced effect on larval dispersal. Most notably, retention near the release site increases (or, conversely, dispersal away from the source decreases) with increasing mortality, for larvae with different swimming abilities—for example, the Norway lobster Nephrops norvegicus (Hill, 1990) and the brittle star Ophiothrix fragilis (Lefebvre et al., 2003). For the polychaete Pectinaria koreni on the eastern Bay of Seine, mortality was shown to have a greater effect on larval loss (quantified as proportion of released larvae that settle) than advection, particularly at low current speeds (Ellien et al., 2004). Similarly, Jackson and Strathmann (1981) showed that, for a "model larval population," increasing larval mortality in the plankton during pre-competence decreases success at larval settlement. For virtual larvae released over a period of 30 days off the west coast of Barbados, a mortality rate of 18% per day resulted in insufficient numbers of larvae reaching downstream locations to maintain populations there (Cowen et al., 2000). Dekshenieks et al. (1997) incorporated a term for predation-induced larval mortality in a model that examined larval vertical distribution of the oyster Crassostrea virginica. In a series of simulations, they examined larval supply using different relationships of mortality with larval size (constant, increasing, decreasing) and with depth (surface, pycnocline, benthos). Larval survival at the end of the planktonic period was extremely low (<2.5%) when mortality was size-dependent, and was much greater when predation was limited to the surface (
88%) than the bottom (14%) (Dekshenieks et al., 1997).
The mortality rates used in the biophysical models are based on laboratory and field estimates provided in the literature. However, the accuracy of the parameterizations is unknown, given the limitations in (1) obtaining accurate estimates in small containers and still water in the laboratory; (2) the small number of estimates from the field; and (3) the inconsistency in the estimates between settings. Rumrill (1990) reviewed mortality rates of benthic invertebrates from most studies (field and laboratory) available at that time, and is frequently the source of the rates used in the models (Jackson and Strathmann, 1981; Dekshenieks et al., 1997; Lefebvre et al., 2003; Ellien et al., 2004). It must be noted, however, that the number of taxa in Rumrill (1990) was not exhaustive, and the values used in the models are often for the same genus or family as in Rumrill, but not necessarily for the same species. In some cases, the mortality values that are used have been derived specifically for the population being modeled (e.g., Hill, 1990).
We propose that larval mortality rates that have been obtained by sampling larval populations over time or across space in the field provide the best estimates for parameterizing biophysical models for several reasons. (1) Perhaps most importantly, these estimates incorporate all sources of mortality (or loss) without the need to understand the relative contributions of different sources. (2) Mortality rates can be estimated for the species and population of choice, rather than relying on extrapolations from other species or areas. (3) Estimates of both population-wide and stage-specific mortality are possible. (4) Approaches have been developed that allow the estimation of mortality rates without tracking larval cohorts or patches, as long as the spatial coverage of the sampling is greater than the scale of advection. To provide accurate measures of mortality, field sampling requires an understanding of the appropriate spatial coverage (i.e., spatial extent of the larval population; spatial scale of advective transport) and temporal resolution (i.e., timing of larval release; developmental periods), but is not exceptionally challenging.
Larval behavior in the water column
Larvae of marine invertebrates are weak swimmers (Young and Chia, 1987; Young, 1995). Locomotion is achieved by mechanisms ranging from ciliary to muscular activity, and swimming speeds are in the order of millimeters to centimeters per second (Chia et al., 1984; Young, 1995; Metaxas, 2001). It has been suggested that larvae have the ability to sense their environment, and effects on swimming speed (acceleration, deceleration, or cessation) and directionality have been recorded in the presence of chemical and physical stimuli (Kingsford et al., 2002). However, with the exception of some large, strong-swimming larvae (ascidian tadpoles, crab zoea, larval lobsters), these measurements have been taken in the laboratory, and mostly with no flow. Consequently, the conditions in the field under which larvae can sustain their ability to maneuver relative to perceived stimuli are not known.
