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Successful validation of a larval dispersal model using genetic parentage data

Successful validation of a larval dispersal model using genetic parentage data Larval dispersal is a critically important yet enigmatic process in marine ecology, evolution, and conservation. Determining the distance and direction that tiny larvae travel in the open ocean continues to be a challenge. Our current understanding of larval dispersal patterns at OPENACCESS management-relevant scales is principally and separately informed by genetic parentage Citation: Bode M, Leis JM, Mason LB, Williamson data and biological-oceanographic (biophysical) models. Parentage datasets provide clear DH, Harrison HB, Choukroun S, et al. (2019) Successful validation of a larval dispersal model evidence of individual larval dispersal events, but their findings are spatially and temporally using genetic parentage data. PLoS Biol 17(7): limited. Biophysical models offer a more complete picture of dispersal patterns at regional e3000380. https://doi.org/10.1371/journal. scales but are of uncertain accuracy. Here, we develop statistical techniques that integrate pbio.3000380 these two important sources of information on larval dispersal. We then apply these meth- Academic Editor: Steven D. Gaines, University of ods to an extensive genetic parentage dataset to successfully validate a high-resolution bio- California, UNITED STATES physical model for the economically important reef fish species Plectropomus maculatus in Received: January 16, 2019 the southern Great Barrier Reef. Our results demonstrate that biophysical models can pro- Accepted: July 2, 2019 vide accurate descriptions of larval dispersal at spatial and temporal scales that are relevant Published: July 12, 2019 to management. They also show that genetic parentage datasets provide enough statistical power to exclude poor biophysical models. Biophysical models that included species-spe- Copyright:© 2019 Bode et al. This is an open access article distributed under the terms of the cific larval behaviour provided markedly better fits to the parentage data than assuming Creative Commons Attribution License, which passive behaviour, but incorrect behavioural assumptions led to worse predictions than permits unrestricted use, distribution, and ignoring behaviour altogether. Our approach capitalises on the complementary strengths of reproduction in any medium, provided the original genetic parentage datasets and high-resolution biophysical models to produce an accurate author and source are credited. picture of larval dispersal patterns at regional scales. The results provide essential empirical Data Availability Statement: All methods are support for the use of accurately parameterised biophysical larval dispersal models in described within the paper and its Supporting Information files. All data files are available marine spatial planning and management. from the GitHub database (accession number doi: 10.5281/zenodo.2558693). Funding: DHW, GPJ, and HBH received funding from Australian Research Council (ARC) Linkage Grant LP100200561 (https://www.arc.gov.au/). MB received funding from Australian Research Council (ARC) Future Fellowship FT170100274 (https:// www.arc.gov.au/). HBH was funded by Australian PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 1 / 13 Validating larval dispersal models with genetic parentage data Research Council (ARC) DECRA DE160101141 Introduction (https://www.arc.gov.au/). DHW, MB, GPJ, HBH, Most marine species have a brief pelagic larval stage that is spent dispersing in open water and SC received funding from the Australian [1,2]. Because suitable habitat is often patchy and isolated, larval dispersal is the primary pro- Research Council (ARC) Centre of Excellence for Coral Reef Studies (https://www.arc.gov.au/). GPJ, cess through which populations of demersal species are connected and replenished. Accurately DHW, HBH, JML, LBM, and SC received funding predicting where larvae settle at the end of their dispersal stage is essential for understanding from the Australian Department of Environment the ecology and evolution of marine populations and species [3,4] and for making decisions and Energy, through the Marine and Tropical about their conservation and sustainable exploitation [5–8]. To this end, recent advances in Science Research Facility, National Environmental biological oceanography and genetics have provided separate and revolutionary insights into Research Program, and National Environmental Science Program (https://www.environment.gov. larval dispersal and population connectivity in the coastal oceans [9]. au/). The funders had no role in study design, data Coupled biological-oceanographic models (hereafter “biophysical” models) can compre- collection and analysis, decision to publish, or hensively describe larval dispersal patterns, simulating the movement of billions of larvae preparation of the manuscript. across entire seascapes [3,10,11]. Increasingly sophisticated biophysical models, with higher Competing interests: The authors have declared resolution and incorporating knowledge of larval biology and behaviour, are widely advocated that no competing interests exist. as decision-support tools for coastal ecosystem management [12–16]. Although the oceano- graphic components of these models are usually validated, their biological components are often underdeveloped and uncertain [17,18]. The resulting model predictions are therefore of unknown accuracy and precision [19]. Genetic parentage techniques have recently been applied to directly measure larval dispersal patterns at both local and regional scales [7,20–22]. Parentage data have provided evidence for local retention of larvae [20] and for multidirectional dispersal over hundreds of kilometres [21,22]. They have also supported marine spatial management and have informed the design of marine reserve networks [7,23]. Although parentage assignments provide strong evidence of specific dispersal events, constraints on the spatial and temporal scales of population sam- pling mean that only a fraction of potential dispersal pathways can be resolved. Nonetheless, parentage datasets have the potential to provide an independent test of biophysical model pre- dictions and to decide whether these models provide credible representations of true larval dis- persal patterns [9]. The validation of biophysical models with parentage data is a crucial next step in marine spatial ecology and conservation [2,5,19,24–26]. Genetic parentage data provide an opportu- nity to validate biophysical models at the spatial and temporal scales that are most relevant to management, using the distance, direction, and timing of known dispersal events. Given that both biophysical models and parentage data describe the sources and destinations of individ- ual larvae, the process of statistical validation is conceptually straightforward. However, it is logistically demanding to assemble the necessary data for several reasons. First, genetic parent- age assignments are expensive to obtain at the requisite intensity and spatial scale [9]. If there are too few assignments, the parentage dataset may not offer the statistical power needed for a rigorous test [27,28]. Second, it is challenging to produce a biophysical model at both the reso- lution and scale needed to match observed assignments, as the observed dispersal events include both small-scale retention of larvae in and around their natal population and long-dis- tance connections over hundreds of kilometres. Third, because ocean currents are often highly variable through time, the model must provide a close temporal match to the measured larval dispersal events [19]. Finally, to isolate the significance of larval biology and behaviour, parent- age data should be tested against a range of different biophysical models, from passive dispersal models to those incorporating the biological and behavioural traits of the study species [17,18,25]. Here, we resolve each of these challenges to validate a biophysical model with a matching genetic parentage dataset. We parameterise a high-resolution biophysical model of larval dis- persal across the southern and central Great Barrier Reef (GBR) for bar-cheeked coral trout PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 2 / 13 Validating larval dispersal models with genetic parentage data (also called the spotted coral grouper, P. maculatus, Serranidae). We develop novel quantita- tive validation techniques and use them to rigorously test this model against an intensive and independent genetic parentage survey of P. maculatus (previously published in [21]). Our results represent a formal validation of a regional-scale biophysical model using genetic par- entage data, thereby integrating two important and complementary sources of larval dispersal information. Materials and methods Genetic parentage assignments and population sampling Between September 2011 and August 2013, a total of 880 adult and 1,190 juvenile P. maculatus were sampled across three reef regions in the southern GBR: the Keppel Islands, the Percy Islands, and the Capricorn Bunker group (Fig 1A and 1B). A panel of 23 microsatellite loci iden- tified 69 parent–offspring relationships within the sample, connecting 18 different patch reefs separated by distances ranging from a few hundred metres to over 200 km. The observed larval dispersal network revealed self-recruitment within each region (including to individual natal reefs) and longer-distance multidirectional dispersal between regions (Fig 1C), creating an observed parentage dispersal matrix (Fig 1D). Each assigned juvenile and a subset of 314 unas- signed juveniles were aged from daily otolith growth rings to determine both the spawn date