High-frequency variability dominates potential connectivity between remote coral reefs

Coral larval dispersal establishes connectivity between reefs, but larval ﬂ uxes vary over timescales from daily to multidecadal due to oceanographic variability. Using a 2-km-resolution ocean model, we simulate daily spawning events from 1993 to 2019 and assess the potential connectivity between all reefs in the tropical south-west Indian Ocean. Although there is a signi ﬁ cant seasonal cycle in potential connectivity, day-to-day variability generally dominates. Larval dispersal pathways on any particular day provide limited information about the dispersal pathways a few days later. The magnitude of this high-frequency variability depends on the local geography and oceanography, with small and isolated reefs generally subject to the most variability. Stochastic oceanographic variability introduces considerable uncertainty to dispersal predictions, imposing fundamental limitations on what simulations can tell us about inter-reef connectivity. Protracted spawning over only a few days can signi ﬁ cantly reduce variability associated with the likelihood of a larva settling. The duration of spawning is therefore a more important parameter in modeling coral connectivity than the exact timing of spawning onset. Finally, we ﬁ nd that a small proportion of spawning events account for the majority of settling larvae, particularly at remote islands, and demonstrate that a time-mean picture of dispersal may be inappropriate for predicting demographic and genetic connectivity. Given the diversity of coral reef environments in the southwest Indian Ocean, we expect that these results will apply to inter-reef coral connectivity across the tropics more broadly, as well as other weakly swimming reef taxa with the potential for long-distance dispersal. Although mature corals are sessile, connectivity can be established between coral reefs through the drift of coral larvae

Edmunds 2023) and is theorized to reduce population growth rates and genetic variance (Hedgecock 1994;Watson et al. 2012).
Despite its importance, coral larval dispersal (and its variability) is challenging to quantify (Edmunds et al. 2018).Genetic indices can be used to infer migration rates between populations, but these approaches struggle with the low genetic differentiation characteristic of many marine taxa, are generally resource intensive, and have limited capacity to capture connectivity variability (Faubet et al. 2007;Lowe and Allendorf 2010).Numerically modeling larval dispersal, usually through Lagrangian approaches, is therefore a primary source of dispersal estimates for coral connectivity.
As broadcasting corals spawn infrequently in shortduration spawning events (Baird et al. 2009), most numerical modeling studies simulate spawning during a certain known (or suspected) spawning period, repeated annually over a certain number of years.Potential connectivity is then often integrated across each spawning period, with some studies focusing on the time-mean or seasonal picture (e.g., Wood et al. 2014;Gamoyo et al. 2019), while others also investigate interannual variability, with varying degrees of complexity (e.g., Wood et al. 2016;Thompson et al. 2018).However, few studies have investigated the consequences of high-frequency potential connectivity variability for ecological applications.Due to the chaotic nature of ocean turbulence, high-frequency current variability introduces considerable, fundamental uncertainty into dispersal predictions, but this uncertainty is poorly understood and appreciated.
The coral reefs of the tropical southwest Indian Ocean represent almost 7% of the global total, but are relatively poorly studied, with only around 3% of observations coming from the region (Souter et al. 2021).Broadcast spawning is thought to generally occur during the northwest monsoon between October and March, although temporal and spatial coverage of spawning observations is poor (Baird et al. 2021).Reef systems within the southwest Indian Ocean are highly diverse (ranging from remote coral islands such as Seychelles, to extensive linear reef systems along the coasts of Kenya and Tanzania), and are exposed to a network of wind-driven surface currents, including the zonal South Equatorial Current and Countercurrent, and a powerful western boundary current (the East Africa Coastal Current) (Fig. 1).Surface currents also follow a strong seasonal cycle, imposed by seasonally reversing monsoonal winds.The geomorphologic and oceanographic diversity in this region therefore means that reef systems in the southwest Indian Ocean are analogous to many other coral reefs across the world, providing an excellent case study for investigating connectivity variability and its drivers.In this study, we set out to answer the following key questions: 1. How does potential connectivity between reefs vary over day-to-day, seasonal, and interannual timescales across the southwest Indian Ocean?
2. What are the physical oceanographic drivers of this variability?3. To what extent is this variability important for understanding demographic and genetic connectivity?