Meroplanktonic invertebrate larvae have been shown to exhibit behavioral responses to cues in the water column (Young, 1995; Metaxas, 2001; Kingsford et al., 2002), although some of the mechanisms for cue detection remain unknown (Kingsford et al., 2002). The expression of some of these behaviors (most notably vertical migration) can vary on a diel cycle or ontogenetically (e.g., Carriker, 1951; Shanks, 1986; Metaxas and Young, 1998b). Most studies have addressed responses to cues by recording effects on vertical (or horizontal) distribution or swimming speed in the laboratory under static flow conditions (Metaxas, 2001; Kingsford et al., 2002). Because of our inability to successfully track larvae (individuals or cohorts; but see Cobb et al., 1989; Bingham and Young, 1991; Shanks, 1985, 1995; Shanks and Wright, 1987; Annis, 2005), studies done in the field have mainly focused on larval vertical distributions relative to features in the water column, such as pycnoclines, fronts, or layers of chlorophyll maxima (Metaxas, 2001).
The most commonly quantified larval behavior in the field is vertical migration. For example, it is well established that crustaceans (e.g., the barnacle Balanus improvisus, the blue crab Callinectes sapidus, the lobster Homarus americanus) regulate their vertical position in the water column over the period of larval development, some stages being found near or at the sea surface while others near the bottom at depths of tens of meters (Harding et al., 1987; Epifanio and Garvine, 2001). Several species (e.g., the oyster Crassostrea virginica, the scallop Placopecten magellanicus, and the green crab Carcinus maenas) are also known to show diel or tidal vertical migration across tens of meters (Forward, 1988; Manuel et al., 1997; Queiroga and Blanton, 2004). Most often, light has been inferred as the cue that drives vertical migration: the stages that migrate toward the surface show positive phototaxis, while the ones that move away from the surface or toward the ocean floor show negative phototaxis (Lang et al., 1979; Forward, 1988). Changes in salinity and pressure have also been implicated as cues for tidal vertical migration (Sulkin, 1984; Tankersley et al., 1995). Several of the studies that have addressed vertical migration have emphasized its importance to larval horizontal transport (Sulkin, 1984; Zeng and Naylor, 1996; Manuel et al., 1997; Kingsford et al., 2002; Shanks and Brink, 2005).
Larvae of many taxa respond to physical characteristics of the water column, such as the salinity and temperature structure, both in the field and in the laboratory (Metaxas, 2001). Additionally, larval behavioral response to biological features of the water column, such as the presence of food (phytoplankton) or predators, has been inferred from distributional studies in the field (Metaxas 2001), as well as from manipulative experiments in the laboratory (Metaxas, 2001; Metaxas and Burdett-Coutts, 2006; Woodson and McManus, 2007; Sameoto and Metaxas, 2008a). The response can be manifested as either aggregation or avoidance of the feature. A few studies have recorded measurable effects of flow characteristics (shear, turbulence) on larval vertical distribution or swimming patterns (Luckenbach and Orth, 1992; Welch et al., 1999; Fuchs et al., 2004; Metaxas et al., 2009; Sameoto et al., Dalhousie University, unpubl. data). Although these studies have alluded to the potential significance of the detected larval responses in larval dispersal, the realized role of larval behavior during larval transport remains elusive.
Larval behavior has been incorporated in some studies using biophysical models to predict larval transport, although not consistently (e.g., Lefebvre et al., 2003; Aiken et al., 2007). Most frequently, the incorporated behavior is vertical migration. Ontogenetic vertical migration has been incorporated for a number of species with different swimming abilities (e.g., lobsters, crabs, scallops, as well as fish) by modifying the vertical position of the tracked particles at different times after their release (i.e.. according to their "age"). For example, modeling studies of the lobster H. americanus and the rock crab Cancer irroratus have released and tracked particles in the top few meters of the water column (Katz et al., 1984; Clancy and Cobb, 1997; Incze and Naimie, 2000), whereas depth of ascent of the sea scallop P. magellanicus (Tremblay et al., 1994) and larval depth for the barnacle B. glandula (Pfeiffer-Herbert et al., 2007) were varied with age. Diel vertical migration has been incorporated in biophysical models that predict larval transport of the green crab C. maenas by modifying the vertical position of individuals depending on time of day (Marta-Almeida et al., 2006; Peliz et al., 2007). Ontogenetic vertical migration is one of the most frequently incorporated behavioral components in models of larval fish transport (Hare et al., 1999; Cowen et al., 2000; James et al., 2002; Paris and Cowen, 2004; Paris et al., 2005, 2007; Fiksen et al., 2007).