and the pelagic larval duration. This allowed a closer parameterisation of the biophysical model and precise temporal match between empirical dispersal vectors and the biophysical model. Underwater visual census (UVC) surveys were conducted on reefs within each of the three regions to establish reef-specific estimates of adult population size. This was combined with P. maculatus fecundity data to estimate the number of propagules released from each reef in the biophysical model. The species’ relative abundance was highly variable among reefs, particu- larly between reserve and nonreserve reefs. For reefs within the study domain where popula- tions were not surveyed, adult densities were approximated by the average density of surveyed reefs with the same protected status within their region. The biophysical model used these pop- ulation estimates to account for the unassigned juveniles during model fitting. For full details of the population sampling and genetic parentage assignments, see S1 Text and reference [21]. Biophysical larval dispersal model The biophysical model was physically and biologically parameterised for the locations and tim- ing of the genetic parentage study. The southern GBR has one of the most complex bathyme- tries on the east Australian coast. A dramatic narrowing of the continental shelf marks the end of the GBR, leaving its reef systems particularly exposed to oceanic influences. The Capricorn Channel divides two geomorphologically distinct coral reef systems—the Percy Islands, Keppel Islands, and Capricorn Bunker group in the inshore and midshelf and the dense Swain Reefs on the outer shelf (Fig 1A and S2 Text). Surface currents are predominantly driven northwest by strong trade winds. However, flows become more variable during the austral summer when P. maculatus spawning is most intense (S2 Text), when tropical lows can cause southward reversals [29,30]. Circulation is also driven by the poleward-flowing East Australian Current, a western boundary current that flows strongest during the summer. The East Australian Current periodically generates strong cyclonic eddy structures, which create mesoscale recirculation patterns that have a particular influence on flow in the Capricorn Channel [31]. These flows are captured by the hydrodynamic component of the biophysical model. The model is based on a temporally implicit 3D barotropic scheme, built from three nested compu- tational grids with resolutions of 1.85 km (1 nautical mile) for the whole GBR, 370 m for the PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 3 / 13 Validating larval dispersal models with genetic parentage data Fig 1. Study region and data. (A) Location of the study region in the southern Great Barrier Reef, Australia. Stars highlight sampled reefs in each region. (B) 16-mm P. maculatus settlement-stage larva. Photo credit: C. Wen. (C) Observed connectivity network between the sampled reefs. Line and reef colours indicate the identity of the source region. Note that bidirectional connections were observed between all three regions. (D) Parentage connectivity matrix for the sampled reefs. Only a few rows and columns contain connections, because only a subset of reefs were sampled. (E) Connectivity matrix generated by the consistent biophysical model simulations, for all reefs in the three regions. Each row and column correspond to a reef in one of the three sampled regions. In both matrices, colours indicate the relative strength of dispersal, with purple > green > red. Biophysical simulations give a more complete picture of regional dispersal patterns, but the genetic parentage data are empirically defensible. The data used in this figure are given in S1 Data. Is, Islands. https://doi.org/10.1371/journal.pbio.3000380.g001 three sample regions, and 74 m around focal reefs. The numerical scheme was developed from the models of James and colleagues [10] and Luick and colleagues [32]. It incorporates a sub- grid scale parameterisation of hydrodynamic impedance around GBR reefs that results in more accurate modelling of currents passing through the complex matrix of reefs in the GBR lagoon. Currents were determined hourly throughout the period July 2011 to July 2013, which encompasses all dispersal events in the parentage dataset. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 4 / 13 Validating larval dispersal models with genetic parentage data The biological larval component is an individual-based model that tracks each propagule in 5-minute time steps from spawning to settlement or mortality. Its behavioural assumptions incorporate the recommendations of North and colleagaues [33] and Staaterman and Paris [17] and include the buoyancy of pelagic eggs, realistic larval sensory ability, behaviour (onto- genetic vertical migration, swimming performance, and orientation), pelagic larval duration and mortality, and adult spawning phenology. Importantly, all of these behaviours exhibit diel, spatial, and ontogenetic variation. They also exhibit individual variation, with the behaviour of each individual larva being sampled from probability distributions. Behavioural parameters were based on empirical data for P. maculatus or the most closely related grouper species for which the required information is known. For each new moon period between July 2011 and July 2013, we simulated the release of eggs from all reef slope habitats within the study domain, creating 24 biophysical dispersal matrices (Fig 1E). To achieve the best estimates of the proba- bilities contained in these matrices, we released as many eggs at each spawning event as com- putationally possible (more than 25 million per event). We repeated these simulations using three different behavioural variants of the model. Two models were plausible representations of P. maculatus larval behaviour, based on best esti- mates for each parameter: a “consistent” behaviour model, in which each larva’s behaviour was consistent within each ontogenetic stage, based on a single sample from each parameter’s probability distribution, and a “varying” behaviour model, in which the behaviour of each larva varied within and between ontogenetic stages, by resampling from each distribution. For example, the average larvae in the consistent and varying models swim at the same depth. However, in the consistent model, a particular larva would maintain a single swimming depth during each ontogenetic stage aside from diel vertical movements, whereas in the varying model, that larva would sample a range of depths over time. Both models are a reasonable interpretation of observational evidence. The final behavioural variant was a “passive” behav- iour model, in which larvae act as neutrally buoyant particles with minimal behaviour (larvae in the consistent and varying models control vertical distribution from hatching and develop horizontal swimming abilities once the caudal fin forms). Our primary goal in simulating the three different behavioural models was not to draw conclusions about specific behavioural parameters, since this would require a much larger set. Rather, we wanted to assess the impor- tance of including larval behaviour (i.e., the passive model, compared with the consistent and varying models) and to determine whether the parentage dataset had enough statistical power to discriminate between different plausible behavioural assumptions (i.e., the varying model, compared with the consistent model). For full details of the hydrodynamic and biological com- ponents of each of the biophysical larval dispersal models, see S2 Text. Results Matching biophysical models with empirical parentage data Biophysical model predictions can be compared with parentage data in different ways, and the amount of agreement will vary between goodness of fit tests. To ensure a robust validation, we performed multiple comparisons between the observed parentage data and the biophysical simulations, with a focus on the scale and direction of larval dispersal—factors that have been identified as important for marine science and management. For full details of each goodness of fit test, see S3 Text. Matching individual larval dispersal events. An obvious initial goodness of fit test is whether the biophysical models can reproduce the particular dispersal events observed in the parentage dataset, including bidirectional dispersal between reef regions (Fig 1C). To give one example, the parentage dataset contains a larva that was sampled on South Island in the Percy PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 5 / 13 Validating larval dispersal models with genetic parentage data Islands, whose parents lived on Polmaise Reef in the Capricorn Bunker group. This larva therefore dispersed more than 230 km (straight-line distance) from its natal reef, and otolith analysis indicates that this dispersal occurred at the end of November 2011. When we look for this same event in the consistent biophysical model simulations, we find that it occurred multi- ple times (S3 Text). We repeated this process for each of the 69 assigned juveniles in the parentage dataset, searching the three biophysical models for matching events. The consistent biophysical model delivered the most matches. Altogether, 66 of the observed dispersal events in the parentage dataset could be spatiotemporally matched to simulated events in this model. The remaining three dispersal events were observed in the consistent model simulations, but not on the pre- cise spawning dates indicated by the otolith analysis (i.e., they were spatially but not temporally matched). This degree of event matching is highly unlikely by random chance (S3 Text). Fur- thermore, neither the varying nor the passive model achieved this level of matching; in fact, neither could recreate the majority of observed events (32 and 34 events