To answer these questions, we present a modeled potential connectivity time series, spanning all coral reefs in the tropical southwest Indian Ocean, as a function of spawning time.We consider larval fluxes between over 8000 4-km 2 reef cells, across 27 yr (for a total of almost 10,000 individual daily spawning events), based on a state-of-the-art 2-km-resolution regional ocean model (Vogt-Vincent and Johnson 2023b).This is the highest resolution (spatial and temporal) connectivity dataset ever generated in this region, allowing us to carry out a detailed investigation into the temporal variability of interreef potential connectivity across scales and oceanographic regimes.The potential connectivity matrices and hydrodynamic data used in this study are freely available, and our analyses can be rerun under different biological parameterizations using the associated code (see Data availability statement section).

Hydrodynamical and larval dispersal models
We generated potential connectivity matrices for coral larval dispersal across the southwest Indian Ocean using Simulating Ecosystem Connectivity with WINDS (SECoW).SECoW is a modeling system combining hydrodynamic data from WINDS (Vogt-Vincent and Johnson 2023b), a regional ocean simulation for the southwest Indian Ocean, with a larval dispersal model based on OceanParcels (Lange and van Sebille 2017;Delandmeter and van Sebille 2019).WINDS is a 1/50 configuration of the CROCO ocean model (Auclair et al. 2019) spanning all coral reefs in the southwest tropical Indian Ocean and is described and validated by Vogt-Vincent and Johnson (2023b).WINDS is forced daily at the boundaries by 3D currents, temperature and salinity from the CMEMS 1/12 global ocean reanalysis and analysis (Lellouche et al. 2021) and 10 tidal constituents (elevations and barotropic currents) from the TPXO9-atlas (Egbert and Erofeeva 2002), and hourly at the surface by the ERA-5 atmospheric reanalysis (Hersbach et al. 2020).SECoW uses 30-min frequency surface current output from WINDS for the years 1993-2020, thereby resolving hydrodynamic variability ranging from tidal to interannual.
The larval dispersal component of SECoW represents coral larvae as positively buoyant, otherwise passive particles, which are advected by surface currents for 120 d after spawning, using a fourth-order explicit Runge-Kutta scheme in OceanParcels.We identified 8088 2 Â 2 km reef cells on the WINDS grid (Fig. 1), and released 1024 particles per cell per day (Supplementary Fig. S1), simulating daily spawning events at midnight from 01 January 1993 to 31 December 2019, for a total of 9861 domain-wide spawning events.We assumed constant fecundity per unit area of reef, and the virtual larvae generated by each spawning event are spread evenly across the 1024 particles released per cell.Following Connolly and Baird (2010), we assumed that coral larvae gain and lose competency at constant rates after a minimum pre-competency period, and die following a time-dependent mortality rate.We further assumed that competent larvae settle at a rate proportional to the reef cover in the occupied cell, which we call the settling rate.This accounts for the capacity of upstream reefs to reduce the larval supply to downstream reefs, while sensibly handling subgrid-scale reef coverage and allowing for the possibility of a larva passing over a reef without settling (Hata et al. 2017).Biological parameters are based on Platygyra daedalea, a widespread coral in the southwest Indian Ocean with an intermediate competency period and mortality rate (Connolly and Baird 2010; Supplementary Fig. S2, Table S1).
The results described in this study are robust with respect to biological parameters (Supplementary Table S2), but alternate versions of the figures in this manuscript for the other four coral species described by Connolly and Baird (2010) are included in the Supplementary Dataset 1.
In this study, we computed two key metrics: • Flux, F ijk : The number of larvae spawning from location i at event k, and settling at location j. • Source strength, S ik : The proportion of larvae from location i and spawning event k that settle anywhere.
We focus mainly on the source strength matrix S ik for individual reef cells.Contrary to flux, source strength is a function of just one location (rather than a pair of locations), so it is more straightforward to investigate geographic dependence and physical oceanographic drivers.When considering the consequences of our findings for connectivity studies, we also consider the flux matrix F ijk for reef groups.The full flux matrix in SECoW has 8088 Â 8088 Â 9861 ≈ 645 Â 10 9 elements so, for tractability, we have formed 180 reef groups (see Supplementary Dataset 1) using an agglomerative clustering algorithm, resulting in a more manageable 180 Â 180 Â 9861 matrix.Full details can be found in the Supplementary Material, Headings 1-3.

High-frequency variability
We quantified the high-frequency (day-to-day) variability of source strength as the 1-d lagged temporal autocorrelation, r 1d .If r 1d is high, source strength on day k is a good predictor of the source strength on day k þ 1. Conversely, low r 1d indicates very high day-to-day reef connectivity variability.Examples are shown in Fig. 2c-e; for instance, compare the relatively steady source strength near Tanga in Tanzania (r 1d ¼ 0:86) to the sporadic source strength at Rémire Island in Seychelles (r 1d ¼ 0:24).We computed r 1d independently for each cell, using the full 1993-2019 daily time series.