The larval response to salinity stratification in the water column has been incorporated into biophysical models in a more complex manner. Dekshenieks et al. (1996) used a size-structured advection-diffusion model to specifically examine the effects of the salinity structure of the water column (well-mixed, partially stratified, and strongly stratified) on the larval vertical distribution of the oyster Crassostrea virginica. In this model, the total vertical advective velocity included a size-dependent component of vertical movement (larger larvae swam faster but also sank deeper), and the percentage of time larvae spent swimming was varied with the rate change in salinity (Dekshenieks et al., 1996). North et al. (2008) examined the effect of differences between two oysters (C. virginica and C. ariakensis) in their responses to haloclines on their horizontal larval transport in Chesapeake Bay (a partially mixed estuarine system). At each time step, they used a threshold gradient in salinity to induce a species-dependent larval response, which was to either move upward toward the surface or downward toward the bottom, in both cases away from the halocline (North et al., 2008).
Although biophysical models may incorporate larval behavior, they do not always directly evaluate its role in larval transport (e.g., James et al., 2002; Pfeiffer-Herbert et al., 2007); in those studies that do, larval behavior is shown to have an impact on larval transport in both weak- and strong-swimming larvae. For example, the depth of ascent for larval scallops had a significant effect on the distribution of potential settlement locations on Georges Bank (Tremblay et al., 1994). Similarly, larval swimming needed to be included in the models that successfully delivered larval lobsters to known sites of settlement; particle transport by currents alone resulted in larval loss from the system (Katz et al., 1994). Including a larval response to the salinity structure of the water column significantly affected both the vertical distribution (Dekshenieks et al., 1996) and horizontal transport (North et al., 2008) of oyster larvae. The importance of diel/tidal vertical migration on larval export/retention has been demonstrated for decapods on a range of scales from the continental shelf of Portugal (Marta-Almeida et al., 2006; Peliz et al., 2007) to low-inflow estuaries (DiBacco et al., 2001). Paris et al. (2005) performed a sensitivity analysis of different scenarios of larval behavior (onset of active behavior and sensing distance to suitable habitat) for Cuban snapper (Lutjanus spp.) and found variable effects of these factors on dispersal distance. A commonly documented effect of vertical migration in fish larvae is increased retention near natal sites (Cowen et al., 2000; James et al., 2002).
It must be noted, however, that not all studies have confirmed that larval behavior can affect dispersal. In a modeling study that examined factors affecting dispersal and connectivity of populations on the southeastern US continental shelf, Edwards et al. (2007) showed that larval vertical position in the water column (surface-fixed, depth-fixed, mid-depth passive) had little effect on the resulting dispersal kernels. For the blue crab Callinectes sapidus, the original hypothesis that vertical migration of megalopae allows their return to settlement sites has been challenged; flow alone has been postulated to regulate megalopal transport (Epifanio and Garvine, 2001).
To quantify the influence of larval behavior on larval transport, biophysical models must parameterize this behavior within realistic boundaries. Currently, these parameterizations are obtained from experimental studies done in the laboratory or from field studies that have measured larval distributions. In some studies, field or laboratory observations are precisely reproduced in the parameterizations, such as larval swimming speeds (Tremblay et al., 1994; Dekshenieks et al., 1996) or direction of response to a cue (e.g., avoidance or aggregation to haloclines) (North et al., 2008). In other studies, larval behavior is broadly based on our understanding from the literature, but the details that are incorporated into models (e.g., precise timing or distance traveled for vertical migration; threshold salinity gradients that induce an avoidance response) are relatively accurate representations (same order of magnitude) rather than precise parameterizations (Tremblay et al., 1994; James et al., 2002; Paris et al., 2005, 2007; Marta-Almeida et al., 2006; Pfeiffer-Herbert et al., 2007; North et al., 2008). The required level of precision in the parameterization of behavioral components of the models is currently unknown, but can only be determined through validation of model output and sensitivity analyses (see MODEL VALIDATION).