could be matched, respectively). Maximum-likelihood model validation. To assess which model provided the best fit to the empirical data, we calculated the likelihood that the observed parentage assignments were generated by each of the three candidate biophysical models. A maximum-likelihood frame- work can be applied by assuming that biophysical model simulations approximate the multi- nomial probability distributions of larval destinations from each source reef. Our likelihood function (S3 Text) incorporates the sampling intensity for both juveniles and adults, the distri- bution of unsampled reefs in the metapopulation, variation in adult populations between source reefs, postsettlement mortality, and the proportion of sampled juveniles that could not be assigned to any genotyped adults, all of which influence model fit [26]. The results showed that the consistent model produced the best fit to the observed data and convincingly outper- formed both the passive and the varying models (Fig 2A). The consistent model provides reasonable predictions of the relative strength of dispersal between reefs in the southern GBR and accurate predictions of the unassigned juveniles sam- pled on each reef (Fig 2B). The confidence bounds around each observation reflect the sam- pling variance inherent in parentage datasets, in which assigned juveniles represent a small proportion of the total recruitment to a population. They also include the uncertainty around our estimates of the adult population size of (and thus the larval output from) each reef. The consistent biophysical model tends to overestimate the amount of dispersal within the regions (green markers), which includes self-recruitment, and underestimate the amount of dispersal between the regions (blue markers). It predicts a number of within-region short-distance dis- persal events that were not observed (green markers along the y-axis). This is unexpected, as juvenile sampling is often biased towards locations near sampled adult populations [9,20], making short-distance dispersal events easier to observe. The two other biophysical models provided poor fits to the data; the varying model predicted almost no between-region recruit- ment, whereas the passive model underestimated both within- and between-region recruit- ment (S3 Text). As well as producing the best fit to the data, a parametric bootstrap goodness of fit test indi- cated that the consistent model produced a statistically good fit to the parentage data. Fig 2A shows that the observed likelihood values fall within the 95% confidence bounds of expected likelihoods, if the biophysical model represents the true dispersal process (S3 Text). In other words, the consistent model would produce parentage data that are indistinguishable from our empirical dataset; this suggests that the consistent model provides an accurate representation of the species’ larval dispersal in the southern GBR. According to this same goodness of fit test, neither the varying nor the passive model provided good fits to the parentage data (Fig 2A). PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 6 / 13 Validating larval dispersal models with genetic parentage data Fig 2. Biophysical model fit. (A) Histograms show probability distributions of the likelihood of the three biophysical models, given the dataset of genetic parentage assignments. The consistent model (blue) provides the unambiguous best fit to the data. The spread of each distribution is caused by sampling and uncertainty about adult population sizes. The overlap of the consistent model with the parametric GoF distribution (shown in grey) indicates a good fit; the lack of overlap for the varying and passive model show them to be poor fits. (B) Scatterplot of observed parentage assignments against the expected number of assignments according to the consistent model. Dashed line shows the 1:1 fit line. Shaded ellipses indicate uncertainty, estimated using multinomial confidence bounds for the parentage data, and random subsampling for the biophysical data. Green indicates assignments within the same group of reefs; blue indicates assignments between reef groups, and black PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 7 / 13 Validating larval dispersal models with genetic parentage data indicates unassigned juveniles (i.e., juveniles whose parents were not among the sampled adults). The data used in this figure are given in S1 Data. GoF, goodness of fit. https://doi.org/10.1371/journal.pbio.3000380.g002 We ran a post hoc power analysis to determine whether the likelihood method in general, and our parentage assignment dataset in particular, were powerful enough to discriminate between alternative biophysical models. When faced with a simulated parentage assignment dataset that was sampled from one of our three biophysical models (at the same intensity as the observed dataset), we were able to identify the correct model 83% of the time (see S3 Text for details). The consistent and passive models were correctly identified from 97% and 94% of par- entage datasets, but the varying model was harder to identify. It was correctly identified from 58% of parentage datasets, whereas the remainder were misclassified as the consistent model. Following previous analyses [34,35], we also calculated the correlation between the observed parentage matrix and equivalent matrices sampled from the three biophysical simu- lation models. We found a consistently high correlation between the observed data and all three biophysical models (Pearson’s r > 0.95), suggesting that this type of test is not useful for identifying the best model. Larval dispersal scale and direction. The distance and direction of larval dispersal are important elements in ecological and evolutionary theory and are central parameters in marine spatial management. They drive source-sink dynamics [36], economic externalities [6,37], and the design and performance of marine reserve networks [7,38]. Useful biophysical models must provide an accurate estimate of these metrics. To measure the distance scale of recruitment predicted by the consistent biophysical model and observed in the parentage assignments, we fit isotropic larval dispersal kernels to both [26]. The two kernels broadly agree, although the consistent model simulations were best fit by a shorter dispersal kernel than the observed parentage data, and this difference was particularly apparent at distances of less than 50 km (Fig 3). However, both kernels readily predicted both within-region connections and also the 200+ km connections observed between different regions. Fig 3 also shows that the consistent biophysical model recreates the directional elements of the parentage dataset for each of the three sampling regions. Neither the passive nor the vary- ing models were able to achieve this (S3 Text). This result also illustrates the influential role played by larval behaviour in determining dispersal patterns: although all three models were forced by the same underlying oceanography, the parameterised larval behaviour of the consis- tent model was needed to accurately predict the directional patterns of observed larval dispersal. Discussion Our results compare three variants of a high-resolution biophysical larval dispersal model (consistent, passive, and varying) with high-quality genetic parentage data, using formal statis- tical comparisons. A suite of tests indicate that our sample of 1,190 P. maculatus juveniles— including 69 positive parentage assignments—could plausibly have been generated by the con- sistent biophysical model. This match holds across several different types of comparison, including event matching, model likelihood, and aggregate estimates of dispersal distance and direction. The goodness of fit is strengthened by the fact that the parentage dataset was power- ful enough to statistically exclude two alternative variants of the biophysical model. The poor fit of the passive model confirms the importance of including larval behaviour and ontogeny in biophysical models, whereas the poor fit of the varying model emphasises the importance of including the correct larval behaviour. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 8 / 13 Validating larval dispersal models with genetic parentage data Fig 3. Scale and direction of dispersal. Dispersal kernels indicating the scale of dispersal observed in the dataset of parentage assignments (grey) and the consistent model simulations (blue). Shaded regions indicate 95% confidence bounds of uncertainty, resulting from sampling variation (adults and juveniles) and uncertain adult population size. The consistent model predicts a larger proportion of short-distance dispersal—and consequently, less long-distance dispersal—than the genetic parentage data. Inset: compass plots illustrating the straight-line direction and distance travelled from each reef group by all larvae in the parentage dataset (black) and in the consistent model (blue). Concentric circles measure distances of 100 km, 200 km, and 300 km (outside circle). Histograms indicate the relative availability of sampled habitat in each direction in the other two regions. The data used in this figure are given in S1 Data. https://doi.org/10.1371/journal.pbio.3000380.g003 Our analysis only considered the fit of three biophysical models from among the very large number that could be created using different values of pelagic larval duration, larval growth rates, swimming ability, and so on. It is possible that one of these untested biophysical models offers a better fit than the consistent model. However, it is important to note that the consistent model is mechanistic and deductive, constructed using direct empirical measurements of model parameters. As a consequence, the superior fit of a model with different (and therefore less realistic) values would not necessarily mean that it offers a better description of P. macula- tus larval dispersal. When confronted with independent data on larval dispersal that was gath- ered using a completely different technique (genetic parentage), the consistent biophysical model provided a reasonable fit along a number of important dimensions. Despite some important deviation, particularly across short dispersal distances (Fig 3), these results represent a validation of this biophysical model. Quantitative comparisons between biophysical simulations and known dispersal trajecto- ries for marine fish are challenging, requiring accurate biophysical predictions over distances 2 5 that range across several orders of magnitude (10 –10 m in our parentage dataset). Past attempts to compare biophysical simulations with parentage data have been limited by small numbers of assignments and informal, qualitative comparisons [27,28,39]. None attempted to compare alternative biophysical models, and without the use of formal statistical methods, inadequate models cannot be rejected, goodness of fit cannot be assessed, and we cannot be confident that any apparent match is not a statistical artefact. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 9 / 13 Validating larval dispersal models with genetic parentage data A number of other analyses have compared biophysical models of larval dispersal with dif- ferent kinds of empirical data, although very few did so quantitatively [34]. Most have been based on recreating genetic distance matrices [11,34,40], but this type of population genetic structure is only evident at large spatial scales and across many generations of dispersal. This makes genetic distance spatially and temporally poorly suited for biophysical model validation [2]. Other comparisons used assignments tests, which identify dispersal trajectories by match- ing larval signatures (genetic or geochemical) to source patches [34,35,41]. Regional assign- ment matrices can be closely correlated with biophysical matrices, but it can be difficult to positively assign larvae at smaller scales (site-level misclassification rates can exceed 50%), because genetic and geochemical differentiation is generally limited between patches in a marine metapopulation [34,42]. This limits the strength of the validation they offer biophysical models for marine spatial management purposes, in which the most important decisions must be made at precise scales [19]. Our analyses integrate biophysical simulation models with genetic parentage data—two descriptions of larval dispersal that have come to dominate marine dispersal research. Each data type has unique strengths: biophysical models are cost-effective and can offer a complete picture of larval dispersal in a region, whereas parentage analyses offer the best direct evidence dispersal at management-relevant scales. When the spatiotemporal coverage of biophysical model predictions is reinforced by the evidence contained in genetic parentage dataset, the result is strongly complementary, opening new avenues in larval dispersal research. For exam- ple, metapopulation viability models require estimates of dispersal between reefs, and particu- larly local retention—the amount of reproductive output that returns to the natal population [5,8,24]. All presently available empirical data, including parentage assignments, can only esti- mate the amount of self-recruitment [24], but empirically validated biophysical models can effectively translate observations of recruitment into conclusions about dispersal. Parentage analyses and biophysical modelling can also inform each other by using larval dispersal simula- tions to guide and prioritise empirical sampling and by using parentage data to understand where and why model predictions fail. Finally, validated biophysical models can help explain unusual events in parentage assignment datasets. For example, the GBR dataset contains simultaneous long-distance dispersal in different directions—from the Percy Islands to the Capricorn Bunker group, for instance. These events are common in the consistent biophysical model simulations, and inspection reveals that the larvae are likely moving under the influence of contrasting inshore and offshore currents (S3 Text; S1 Animation). The observed match between an extensive genetic parentage dataset and a high-resolution dispersal simulation represents an important and overdue validation of biophysical models. Biophysical models are the foundation of important new theories in marine ecology and evolu- tion, and their predictions are being incorporated into decision-support tools for marine spa- tial planning and policy. Given this widespread usage, establishing the credibility of these models is a matter of urgency. Our observed match between models and data in the southern GBR provides reassuring support for existing applications of biophysical models worldwide, but also directions for future improvement. The methods we have developed provide a tem- plate for such future validation efforts. Supporting information S1 Text. Full description of the genetic parentage dataset, including the adult abundance surveys. (DOCX) PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 10 / 13 Validating larval dispersal models with genetic parentage data S2 Text. Full description of the biophysical larval dispersal model, including the oceano- graphic and biological components. (DOCX) S3 Text. Full description of the statistical matching methods, including event matching, likelihood model, directional matching, and dispersal kernel fitting. (DOCX) S1 Animation. Animation of long-distance bidirectional larval dispersal in the Southern Great Barrier Reef. Simulations are generated by the consistent biophysical model, recreating the 26/07/2011 spawning event. Red larvae were spawned in the Capricorn Bunker group; blue larvae were spawned in the Percy Islands. Note that these larvae were selected for illustrative purposes and are neither all the larvae that were released from these two reef groups nor the only ones that travelled between them. (GIF) S1 Data. Spreadsheet containing the data illustrated in Fig 1, Fig 2 and Fig 3. (XLSX) Acknowledgments The research benefited from discussions with M. Ashcroft, L. Bode, P. Flemons, M. James, S. King, and R. J. Pears. Author Contributions Conceptualization: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Data curation: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Formal analysis: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Funding acquisition: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Investigation: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Methodology: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Project administration: Hugo B. Harrison, Geoffrey P. Jones. Resources: Luciano B. Mason, David H. Williamson, Geoffrey P. Jones. Software: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, Severine Choukroun. Validation: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Visualization: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Writing – original draft: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. William- son, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 11 / 13 Validating larval dispersal models with genetic parentage data Writing – review & editing: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Wil- liamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. References 1. Shanks A. Pelagic larval duration and dispersal distance revisited. The Biological Bulletin. 2009; 216:373–458. https://doi.org/10.1086/BBLv216n3p373 PMID: 19556601 2. Cowen RK, Sponaugle S. Larval dispersal and marine population connectivity. 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Burgess SC, Nickols KJ, Griesemer CD, Barnett LAK, Dedrick AG, Satterthwaite EV, et al. Beyond con- nectivity: how empirical methods can quantify population persistence to improve marine protected-area design. Ecological Applications. 2014; 24:257–70. PMID: 24689139 25. Buston PM, D’Aloia CC. Marine Ecology: Reaping the Benefits of Local Dispersal. Current Biology. 2013; 23:R351–3. https://doi.org/10.1016/j.cub.2013.03.056 PMID: 23660355 26. Bode M, Williamson DH, Harrison HB, Outram N, Jones GP. Estimating dispersal kernels using genetic parentage data. Methods in Ecology and Evolution. 2017; 9:490–501. 27. Christie MR, Johnson DW, Stallings CD, Hixon MA. Self-recruitment and sweepstakes reproduction amid extensive gene flow in a coral-reef fish. Mol Ecol. 2010; 19:1042–57. https://doi.org/10.1111/j. 1365-294X.2010.04524.x PMID: 20089121 28. Le Port A, Montgomery JC, Smith ANH, Croucher AE, McLeod IM, Lavery SD. 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ICES Cooperative Research Report. Copenhagen, Denmark: Interna- tional Council for the Exploration of the Sea; 2009. Available from: https://archimer.ifremer.fr/doc/ 00157/26792/24888.pdf 34. Nolasco R, Gomes I, Peteiro L, Albuquerque R, Luna T, Dubert J, et al. Independent estimates of marine population connectivity are more concordant when accounting for uncertainties in larval origins. Scientific Reports. 2018; 8(1):2641. https://doi.org/10.1038/s41598-018-19833-w PMID: 29422505 35. Schunter C, Carbonell JC, MacPherson E, Tintore ´ J, Vijande EV, Pascual A, et al. Matching genetics with oceanography: directional gene flow in a Mediterranean fish species. Mol Ecol. 2011; 20: 5167– 5181. https://doi.org/10.1111/j.1365-294X.2011.05355.x PMID: 22097887 36. Bode M, Bode L, Armsworth PR. Larval dispersal reveals regional sources and sinks in the Great Bar- rier Reef. Mar Ecol Prog Ser. 2006; 308:17–25. 37. Bode M, Sanchirico JN, Armsworth PR. Returns from matching management resolution to ecological variation in a coral reef fishery. Proceedings of the Royal Society B: Biological Sciences. 