To investigate the physical drivers of r 1d , we first split all reef cells into six groups based on their hydrogeography, as different physical drivers may dominate in different oceanographic regimes.Within each group, we then carried out ordinary least-squares regression with seven potential explanatory variables we hypothesized could explain spatial variation in r 1d , using the statsmodels Python package.These explanatory variables were (1) mean surface current speed, (2) mean surface high-frequency (1/30-1 d À1 ) current speed, (3) mean surface sub-daily current speed, (4) nearby reef fraction, (5) weighted downstream connection distance, (6) distance to land, and (7) mean source strength.Further details can be found in the Supplementary Material, Heading 4. These variables were all strongly positively skewed, so we used the logarithm in the regression calculation.We identified the strongest explanatory variable on the basis of the R 2 value.We also carried out a multivariate ordinary least-squares regression (on pairs of explanatory variables), but this generally only led to a minor improvement in explanatory power (Supplementary Fig. S3).

Seasonal variability
To assess the strength of the regular seasonal cycle in source strength, we computed the correlation for each reef cell between monthly mean source strength and the regular seasonal cycle (i.e., the monthly climatological source strength) averaged across 1993-2019, specifically extracting the R 2 value.We also carried out an Empirical Orthogonal Function analysis of the monthly mean source strength matrix, decomposing the time-varying matrix into a set of principal components and associated basis functions.A similar analysis was previously carried out by Thompson et al. (2018) to investigate interannual connectivity variability.In our analyses, the first principal component (PC1) always corresponded to a seasonal cycle.To investigate how connectivity variability across the southwest Indian Ocean responds to the seasonal cycle, we computed the correlation of the monthly mean source strength time series at each reef cell with PC1, r PC1,S .To interpret the physical oceanographic drivers of this variability, we also computed the correlation between PC1 and the monthly-mean surface current speed, and the zonal u and meridional v components of the surface current velocity.The latter results in a new vector field, r PC1,u , r PC1,v ð Þ , returning the correlation of each component with the seasonal cycle (PC1).For interpretation, this vector points in the direction of where the surface current is intensified (but not necessarily oriented) when PC1 is more positive.

High-frequency variability
Temporal variability in reef source strength across the southwest Indian Ocean is summarized in Fig. 2, spanning a wide range of timescales, from days to multiple years.However, the source strength at most reefs simulated by SECoW is dominated by high-frequency variability on the order of days to weeks.As shown by Fig. 2a, a low-pass filter with a threshold of longer than $ 20 d removes most of the variance in daily source strength for the vast majority of reef cells within the southwest Indian Ocean.Although an annual cycle is detectable at most sites, this variability is only dominant at a small minority of sites.High-frequency potential connectivity variability (using the 1-d lagged autocorrelation of source strength, r 1d , as a proxy, with lower values corresponding to greater high-frequency variability) varies enormously across the southwest Indian Ocean (Fig. 3).In our simulations, remote reefs far from land are associated with a greater level of high-frequency potential connectivity variability, such as many of the atolls belonging to the Amirante Islands in Seychelles (Fig. 3b, west) and Bank du Geyser (Fig. 3e, east).Due to the chaotic nature of larval dispersal, the larval trajectories associated with two spawning events separated by a day may diverge significantly.For areas of high and continuous reef cover, divergent trajectories are still likely to intercept other reefs, moderating the impact on r 1d .However, for remote reefs, these divergent trajectories could be the difference between a dense larval filament reaching one of the few nearby destination reefs or completely missing it, resulting in source strength that can vary enormously from day-to-day.While the presence of coastline reduces the degrees of freedom for larval dispersal (suppressing source strength variability), this does not affect remote reefs that are far from land.As a result, source strength from these remote reefs is highly inconsistent and driven by short-lived settling pulses between reefs.A similar effect is seen at reefs further away from land along the Quirimbas Archipelago in Mozambique (Fig. 3d).