Several complementary approaches are needed if we are to obtain realistic parameterizations of larval behavior. Measures of behavior are relatively easy to obtain in the laboratory, and have been used either as first-order estimates or to bound the ranges used in the biological components in the models. For example, relationships between temperature, salinity, and food concentration with swimming speeds can be easily measured for a range of larval taxa. Similarly, we can expand the number of experiments that examine the effects of physicochemical and biological cues on swimming performance or population distributions. As in North et al. (2008), these experiments can provide threshold values that induce a response. We do caution that these values can be species-specific (e.g., salinity; Sameoto and Metaxas, 2008b) or population-specific (e.g., vertical migration; Tremblay and Sinclair, 1990; Manuel et al., 1996), and need to be derived for each species and system of interest. At a more advanced stage, trade-offs between potential behavioral responses given the multiple cues that larvae will sample concurrently can be incorporated in the models using dynamic programming, such as individual-based neural networks (Werner et al., 2007). A similar approach has recently been applied to the dispersal of larvae of the cod Gadus morhua in northern Norway (Fiksen et al., 2007).
As discussed above, validating larval behaviors in the field, although logistically challenging, is possible. Distributional changes are relatively easy to measure; however, measurements must be taken at the appropriate resolution to avoid aliasing. For example, high temporal resolution (hours) of changes in vertical distribution is needed, and has been used (e.g., DiBacco et al., 2001) to evaluate vertical migration on tidal and diel scales, and high spatial resolution (meters) is needed to evaluate vertical migration in response to physical or biological features in the water column.
To date, larval behavior has only been examined in situ at the individual level, by releasing and tracking small numbers of individuals in a small number of studies (see above). These observations have not been made at the population level using controlled larval releases; however, it may be feasible in certain systems to track released larval patches or cohorts over short periods of time (days) (e.g., Arnold et al., 2005). Enclosed bays with strong (stable) stratification (temperature or salinity) and predictable, advective circulation (e.g., fjord-like) are such physical systems, and certain taxa of larvae that are easy to culture in large numbers in the laboratory (e.g., echinoids, bivalves) may be appropriate biological systems. Small passive drifters, released concurrently with and exposed to the same scales of the flow regime as the larvae, can provide estimates of transport in the absence of larval behavior (e.g., Taggart and Ruddick, 2006; Gawarkiewicz et al., 2007). During these releases, sampling resolution would have to be high, both temporally and spatially, to reflect the processes and structures of interest. The use of experimental mesocosms can provide an initial, more tractable approach, at scales intermediate between laboratory experiments and in situ releases. Advances in available technologies may facilitate larval tracking of many individuals over short time scales (tens of minutes) (e.g., Genin et al., 2005).
In sum, different approaches can be used to accurately parameterize larval behaviors that are relevant to the specific biological and physical systems of interest. Recently, Leis (2007) reviewed factors that must be considered when integrating behavior in biophysical models of dispersal for demersal fish. Many of his recommendations are similar to ours. In the end, only accurate estimates will allow us to test the relative importance of larval behavior in larval transport and supply to potentially suitable habitats for settlement.
Larval behavior during settlement
Without successful larval settlement and recruitment into the adult population, physical movement of individuals among populations (and thus connectivity) of benthic invertebrates is limited. In turn, settlement and recruitment cannot be successful unless competent larvae encounter appropriate substratum for settlement. The precise mechanisms used by larvae to locate appropriate settlement substrata are not completely understood, but larvae of many taxa respond behaviorally to a variety of biotic (chemical) and abiotic (light, water movement, pressure, salinity, temperature, and gravity) stimuli (Kingsford et al., 2002). Biotic stimuli, such as chemicals produced by conspecifics or prey, can act as strong cues for larval behavior at settlement for many benthic species (Hadfield and Paul, 2001). For example, the veligers of the nudibrach Phestilla sibogae cease swimming, sink, and undergo metamorphosis on the benthos when they encounter plumes of a chemical cue emitted by its prey, the coral Porites compressa (Hadfield and Koehl, 2004). Larvae of the sponge Luffariella variabilis respond faster to the presence of conspecifics and a chemical cue produced by conspecifics than to seawater (Ettinger-Epstein et al., 2008). Abiotic stimuli, such as light levels, can also act as settlement cues; for example, the proportion of settling larvae of L. variabilis decreased with increasing light intensity (Ettinger-Epstein et al., 2008). It has been shown that above a threshold of turbulent kinetic energy, larvae of the mud snail Ilyanassa obsoleta stop swimming and sink to the benthos (Fuchs et al., 2004). Sound, particularly that associated with reefs, has been considered a strong cue for location of settlement substrata by larval fish (Tolimieri et al., 2000; Simpson et al., 2004). Recently, larvae of some invertebrate species of decapods have also been shown to display directional movement in response to sound (Radford et al., 2007). As for reefs, distinctive sounds have been associated with particular habitats dominated by invertebrates, such as urchin barrens (Radford et al., 2008), underscoring the potential for sound as a navigation cue for invertebrate larvae.