2016; 283: 20152828. https://doi.org/10.1098/rspb.2015.2828 PMID: 26984622 38. Hastings A, Botsford LW. Comparing designs of marine reserves for fisheries and for biodiversity. Eco- logical Applications. 2003; 13:S65–S70. 39. Klein M, Teixeira S, Assis J, Serrão EA, Gonc ¸ alves EJ, Borges R. High Interannual Variability in Con- nectivity and Genetic Pool of a Temperate Clingfish Matches Oceanographic Transport Predictions. PLoS ONE. 2016; 11(12):e0165881. https://doi.org/10.1371/journal.pone.0165881 PMID: 27911952 40. Sunday JM, Popovic I, Palen WJ, Foreman MGG, Hart MW. Ocean circulation model predicts high genetic structure observed in a long-lived pelagic developer. Mol Ecol. 2014; 23:5036–47. https://doi. org/10.1111/mec.12924 PMID: 25231198 41. Alberto F, Raimondi P, Reed DC, Watson JR, Siegel DA, Mitarai S, et al. Isolation by oceanographic distance explains genetic structure for Macrocystis pyrifera in the Santa Barbara Channel. Mol Ecol. 2011; 20:2543–54. https://doi.org/10.1111/j.1365-294X.2011.05117.x PMID: 21535280 42. Saenz-Agudelo P, Jones GP, Thorrold SR, Planes S. Estimating connectivity in marine populations: an empirical evaluation of assignment tests and parentage analysis under different gene flow scenarios. Mol Ecol. 2009; 18:1765–76. https://doi.org/10.1111/j.1365-294X.2009.04109.x PMID: 19243510 PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 13 / 13 http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png PLoS Biology Public Library of Science (PLoS) Journal

Successful validation of a larval dispersal model using genetic parentage data

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Copyright: © 2019 Bode et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability: All methods are described within the paper and its Supporting Information files. All data files are available from the GitHub database (accession number doi: 10.5281/zenodo.2558693). Funding: DHW, GPJ, and HBH received funding from Australian Research Council (ARC) Linkage Grant LP100200561 (https://www.arc.gov.au/). MB received funding from Australian Research Council (ARC) Future Fellowship FT170100274 (https://www.arc.gov.au/). HBH was funded by Australian Research Council (ARC) DECRA DE160101141 (https://www.arc.gov.au/). DHW, MB, GPJ, HBH, and SC received funding from the Australian Research Council (ARC) Centre of Excellence for Coral Reef Studies (https://www.arc.gov.au/). GPJ, DHW, HBH, JML, LBM, and SC received funding from the Australian Department of Environment and Energy, through the Marine and Tropical Science Research Facility, National Environmental Research Program, and National Environmental Science Program (https://www.environment.gov.au/). The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist.
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Abstract

Larval dispersal is a critically important yet enigmatic process in marine ecology, evolution, and conservation. Determining the distance and direction that tiny larvae travel in the open ocean continues to be a challenge. Our current understanding of larval dispersal patterns at OPENACCESS management-relevant scales is principally and separately informed by genetic parentage Citation: Bode M, Leis JM, Mason LB, Williamson data and biological-oceanographic (biophysical) models. Parentage datasets provide clear DH, Harrison HB, Choukroun S, et al. (2019) Successful validation of a larval dispersal model evidence of individual larval dispersal events, but their findings are spatially and temporally using genetic parentage data. PLoS Biol 17(7): limited. Biophysical models offer a more complete picture of dispersal patterns at regional e3000380. https://doi.org/10.1371/journal. scales but are of uncertain accuracy. Here, we develop statistical techniques that integrate pbio.3000380 these two important sources of information on larval dispersal. We then apply these meth- Academic Editor: Steven D. Gaines, University of ods to an extensive genetic parentage dataset to successfully validate a high-resolution bio- California, UNITED STATES physical model for the economically important reef fish species Plectropomus maculatus in Received: January 16, 2019 the southern Great Barrier Reef. Our results demonstrate that biophysical models can pro- Accepted: July 2, 2019 vide accurate descriptions of larval dispersal at spatial and temporal scales that are relevant Published: July 12, 2019 to management. They also show that genetic parentage datasets provide enough statistical power to exclude poor biophysical models. Biophysical models that included species-spe- Copyright:© 2019 Bode et al. This is an open access article distributed under the terms of the cific larval behaviour provided markedly better fits to the parentage data than assuming Creative Commons Attribution License, which passive behaviour, but incorrect behavioural assumptions led to worse predictions than permits unrestricted use, distribution, and ignoring behaviour altogether. Our approach capitalises on the complementary strengths of reproduction in any medium, provided the original genetic parentage datasets and high-resolution biophysical models to produce an accurate author and source are credited. picture of larval dispersal patterns at regional scales. The results provide essential empirical Data Availability Statement: All methods are support for the use of accurately parameterised biophysical larval dispersal models in described within the paper and its Supporting Information files. All data files are available marine spatial planning and management. from the GitHub database (accession number doi: 10.5281/zenodo.2558693). Funding: DHW, GPJ, and HBH received funding from Australian Research Council (ARC) Linkage Grant LP100200561 (https://www.arc.gov.au/). MB received funding from Australian Research Council (ARC) Future Fellowship FT170100274 (https:// www.arc.gov.au/). HBH was funded by Australian PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 1 / 13 Validating larval dispersal models with genetic parentage data Research Council (ARC) DECRA DE160101141 Introduction (https://www.arc.gov.au/). DHW, MB, GPJ, HBH, Most marine species have a brief pelagic larval stage that is spent dispersing in open water and SC received funding from the Australian [1,2]. Because suitable habitat is often patchy and isolated, larval dispersal is the primary pro- Research Council (ARC) Centre of Excellence for Coral Reef Studies (https://www.arc.gov.au/). GPJ, cess through which populations of demersal species are connected and replenished. Accurately DHW, HBH, JML, LBM, and SC received funding predicting where larvae settle at the end of their dispersal stage is essential for understanding from the Australian Department of Environment the ecology and evolution of marine populations and species [3,4] and for making decisions and Energy, through the Marine and Tropical about their conservation and sustainable exploitation [5–8]. To this end, recent advances in Science Research Facility, National Environmental biological oceanography and genetics have provided separate and revolutionary insights into Research Program, and National Environmental Science Program (https://www.environment.gov. larval dispersal and population connectivity in the coastal oceans [9]. au/). The funders had no role in study design, data Coupled biological-oceanographic models (hereafter “biophysical” models) can compre- collection and analysis, decision to publish, or hensively describe larval dispersal patterns, simulating the movement of billions of larvae preparation of the manuscript. across entire seascapes [3,10,11]. Increasingly sophisticated biophysical models, with higher Competing interests: The authors have declared resolution and incorporating knowledge of larval biology and behaviour, are widely advocated that no competing interests exist. as decision-support tools for coastal ecosystem management [12–16]. Although the oceano- graphic components of these models are usually validated, their biological components are often underdeveloped and uncertain [17,18]. The resulting model predictions are therefore of unknown accuracy and precision [19]. Genetic parentage techniques have recently been applied to directly measure larval dispersal patterns at both local and regional scales [7,20–22]. Parentage data have provided evidence for local retention of larvae [20] and for multidirectional dispersal over hundreds of kilometres [21,22]. They have also supported marine spatial management and have informed the design of marine reserve networks [7,23]. Although parentage assignments provide strong evidence of specific dispersal events, constraints on the spatial and temporal scales of population sam- pling mean that only a fraction of potential dispersal pathways can be resolved. Nonetheless, parentage datasets have the potential to provide an independent test of biophysical model pre- dictions and to decide whether these models provide credible representations of true larval dis- persal patterns [9]. The validation of biophysical models with parentage data is a crucial next step in marine spatial ecology and conservation [2,5,19,24–26]. Genetic parentage data provide an opportu- nity to validate biophysical models at the spatial and temporal scales that are most relevant to management, using the distance, direction, and timing of known dispersal events. Given that both biophysical models and parentage data describe the sources and destinations of individ- ual larvae, the process of statistical validation is conceptually straightforward. However, it is logistically demanding to assemble the necessary data for several reasons. First, genetic parent- age assignments are expensive to obtain at the requisite intensity and spatial