For some islands, the orientation of the coastline relative to prevailing ocean currents drives dispersal variability.The east and north coasts of Ngazidja and Mwali (Comoros, Fig. 3e) face surface currents entering the Mozambique Channel, thereby trapping larvae against the coast, resulting in consistent settling.For instance, larvae spawning from the east coast of Ngazidja generally settle at reefs along the same coastline, whereas a greater proportion of larvae spawning from the opposite side of Ngazidja settle at other islands (which are lower-probability connections, and hence subject to greater variability).A complex set of flow reversals and wake eddies are generated as the East Africa Coastal Current is diverted by headlands and islands, resulting in highly localized connectivity regimes.For instance, as described in Mayorga-Adame et al. (2016, 2017), flow reversals are generated around Zanzibar Island and Pemba Island (Supplementary Fig. S5).Flow is weakened in the wake of a peninsula on the east coast of Zanzibar, trapping larvae near their source reefs, occasionally exacerbated by convergent flow towards the coast.Conversely, west of Pemba Island, currents are often seaward, enabling larvae to drift away from the coast and enter the East Africa Coastal Current, again facilitating longer distance, less reliable connections.
Figure 4 shows that, for much of the southwest Indian Ocean, a large proportion of this variability can also be quantitatively explained by several key metrics.For islands in the path of the East Africa Coastal Current and Northeast Madagascar Current (Fig. 4a,d), the weighted connection distance (i.e., the weighted mean distance from a reef cell to downstream settlement reefs) explains around half of the variance in r 1d .For other remote islands (Fig. 4e), this rises to almost two thirds.Larvae in these settings tend to travel greater distances (due to a combination of current speed and/or relatively few nearby reefs) so the proximity of downstream reefs is a strong predictor of day-to-day potential connectivity variability.Unfortunately, weighted connection distance is a less-generalizable metric for decision-making, as this cannot be easily measured without running a larval dispersal model.For the East Africa Coastal Current, weighted connection distance was the only metric acting as a reasonable predictor for r 1d .However, as can be seen in Supplementary Fig. S3, there was a significant (negative) correlation between the local mean current speed and r 1d for islands around the Northeast Madagascar Current (R 2 ¼ 0:47) and other remote islands (R 2 ¼ 0:51).The local current speed near remote island reefs may therefore be a reasonable first-order predictor of the magnitude of high-frequency potential connectivity variability.The simple explanation is that greater current speeds are more likely to transport larvae away from the remote island, and into the open ocean, where chances for settlement will be rare and sporadic.
For reefs along the coasts of Mozambique and Madagascar, the distance to land was generally the strongest explanatory variable for r 1d (Fig. 4b, c).In the case of Mozambique, several other explanatory variables also performed similarly well, namely the weighted connection distance (R 2 ¼ 0:50) and the high-frequency current speed (R 2 ¼ 0:43, Supplementary Fig. S3).For Madagascar, none of the predictor variables were particularly strong, perhaps due to the highly complex coastline and multiple oceanographic regimes.Finally, highfrequency potential connectivity variability at the Chagos Archipelago is only weakly correlated with any of the explanatory variables we tested.As hinted at by the general increase in variability towards parts of the Great Chagos Bank with lower reef cover, there is weak positive correlation between nearby reef fraction and r 1d .However, with minor exceptions, r 1d does not vary by much across the archipelago, with moderate-to-high r 1d across most reefs (Fig. 3c).
In summary, a rule of thumb for estimating high-frequency potential connectivity variability is as follows.For reefs at remote atolls lacking substantial land, r 1d is likely to be very low (with highly sporadic and pulsed source strength).For reefs associated with substantial islands that are nonetheless remote, the local current speed may be a reasonable indicator of r 1d , with higher local current speeds associated with lesspredictable potential connectivity.For reefs near continental coasts, predicting potential connectivity variability without a larval dispersal model is likely to be challenging, although consideration of local geography and ocean dynamics may be helpful.For instance, potential connectivity variability will likely be greater for reefs further from the coast, and lower within enclosed bays.Consideration of whether local ocean currents hinder or facilitate long-distance dispersal may also provide insights into potential connectivity variability as, the more likely long-distance dispersal is, the less reliable connectivity is likely to be.Finally, for exceptional regions of extensive reef cover such as the Chagos Archipelago, potential connectivity variability will generally be lower, but may increase in isolated sectors with lower reef cover.The exact ranking of predictors varies slightly based on biological parameters (Supplementary Table S2), but the rule of thumb above is rather robust.