It has been suggested that larval behavioral responses to sensory cues can significantly affect spatial patterns in settlement and recruitment (Kingsford et al., 2002), and ultimately contribute to spatial patterns in adult abundance; however, most evidence has been collected for relatively small (centimeters to meters) spatial scales. For example, settlers of the bryozoan Membranipora membranacea are found primarily at the proximal ends of laminarian algae (Seed, 1976), a pattern on spatial scales of centimeters to meters that has been attributed to preferential larval settlement in response to chemical or tactile (level of damage of the host kelp related to age) cues (Brumbaugh et al., 1994). Larvae that settle gregariously and in darkness, such as the sponge L. variabilis, are distributed patchily in cryptic habitats in the field (Ettinger-Epstein et al., 2008). In the Gulf of California, larvae of the intertidal barnacle Cthamalus anisopoma settled in response to chemical cues both from conspecifics and from other cohabitants, including predators, in the upper intertidal zone (Raimondi, 1988). In combination, these settlement cues contributed to the vertical zonation in distribution exhibited by adults (Raimondi, 1988). Cyprids of the barnacle Balanus improvisus do not settle when water velocities are higher than those in which juveniles can feed effectively, and this may contribute to spatial patterns in adult abundance (Larsson and Jonsson, 2006), depending on spatial and temporal patterns in hydrodynamics. A suite of larval behaviors, including upward swimming, settlement on the undersides of overhangs, and settlement in response to molecules produced by crustose red algae, drives the adult distribution of the coral Agaricia humilis (Raimondi and Morse, 2000).
When settlement behavior is incorporated into large-scale transport models, it is only at an elementary level: particles representing larvae are allowed to settle only within a defined "sensory zone" of suitable substrata (Paris et al., 2007). For example, North et al. (2008) allowed oyster larvae to settle only in grids containing culch, a known inducer of oyster larval settlement (Tamburri et al., 1996). Similarly, in a simulation of larval transport in the English Channel, Barnay et al. (2003) allowed particles representing the polychaete Owenia fusiformis to settle only when the appropriate substrata were present. In a simulation of dispersal of larvae of the coral Acropora palmata in the Caribbean, larvae were allowed to settle only at a maximum distance of 9 km from a coral reef (Baums et al., 2006). At these large scales and coarse resolutions, only a few studies have explicitly tested the role of settlement behavior on larval transport. For example, Tremblay et al. (1994) found significant effects of both the depth of downward vertical migration of competent larvae and the length of search period for suitable substrate on the patterns of larval transport for the sea scallop Placopecten magellanicus.
On smaller (millimeter to meter) scales, modeling experiments have demonstrated that larval behavioral responses to settlement cues can significantly affect transport to the benthos. Using a one-dimension (vertical) model, Eckman et al. (1994) showed that the rate of larval transport to the benthos can be significantly enhanced if settling velocity increases in response to a concentration gradient of a chemical cue. However, chemicals released into a turbulent water column (or benthic boundary layer) form filamentous streams of high concentrations of the cue interspersed with "clean" water, rather than continuous concentration gradients (Koehl et al., 2007). An individual-based numerical model of the nudibranch Phestilla sibogae that incorporated net flow, monochromatic waves, and turbulence showed that the rate at which larvae were transported to the benthos was reduced if a behavioral response to stop swimming only in the presence of cue, rather than continuously sinking, was included (Koehl et al., 2007). Inclusion of a behavioral response of competent larvae of Ilyanassa obsoleta to turbulence into an advection-diffusion model significantly increased their transport to the benthos in highly energetic (e.g., tidal) environments (Fuchs et al., 2007). On the basis of these studies, we conclude that settlement behavior can only be incorporated into biophysical models if they can be resolved at these fine scales of millimeters to meters.