scale [9]. If there are too few assignments, the parentage dataset may not offer the statistical power needed for a rigorous test [27,28]. Second, it is challenging to produce a biophysical model at both the reso- lution and scale needed to match observed assignments, as the observed dispersal events include both small-scale retention of larvae in and around their natal population and long-dis- tance connections over hundreds of kilometres. Third, because ocean currents are often highly variable through time, the model must provide a close temporal match to the measured larval dispersal events [19]. Finally, to isolate the significance of larval biology and behaviour, parent- age data should be tested against a range of different biophysical models, from passive dispersal models to those incorporating the biological and behavioural traits of the study species [17,18,25]. Here, we resolve each of these challenges to validate a biophysical model with a matching genetic parentage dataset. We parameterise a high-resolution biophysical model of larval dis- persal across the southern and central Great Barrier Reef (GBR) for bar-cheeked coral trout PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 2 / 13 Validating larval dispersal models with genetic parentage data (also called the spotted coral grouper, P. maculatus, Serranidae). We develop novel quantita- tive validation techniques and use them to rigorously test this model against an intensive and independent genetic parentage survey of P. maculatus (previously published in [21]). Our results represent a formal validation of a regional-scale biophysical model using genetic par- entage data, thereby integrating two important and complementary sources of larval dispersal information. Materials and methods Genetic parentage assignments and population sampling Between September 2011 and August 2013, a total of 880 adult and 1,190 juvenile P. maculatus were sampled across three reef regions in the southern GBR: the Keppel Islands, the Percy Islands, and the Capricorn Bunker group (Fig 1A and 1B). A panel of 23 microsatellite loci iden- tified 69 parent–offspring relationships within the sample, connecting 18 different patch reefs separated by distances ranging from a few hundred metres to over 200 km. The observed larval dispersal network revealed self-recruitment within each region (including to individual natal reefs) and longer-distance multidirectional dispersal between regions (Fig 1C), creating an observed parentage dispersal matrix (Fig 1D). Each assigned juvenile and a subset of 314 unas- signed juveniles were aged from daily otolith growth rings to determine both the spawn date and the pelagic larval duration. This allowed a closer parameterisation of the biophysical model and precise temporal match between empirical dispersal vectors and the biophysical model. Underwater visual census (UVC) surveys were conducted on reefs within each of the three regions to establish reef-specific estimates of adult population size. This was combined with P. maculatus fecundity data to estimate the number of propagules released from each reef in the biophysical model. The species’ relative abundance was highly variable among reefs, particu- larly between reserve and nonreserve reefs. For reefs within the study domain where popula- tions were not surveyed, adult densities were approximated by the average density of surveyed reefs with the same protected status within their region. The biophysical model used these pop- ulation estimates to account for the unassigned juveniles during model fitting. For full details of the population sampling and genetic parentage assignments, see S1 Text and reference [21]. Biophysical larval dispersal model The biophysical model was physically and biologically parameterised for the locations and tim- ing of the genetic parentage study. The southern GBR has one of the most complex bathyme- tries on the east Australian coast. A dramatic narrowing of the continental shelf marks the end of the GBR, leaving its reef systems particularly exposed to oceanic influences. The Capricorn Channel divides two geomorphologically distinct coral reef systems—the Percy Islands, Keppel Islands, and Capricorn Bunker group in the inshore and midshelf and the dense Swain Reefs on the outer shelf (Fig 1A and S2 Text). Surface currents are predominantly driven northwest by strong trade winds. However, flows become more variable during the austral summer when P. maculatus spawning is most intense (S2 Text), when tropical lows can cause southward reversals [29,30]. Circulation is also driven by the poleward-flowing East Australian Current, a western boundary current that flows strongest during the summer. The East Australian Current periodically generates strong cyclonic eddy structures, which create mesoscale recirculation patterns that have a particular influence on flow in the Capricorn Channel [31]. These flows are captured by the hydrodynamic component of the biophysical model. The model is based on a temporally implicit 3D barotropic scheme, built from three nested compu- tational grids with resolutions of 1.85 km (1 nautical mile) for the whole GBR, 370 m for the PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 3 / 13 Validating larval dispersal models with genetic parentage data Fig 1. Study region and data. (A) Location of the study region in the southern Great Barrier Reef, Australia. Stars highlight sampled reefs in each region. (B) 16-mm P. maculatus settlement-stage larva. Photo credit: C. Wen. (C) Observed connectivity network between the sampled reefs. Line and reef colours indicate the identity of the source region. Note that bidirectional connections were observed between all three regions. (D) Parentage connectivity matrix for the sampled reefs. Only a few rows and columns contain connections, because only a subset of reefs were sampled. (E) Connectivity matrix generated by the consistent biophysical model simulations, for all reefs in the three regions. Each row and column correspond to a reef in one of the three sampled regions. In both matrices, colours indicate the relative strength of dispersal, with purple > green > red. Biophysical simulations give a more complete picture of regional dispersal patterns, but the genetic parentage data are empirically defensible. The data used in this figure are given in S1 Data. Is, Islands. https://doi.org/10.1371/journal.pbio.3000380.g001 three sample regions, and 74 m around focal reefs. The numerical scheme was developed from the models of James and colleagues [10] and Luick and colleagues [32]. It incorporates a sub- grid scale parameterisation of hydrodynamic impedance around GBR reefs that results in more accurate modelling of currents passing through the complex matrix of reefs in the GBR lagoon. Currents were determined hourly throughout the period July 2011 to July 2013, which encompasses all dispersal events in the parentage dataset. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 4 / 13 Validating larval dispersal models with genetic parentage data The biological larval component is an individual-based model that tracks each propagule in 5-minute time steps from spawning to settlement or mortality. Its behavioural assumptions incorporate the recommendations of North and colleagaues [33] and Staaterman and Paris [17] and include the buoyancy of pelagic eggs, realistic larval sensory ability, behaviour (onto- genetic vertical migration, swimming performance, and orientation), pelagic larval duration and mortality, and adult spawning phenology. Importantly, all of these behaviours exhibit diel, spatial, and ontogenetic variation. They also exhibit individual variation, with the behaviour of each individual larva being sampled from probability distributions. Behavioural parameters were based on empirical data for P. maculatus or the most closely related grouper species for which the required information is known. For each new moon period between July 2011 and July 2013, we simulated the release of eggs from all reef slope habitats within the study domain, creating 24 biophysical dispersal matrices (Fig 1E). To achieve the best estimates of the proba- bilities contained in these matrices, we released as many eggs at each spawning event as com- putationally possible (more than 25 million per event). We repeated these simulations using three different behavioural variants of the model. Two models were plausible representations of P. maculatus larval behaviour, based on best esti- mates for each parameter: a “consistent” behaviour model, in which each larva’s behaviour was consistent within each ontogenetic stage, based on a single sample from each parameter’s probability distribution, and a “varying” behaviour model, in which the behaviour of each larva varied within and between ontogenetic stages, by resampling from each distribution. For example, the average larvae in the consistent and varying models swim at the same depth. However, in the consistent model, a particular larva would maintain a single swimming depth during each ontogenetic stage aside from diel vertical movements, whereas in the varying model, that larva would sample a range of depths over time. Both models are a reasonable interpretation of observational evidence. The final behavioural variant was a “passive” behav- iour model, in which larvae act as neutrally buoyant particles with minimal behaviour (larvae in the consistent and varying models control vertical distribution from hatching and develop horizontal swimming abilities once the caudal fin forms). Our primary goal in simulating the three different behavioural models was not to draw conclusions about specific behavioural parameters, since this would require a much larger set. Rather, we wanted to assess the impor- tance of including larval