Seasonal variability
Once high-frequency variability is removed from the source strength time series for each cell by computing monthly means, the dominant residual signal is the seasonal cycle.The regular (mean) seasonal cycle explains a median of 25.6% of the variance in monthly mean source strength across reef cells, rising to 65.0% for reefs under the influence of the East Africa Coastal Current.Decomposing the monthly mean source strength matrix into a set of Empirical Orthogonal Functions, we unsurprisingly find that the dominant Empirical Orthogonal Function corresponds to the seasonal monsoonal cycle (PC1, Fig. 5b), switching sign between the northwest monsoon (broadly December to February) and southeast monsoon (broadly June to August).PC1 explains 26.9% of the variance in monthly mean source strength, more than double that of the next principal component (Supplementary Fig. S6), and is very stable, with only minor interannual variation.PC1 is strongly linked to the strength of the East Africa Coastal Current and Northeast Madagascar Current, as well as to the position and strength of the South Equatorial Current and South Equatorial Countercurrent (Fig. 5a).In addition to current strength, current direction is strongly correlated with PC1, most notably for reefs in Somalia, Seychelles, and the Chagos Archipelago.
In many cases, seasonal variability in current speed and source strength are anticorrelated.For instance, the source strength for most reefs along the path of the East Africa Coastal Current is suppressed when the current is at its strongest (e.g., Fig. 6a).Although faster currents enable long-distance connections, due to the effects of mortality, dispersion and competency loss, these connections are practically always weaker than the short-distance connections that are simultaneously suppressed.Some local exceptions exist, such as in the west Zanzibar Channel, where stronger northward flow during the southeast monsoon facilitates the flow of larvae towards higher reef cover in the north.However, in general, this pattern is robust along the Tanzanian and Kenyan coasts, and reefs at the north tip of Madagascar, in the path of the Northeast Madagascar Current.
At other locations, seasonal variations in current direction appear to have a greater influence on source strength variability.This is clearest at the Chagos Archipelago (Fig. 6e), where southwestward currents suppress source strength in the southwest of the Archipelago during the southeast monsoon.For these marginal atolls, southwestward larval transport sends larvae directly into the open ocean, resulting in almost inevitable death (however, note that correlation with PC1 is generally quite weak across the Chagos Archipelago).
Although the intensification of the Northeast Madagascar Current during the southeast monsoon explains the anticorrelation of source strength with PC1 in northernmost Madagascar, this anticorrelation continues along ocean-facing reefs across much of the northwest coast.Here, an offshore component to currents along the coast develops during the southeast monsoon, transporting larvae off the Madagascan shelf.An energetic mesoscale eddy field within the Mozambique Channel rapidly transports larvae away from Madagascar once they leave the shelf, resulting in low source strength during the southeast monsoon (compare high retention during the northwest monsoon in Supplementary Animation S5, to low retention during the southeast monsoon in Supplementary Animation S6).
In general, SECoW suggests that seasonal variability in source strength is strong and largely synchronous, if spatially heterogeneous, along the path of the East Africa Coastal Current.This is also true for the Northeast Madagascar Current, but to a lesser extent, due to the lack of continuous reef cover.Interannual variability is generally small compared to highfrequency variability (Fig. 2a), and is largely stochastic (driven by mesoscale ocean variability) rather than being explained by large-scale and synchronous changes in winds and ocean currents.Although climate models such as the Indian Ocean Dipole are associated with zonal current variability in the Indian Ocean (Schott et al. 2009), any effect on potential connectivity in our simulation is negligible compared to seasonality and stochastic variability.

Limitations
Although our simulations account simplistically for biological processes such as mortality, competency acquisition and loss, and settling rates depending on available reef cover, we do not incorporate environmental influences on coral larval mortality and competency, such as temperature (Nozawa and Harrison 2007).For instance, during Indian Ocean Dipole events, the temperature of the upper ocean rises in the west Indian Ocean.Although we found no significant effect of the Indian Ocean Dipole on potential connectivity in SECoW, it is possible that realized dispersal is nevertheless suppressed during Indian Ocean Dipole events due to the increased larval mortality rate.On the other hand, Indian Ocean Dipole events are generally most strongly expressed in the west Indian Ocean during October to November, which only affects the earliest part of the spawning season (broadly October to March; Baird et al. 2021;Koester et al. 2021).In addition to interannual temperature variability, temperature also varies over shorter timeframes and spatial scales, from meso-to frontal.This high-frequency temperature variability could add a further stochastic component to dispersal, particularly if a dense larval filament were subjected to protracted high or low temperatures by entrapment in an eddy or front.Including a dependence of larval mortality on temperature would add yet another degree of freedom to our larval biological parameterization, so we do not investigate this in the present study.However, daily surface temperature is available within WINDS (Vogt-Vincent and Johnson 2023b), so this could be included in a future dispersal model.