For settlement behavior to be incorporated in biophysical transport models, both their biological and physical components must be improved. Most importantly, the behavioral mechanisms that regulate settlement to the benthos must become better known. Firstly, the relationship between spatial and temporal patterns in larval (including ontogenetic changes in distribution) and settler abundance should be quantified for a given species in a given region, particularly if settler abundance is used to validate model outcomes. If post-settlement processes such as predation have a strong (and variable) influence on the abundance of settlers, then using measures of settlement to validate transport models is not advisable. Secondly, the cues that trigger behavioral changes leading to settlement should be identified, and the concentrations that induce a response measured, under controlled conditions in the laboratory. Although many studies have measured the outcome of the response to cues (typically as percentage of larvae that settle) in laboratory experiments, less is known about the behaviors (cessation of swimming or directional swimming) that give rise to the observed patterns. The distributional patterns of the cues (e.g., chemical, hydrodynamic, light, sound) that are shown to induce movement of larvae from the water column to the benthos must be measured in the field (e.g., Hadfield and Koehl, 2004). These distributions can set the spatial scales over which behavior at settlement may be relevant.
Because settlement and recruitment can vary on small (tens to hundreds of meters) horizontal spatial scales (Ladah et al., 2005; Porri et al., 2006), there is a significant mismatch between the spatial (millimeter to meter) scales over which settlement behavior occurs and the spatial resolution of oceanic circulation models (hundreds of meters to kilometers). The constraint of mismatched scales can be partially addressed by nesting successively smaller grids near the shoreline within the coarser grids of circulation (but see MODEL VALIDATION for trade-offs). Alternatively, a first approach can be to parameterize settlement behavior and incorporate it in existing models. For example, particles representing larvae could "sink" at a rate approximating observed settlement rates when located within the model grids nearest to the coast. Since larval transport occurs in the water column and before settlement, the incorporation of settlement behavior into larval transport models would be relevant only if (1) larval descent into the benthos in response to a cue alters their horizontal distance by moving them into a different water layer; and (2) model validation is based on comparing spatiotemporal patterns of settling larvae to those of settlers or recruits (see MODEL VALIDATION). Whether settlement behavior has a significant effect on the outcome of larval transport models remains to be determined.
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Model Validation |
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A significant challenge of model validation is that the response variables, such as the dispersal kernel (Siegel et al., 2003; Aiken et al., 2007; Edwards et al., 2007), larval trajectories and "dispersal paths" (Pfeiffer-Herbert et al., 2007), and mean dispersal distance (Edwards et al., 2007; North et al., 2008) focus on a transitionary phase between two life-history stages that occupy different habitats (the plankton and the substratum) and are sampled by different approaches—temporally discrete for larvae and time-integrative for settlers (Pineda, 2000). Specifically, these variables are calculated for settling larvae, which have undergone dispersal, survived the planktonic period, and been delivered to the point of settlement, but have not yet settled and metamorphosed. Larval transport ends at the onset of settlement.