behaviour (i.e., the passive model, compared with the consistent and varying models) and to determine whether the parentage dataset had enough statistical power to discriminate between different plausible behavioural assumptions (i.e., the varying model, compared with the consistent model). For full details of the hydrodynamic and biological com- ponents of each of the biophysical larval dispersal models, see S2 Text. Results Matching biophysical models with empirical parentage data Biophysical model predictions can be compared with parentage data in different ways, and the amount of agreement will vary between goodness of fit tests. To ensure a robust validation, we performed multiple comparisons between the observed parentage data and the biophysical simulations, with a focus on the scale and direction of larval dispersal—factors that have been identified as important for marine science and management. For full details of each goodness of fit test, see S3 Text. Matching individual larval dispersal events. An obvious initial goodness of fit test is whether the biophysical models can reproduce the particular dispersal events observed in the parentage dataset, including bidirectional dispersal between reef regions (Fig 1C). To give one example, the parentage dataset contains a larva that was sampled on South Island in the Percy PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 5 / 13 Validating larval dispersal models with genetic parentage data Islands, whose parents lived on Polmaise Reef in the Capricorn Bunker group. This larva therefore dispersed more than 230 km (straight-line distance) from its natal reef, and otolith analysis indicates that this dispersal occurred at the end of November 2011. When we look for this same event in the consistent biophysical model simulations, we find that it occurred multi- ple times (S3 Text). We repeated this process for each of the 69 assigned juveniles in the parentage dataset, searching the three biophysical models for matching events. The consistent biophysical model delivered the most matches. Altogether, 66 of the observed dispersal events in the parentage dataset could be spatiotemporally matched to simulated events in this model. The remaining three dispersal events were observed in the consistent model simulations, but not on the pre- cise spawning dates indicated by the otolith analysis (i.e., they were spatially but not temporally matched). This degree of event matching is highly unlikely by random chance (S3 Text). Fur- thermore, neither the varying nor the passive model achieved this level of matching; in fact, neither could recreate the majority of observed events (32 and 34 events could be matched, respectively). Maximum-likelihood model validation. To assess which model provided the best fit to the empirical data, we calculated the likelihood that the observed parentage assignments were generated by each of the three candidate biophysical models. A maximum-likelihood frame- work can be applied by assuming that biophysical model simulations approximate the multi- nomial probability distributions of larval destinations from each source reef. Our likelihood function (S3 Text) incorporates the sampling intensity for both juveniles and adults, the distri- bution of unsampled reefs in the metapopulation, variation in adult populations between source reefs, postsettlement mortality, and the proportion of sampled juveniles that could not be assigned to any genotyped adults, all of which influence model fit [26]. The results showed that the consistent model produced the best fit to the observed data and convincingly outper- formed both the passive and the varying models (Fig 2A). The consistent model provides reasonable predictions of the relative strength of dispersal between reefs in the southern GBR and accurate predictions of the unassigned juveniles sam- pled on each reef (Fig 2B). The confidence bounds around each observation reflect the sam- pling variance inherent in parentage datasets, in which assigned juveniles represent a small proportion of the total recruitment to a population. They also include the uncertainty around our estimates of the adult population size of (and thus the larval output from) each reef. The consistent biophysical model tends to overestimate the amount of dispersal within the regions (green markers), which includes self-recruitment, and underestimate the amount of dispersal between the regions (blue markers). It predicts a number of within-region short-distance dis- persal events that were not observed (green markers along the y-axis). This is unexpected, as juvenile sampling is often biased towards locations near sampled adult populations [9,20], making short-distance dispersal events easier to observe. The two other biophysical models provided poor fits to the data; the varying model predicted almost no between-region recruit- ment, whereas the passive model underestimated both within- and between-region recruit- ment (S3 Text). As well as producing the best fit to the data, a parametric bootstrap goodness of fit test indi- cated that the consistent model produced a statistically good fit to the parentage data. Fig 2A shows that the observed likelihood values fall within the 95% confidence bounds of expected likelihoods, if the biophysical model represents the true dispersal process (S3 Text). In other words, the consistent model would produce parentage data that are indistinguishable from our empirical dataset; this suggests that the consistent model provides an accurate representation of the species’ larval dispersal in the southern GBR. According to this same goodness of fit test, neither the varying nor the passive model provided good fits to the parentage data (Fig 2A). PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 6 / 13 Validating larval dispersal models with genetic parentage data Fig 2. Biophysical model fit. (A) Histograms show probability distributions of the likelihood of the three biophysical models, given the dataset of genetic parentage assignments. The consistent model (blue) provides the unambiguous best fit to the data. The spread of each distribution is caused by sampling and uncertainty about adult population sizes. The overlap of the consistent model with the parametric GoF distribution (shown in grey) indicates a good fit; the lack of overlap for the varying and passive model show them to be poor fits. (B) Scatterplot of observed parentage assignments against the expected number of assignments according to the consistent model. Dashed line shows the 1:1 fit line. Shaded ellipses indicate uncertainty, estimated using multinomial confidence bounds for the parentage data, and random subsampling for the biophysical data. Green indicates assignments within the same group of reefs; blue indicates assignments between reef groups, and black PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 7 / 13 Validating larval dispersal models with genetic parentage data indicates unassigned juveniles (i.e., juveniles whose parents were not among the sampled adults). The data used in this figure are given in S1 Data. GoF, goodness of fit. https://doi.org/10.1371/journal.pbio.3000380.g002 We ran a post hoc power analysis to determine whether the likelihood method in general, and our parentage assignment dataset in particular, were powerful enough to discriminate between alternative biophysical models. When faced with a simulated parentage assignment dataset that was sampled from one of our three biophysical models (at the same intensity as the observed dataset), we were able to identify the correct model 83% of the time (see S3 Text for details). The consistent and passive models were correctly identified from 97% and 94% of par- entage datasets, but the varying model was harder to identify. It was correctly identified from 58% of parentage datasets, whereas the remainder were misclassified as the consistent model. Following previous analyses [34,35], we also calculated the correlation between the observed parentage matrix and equivalent matrices sampled from the three biophysical simu- lation models. We found a consistently high correlation between the observed data and all three biophysical models (Pearson’s r > 0.95), suggesting that this type of test is not useful for identifying the best model. Larval dispersal scale and direction. The distance and direction of larval dispersal are important elements in ecological and evolutionary theory and are central parameters in marine spatial management. They drive source-sink dynamics [36], economic externalities [6,37], and the design and performance of marine reserve networks [7,38]. Useful biophysical models must provide an accurate estimate of these metrics. To measure the distance scale of recruitment predicted by the consistent biophysical model and observed in the parentage assignments, we fit isotropic larval dispersal kernels to both [26]. The two kernels broadly agree, although the consistent model simulations were best fit by a shorter dispersal kernel than the observed parentage data, and this difference was particularly apparent at distances of less than 50 km (Fig 3). However, both kernels readily predicted both within-region connections and also the 200+ km connections observed between different regions. Fig 3 also shows that the consistent biophysical model recreates the directional elements of the parentage dataset for each of the three sampling regions. Neither the passive nor the vary- ing models were able to achieve this (S3 Text). This result also illustrates the influential role played by larval behaviour in determining dispersal patterns: although all three models were forced by the same underlying oceanography, the parameterised larval behaviour of the consis- tent model was needed to accurately predict the directional patterns of observed larval dispersal. Discussion Our results compare three variants of a high-resolution biophysical larval dispersal model (consistent, passive, and varying) with high-quality genetic parentage data, using formal statis- tical comparisons. A suite of tests indicate that our sample of 1,190 P. maculatus juveniles— including 69 positive parentage assignments—could plausibly have been generated by the con- sistent biophysical model. This match holds across several different types of comparison, including event matching, model likelihood, and aggregate estimates of dispersal distance and direction. The goodness of fit is strengthened by the fact that the parentage dataset was power- ful enough to statistically exclude two alternative variants of the biophysical model. The poor fit of the passive model confirms the importance of including larval behaviour and ontogeny in biophysical models, whereas the poor fit of the varying model emphasises the importance of including the correct larval behaviour. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 8 / 13 Validating larval dispersal models with genetic parentage data Fig 3. Scale and direction of dispersal. Dispersal kernels indicating the scale of dispersal observed in the dataset of parentage assignments (grey) and the consistent model simulations (blue). Shaded regions indicate 95% confidence bounds of uncertainty, resulting from sampling variation (adults and juveniles) and uncertain adult population size. The consistent model predicts a larger proportion of short-distance dispersal—and consequently, less long-distance dispersal—than the genetic parentage data. Inset: compass plots illustrating the straight-line direction and distance travelled from each reef group by all larvae in the parentage dataset (black) and in the consistent model (blue). Concentric circles measure distances of 100 km, 200 km, and 300 km (outside circle). Histograms indicate the relative availability of sampled habitat in each direction in the other two regions. The data used in this figure are given in S1 Data. https://doi.org/10.1371/journal.pbio.3000380.g003 Our analysis only considered the fit of three biophysical models from among the very large number that could be created using different values of pelagic larval duration, larval growth rates, swimming ability, and so on. It is possible that one of these untested biophysical models offers a better fit than the consistent model. However, it is important to note that the consistent model is mechanistic and deductive, constructed using direct empirical measurements of model parameters. As a consequence, the superior fit of a model with different (and therefore less realistic) values would not necessarily mean that it offers a better description of P. macula- tus larval dispersal. When confronted with independent data on larval dispersal that was gath- ered using a completely different technique (genetic parentage), the consistent biophysical model provided a reasonable fit along a number of important dimensions. Despite some important deviation, particularly across short dispersal distances (Fig 3), these results represent a validation of this biophysical model. Quantitative comparisons between biophysical simulations and known dispersal trajecto- ries for marine fish are challenging, requiring accurate biophysical predictions over distances 2 5 that range across several orders of magnitude (10 –10 m in our parentage dataset). Past attempts to compare biophysical simulations with parentage data have been limited by small numbers of assignments and informal, qualitative comparisons [27,28,39]. None attempted to compare alternative biophysical models, and without the use of formal statistical methods, inadequate models cannot be rejected, goodness of fit cannot be assessed, and we cannot be confident that any apparent match is not a statistical artefact. PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 9 / 13 Validating larval dispersal models with genetic parentage data A number of other analyses have compared biophysical models of larval dispersal with dif- ferent kinds of empirical data, although very few did so quantitatively [34]. Most have been based on recreating genetic distance matrices [11,34,40], but this type of population genetic structure is only evident at large spatial scales and across many generations of dispersal. This makes genetic distance spatially and temporally poorly suited for biophysical model validation [2]. Other comparisons used assignments tests, which identify dispersal trajectories by match- ing larval signatures (genetic or geochemical) to source patches [34,35,41]. Regional assign- ment matrices can be closely correlated with biophysical matrices, but it can be difficult to positively assign larvae at smaller scales (site-level misclassification rates can exceed 50%), because genetic and geochemical differentiation is generally limited between patches in a marine metapopulation [34,42]. This limits the strength of the validation they offer biophysical models for marine spatial management purposes, in which the most important decisions must be made at precise scales [19]. Our analyses integrate biophysical simulation models with genetic parentage data—two descriptions of larval dispersal that have come to dominate marine dispersal research. Each data type has unique strengths: biophysical models are cost-effective and can offer a complete picture of larval dispersal in a region, whereas parentage analyses offer the best direct evidence dispersal at management-relevant scales. When the spatiotemporal coverage of biophysical model predictions is reinforced by the evidence contained in genetic parentage dataset, the result is strongly complementary, opening new avenues in larval dispersal research. For exam- ple, metapopulation viability models require estimates of dispersal between reefs, and particu- larly local retention—the amount of reproductive output that returns to the natal population [5,8,24]. All presently available empirical data, including parentage assignments, can only esti- mate the amount of self-recruitment [24], but empirically validated biophysical models can effectively translate observations of recruitment into conclusions about dispersal. Parentage analyses and biophysical modelling can also inform each other by using larval dispersal simula- tions to guide and prioritise empirical sampling and by using parentage data to understand where and why model predictions fail. Finally, validated biophysical models can help explain unusual events in parentage assignment datasets. For example, the GBR dataset contains simultaneous long-distance dispersal in different directions—from the Percy Islands to the Capricorn Bunker group, for instance. These events are common in the consistent biophysical model simulations, and inspection reveals that the larvae are likely moving under the influence of contrasting inshore and offshore currents (S3 Text; S1 Animation). The observed match between an extensive genetic parentage dataset and a high-resolution dispersal simulation represents an important and overdue validation of biophysical models. Biophysical models are the foundation of important new theories in marine ecology and evolu- tion, and their predictions are being incorporated into decision-support tools for marine spa- tial planning and policy. Given this widespread usage, establishing the credibility of these models is a matter of urgency. Our observed match between models and data in the southern GBR provides reassuring support for existing applications of biophysical models worldwide, but also directions for future improvement. The methods we have developed provide a tem- plate for such future validation efforts. Supporting information S1 Text. Full description of the genetic parentage dataset, including the adult abundance surveys. (DOCX) PLOS Biology | https://doi.org/10.1371/journal.pbio.3000380 July 12, 2019 10 / 13 Validating larval dispersal models with genetic parentage data S2 Text. Full description of the biophysical larval dispersal model, including the oceano- graphic and biological components. (DOCX) S3 Text. Full description of the statistical matching methods, including event matching, likelihood model, directional matching, and dispersal kernel fitting. (DOCX) S1 Animation. Animation of long-distance bidirectional larval dispersal in the Southern Great Barrier Reef. Simulations are generated by the consistent biophysical model, recreating the 26/07/2011 spawning event. Red larvae were spawned in the Capricorn Bunker group; blue larvae were spawned in the Percy Islands. Note that these larvae were selected for illustrative purposes and are neither all the larvae that were released from these two reef groups nor the only ones that travelled between them. (GIF) S1 Data. Spreadsheet containing the data illustrated in Fig 1, Fig 2 and Fig 3. (XLSX) Acknowledgments The research benefited from discussions with M. Ashcroft, L. Bode, P. Flemons, M. James, S. King, and R. J. Pears. Author Contributions Conceptualization: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Data curation: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Formal analysis: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Funding acquisition: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Investigation: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Methodology: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, David H. Williamson, Hugo B. Harrison, Severine Choukroun, Geoffrey P. Jones. Project administration: Hugo B. Harrison, Geoffrey P. Jones. Resources: Luciano B. Mason, David H. Williamson, Geoffrey P. Jones. Software: Michael Bode, Jeffrey M. Leis, Luciano B. Mason, Severine Choukroun. 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