Using the number of settlers or recruits to validate model projections of the number of settling larvae is generally inappropriate unless a known relationship exists between larval supply and settlement, on the basis of which general trends can be extrapolated and first-order predictions (e.g., general spatial patterns) may be possible. A correlation between larval abundance and settlement has been recorded (Minchinton and Scheibling, 1991; Tapia and Pineda, 2007), but not consistently (Porri et al., 2006; Rilov et al., 2008). For example, larvae of intertidal species may settle on suitable subtidal substrate (Rilov et al., 2008), resulting in decreased settlement in the intertidal zone. Conversely, when available substrate is limited, there may be an "intensification" of settlement rate (Pineda, 2000). Biological or physical processes occurring in the surf zone may also decouple the relationship between larval abundance at hundreds of meters from shore and settlement on the shore (Rilov et al., 2008). Larval and benthic stages are affected by a different suite of biological and physical processes that operate on different scales, the most obvious example being that of advection. The magnitude of these differences may be smaller for fish, the benthic stages of which also inhabit the water column, than for benthic invertebrates, which spend their adult life "attached" to the two-dimensional ocean floor. For some species and geographic locations, the settlement period can last several days, during which factors such as food and space availability, predation, and resuspension can significantly influence settler mortality (Hunt and Scheibling, 1997). Settlement success can vary greatly both spatially and temporally, and there may be density-dependent effects of recruitment on the rate of settlement (Hunt and Scheibling, 1997). The degree of motility of the benthic stage will introduce another source of error in the estimate of dispersal distance: for more sedentary species (such as barnacles, molluscs, and gastropods), the locations of larval delivery and settlement may vary by meters, whereas greater discrepancies may arise with increasing settler or recruit motility (e.g., for decapods and fish).
Different approaches of varying accuracy have been used to validate the outcomes of model simulations. In several studies, the accuracy of model predictions was confirmed where larvae were delivered to geographic locations of known adult populations (i.e., at scales of tens to hundreds of kilometers; Katz et al., 1994; Johnson and Perry, 1999; Incze et al., 2000; James et al., 2002; Paris et al., 2005) or when spatial patterns in larval transport corresponded to the observed spatial patterns of recruits along the coastline (Pfeiffer-Herbert et al., 2007). A few studies have made direct comparisons between simulated and observed horizontal or vertical patterns of larval abundance. For example, the model used to simulate patterns of oyster larvae relative to a halocline in Dekshenieks et al. (1996) was used to predict "reasonably well" the vertical distribution of oyster larvae in an earlier study in New Jersey (Carriker, 1951). Ellien et al. (2004) and Peliz et al. (2007) evaluated the role of different factors in larval dispersal pathways by directly comparing simulated with observed larval distributions of polychaetes and decapods, respectively. For larval fish, Paris and Cowen (2004) observed similar patterns in the vertical distributions of virtual and sampled early-stage larvae of Stegastes partitus off the west coast of Barbados. Perhaps the most comprehensive approach to model validation was achieved for a cohort of larval Mercenaria, released in a well-defined, semi-enclosed, microtidal lagoon in Florida (Arnold et al., 2005). The tractability of the system allowed for the comparison of three different approaches applied concurrently to measure transport: (1) measurement of advective transport using subsurface drifters and of diffusive transport using released SF6; (2) modeling transport with a circulation model coupled with a Langrangian particle-trajectory model; and (3) sampling of released larvae. Unfortunately, although this approach allows for a convincing validation, it is also extremely resource-demanding and its use may not be amenable to highly advective/diffusive systems, such as open coastlines.
An alternative approach for model validation, which, however, does not allow for mechanistic inferences about observed patterns, is larval "tagging" (geochemical or genetic), used to assign natal origin to dispersing or settling larvae. Although only applicable to larval taxa with "hard" body parts, elemental fingerprinting of larval shells and statoliths has been developed and used successfully to assign origin in a handful of studies with benthic invertebrates (DiBacco and Levin, 2000; Zacherl et al., 2003; Becker et al., 2007). This technique, although promising, also has some limitations: (1) it requires detectable differences in the trace element composition of seawater between natal sites; (2) trace-element deposition can vary with other environmental conditions at the natal site, such as temperature and salinity, as well as growth rate; and (3) sample processing is quite costly and its effectiveness is inconsistent (Strasser et al., 2007, 2008; Lloyd et al., 2008). In contrast, elemental fingerprinting of otoliths to assess natal origin is well established for fish (Campana, 1999; Thorrold et al., 2001, 2007). Genetic fingerprinting for assignment of population origin is an alternative approach that, however, can also involve several challenges (Manel et al., 2005; Cowen and Sponaugle, 2009). For example, the potential source populations must be known and distinguishable by detectable genetic differentiation (Hedgecock et al., 2007).
Another constraint placed on the validation of biophysical models is the mismatch in relevant scales and realized resolution of parameter estimation between biological and physical processes. In the biophysical models described above, the grid resolution for physical processes is greater than 1 km (Ellien et al., 2004; Baums et al., 2006; Peliz et al., 2007; Pfeiffer-Herbet et al., 2007; North et al., 2008), although the relevant scales may be much smaller—that is, centimeters to meters for diffusion, much smaller than for advection (Largier, 2003). Nested grids of higher resolution (hundreds of meters to 1 kilometer) can be incorporated to focus on areas of interest at the expense of a broader horizontal coverage (Peliz et al., 2007; Pfeiffert-Herbet et al., 2007). The smaller the sampling area of interest, the higher the grid resolution can be (e.g., Arnold et al., 2005). In contrast, larval abundance can vary over scales of tens to hundreds of meters, and sampling can incorporate this level of resolution (Di Bacco et al., 2001; Natunewicz and Epifanio, 2001; Ellien et al., 2004; Arnold et al., 2005; Tapia and Pineda, 2007), particularly in semi-enclosed bays. The physical and biological components of the models can be better matched vertically: most circulation models can be resolved to scales of meters to tens of meters, a degree of resolution that can also be achieved in larval sampling. However, this may not be the case if settlement behavior is included in the models. The temporal resolutions of the biological and physical processes are mismatched in the opposite direction relative to the spatial resolutions. The circulation and particle-trajectory models in the above studies are resolved at frequencies of tens of seconds to minutes, whereas larval sampling typically occurs at minimum frequencies of hours to days. Although higher frequencies may provide more appropriate scales for biological processes, it is currently not possible to achieve them. The interpolation required to match the spatial and temporal scales between processes inevitably reduces the accuracy of the estimates taken at the coarser resolution, and the relationship of the interpolated to the real values is not known.
Adequate validation of the overall performance of biophysical models, as well as that of the individual components, at the appropriate spatial and temporal scales, is absolutely necessary. However, the considerable challenges that must be overcome to achieve validation may make it impractical except in certain biological and physical systems where the obstacles are more tractable.
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Biophysical models have shown potentially significant effects of the duration of the larval period, mortality rates, and larval behavior in the plankton on larval transport. It is likely, although not extensively tested, that behavior of settling larvae can show similar influence. Because of the potential significance of the biological components, their parameterization requires more accurate estimates that are specific to both both species and habitat (or location). For parameters where first-order estimates do not exist, they should be obtained either in the laboratory or the field. For parameters for which such estimates do exist, we must turn our attention to obtaining field-generated measures of greater accuracy.
Advances in the estimation of the response variables used in the models must also be made, to provide us with the ability to validate model performance. To avoid the pitfalls associated with the common current practice of validating larval abundance using settler or recruit abundance, possible approaches include (1) improving our techniques for measuring larval abundance after larval delivery to the settlement habitat, but immediately prior to settlement; and (2) incorporating components for settlement into the models. Although the latter approach may not be immediately feasible, it may be achievable in a shorter term than the former. Some simple models of behavior at settlement already exist (see Larval behavior during settlement) and can be linked to the large-scale biophysical models. The approach would most likely require greater spatial resolution of the models at least near the coastal benthos, and consequently more computational power. However, given the rapid advances in computing, greater power at a lower cost will most likely be achievable within a few years.
The significant challenge of the mismatch of scales between the biological and physical processes may be more difficult to overcome in the near future. It is unlikely that an increase in the temporal resolution of the measurements of biological processes in the field is feasible, but an increase in the spatial resolution of the physical processes is likely achievable (also by increased computing power). We believe this to be particularly important, because it is unknown whether the scales of the physical processes currently being used are even relevant to the scales that larvae experience. Similarly, drifters that are frequently used to validate the physical processes in models are also not exposed to fluid motion at the same scales as larvae.
Biophysical models show great promise as predictive tools of larval transport. Their development entails an interdisciplinary approach that combines larval biology and physical oceanography, two disciplines with different sampling approaches, at different spatial and temporal resolutions. To maximize the power of the approach, we must be cautious about these differences and the limitations that may arise as a result.
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  R. B. Emlet, S. A. Maslakova, A. L. Shanks, and C. M. Young Biological Bulletin Virtual Symposium: Biology of Marine Invertebrate Larvae Biol. Bull., June 1, 2009; 216(3): 201 - 202. [Full Text] [PDF]
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