WINDS is the highest resolution ocean model that has been run on such large spatial and temporal scales in the southwest Indian Ocean, but the approximately 2 km resolution is still insufficient to resolve flow on a reef scale, mostly reflecting dispersal between reefs.As a result, although we expect SECoW to reasonably simulate larval dispersal within the open ocean, larval retention may be overestimated by our simulations along continental coastlines (Dauhajre et al. 2019), and underestimated around atolls (Grimaldi et al. 2022).Given that long-distance connections are associated with greater high-frequency potential connectivity variability, our study may underestimate source strength variability for reefs across East Africa and Madagascar.Conversely, it is likely that our study overestimates potential connectivity variability for larvae originating from remote coral atolls.The highest frequency of variability we consider in this study is 1 d À1 .Larval dispersal will vary at even higher frequencies, for instance following tidal cycles (Grimaldi et al. 2022).However, although particles in SECoW do experience tides, which are reproduced well by WINDS over the open ocean (Vogt-Vincent and Johnson 2023b), complex, reef-scale interactions between tides, waves, and reef geomorphology will not be reasonably represented.We therefore do not investigate the variability of larval dispersal with respect to tidal phase.
By considering total reef area, SECoW certainly overestimates the distribution of any one particular coral species, and further assumes that coral fecundity is constant.These assumptions are necessary due to the lack of data in the southwest Indian Ocean, but they are nevertheless important limitations.Insofar as potential connectivity variability is concerned, temporal variability in fecundity, both stochastic and as a response to environmental stress (Levitan et al. 2014;Hartmann et al. 2018;Pratchett et al. 2019), may be particularly important.Again, it is not clear to what extent this may amplify or dampen connectivity variability induced by ocean currents.

Consequences for demographic and genetic connectivity studies
"Interannual" connectivity variability for short spawning events is dominated by high-frequency variability The importance of interannual variability for potential connectivity is recognized by some modeling studies.For instance, Thompson et al. (2018) investigated potential connectivity in the Coral Triangle using a 47-yr hindcast, and found that at least 20 yr of simulated spawning events were required to reasonably represent interannual connectivity variability.This is concerning, as many (if not most) larval dispersal modeling studies continue to use considerably shorter timespans.What was not clear, however, is whether this variability in potential connectivity between annual spawning events reflected genuine low-frequency (interannual) oceanographic variability, or whether this simply reflects underlying high-frequency variability in surface currents.
To test this, we consider five hypothetical types of spawning behavior: (1) a spawning event lasting 1 d every year, (2) a spawning event lasting 5 d every year, (3) a spawning event lasting 1 month every year, (4) continuous year-round spawning, and (5) a spawning event lasting 1 d every 10 d.For each type of spawning behavior, we compute the coefficient of variation (i.e., the standard deviation divided by the mean) for source strength and flux as a function of the number of spawning events (up to 27), and take the median across all reef cells and connections (see Supplementary Material, Heading 4).
The solid black line in Fig. 7 shows how the coefficient of variation of (a) source strength and (b) flux for an annual 1-d spawning event increases with the number of spawning events (years).Despite representing an entirely different region, Fig. 7b shows a strong resemblance to the results of Thompson et al. (2018), with several decades of data (tens of spawning events) required to adequately characterize the variability associated with potential connectivity between reefs.In contrast to flux, interannual variability in source strength (Fig. 7a) can be reasonably represented by only around 10 yr of data.
If interannual variability in potential connectivity were driven by interannual oceanographic variability, we would not expect the coefficient of variation to be sensitive to spawning duration (below a year).However, for source strength, the interannual variability falls rapidly with increased spawning event duration.This demonstrates that protracted spawning, even as little as a few days, is an effective method of improving source strength stability (i.e., the predictability of larvae settling anywhere).
The teal line in Fig. 7 shows the coefficient of variation for source strength (a) and flux (b) for a simulated 1-d spawning event occurring every 10 d, rather than every year.Despite the fact that this time series captures zero interannual variability and is based on a biologically unrealistic spawning scenario, the median coefficient of variation is practically indistinguishable between 1-d spawning events every 10 d vs. every year.This strongly suggests that, to first-order, interannual dispersal variability for short spawning events reflects stochastic high-

a b
Source streng g g g Flux Fig. 7. (a) Source strength coefficient of variation (CV) across reef cells with a significant detectable source strength in SECoW for (black) annual spawning events from 1993 to 2019, assuming spawning takes place over (solid) 1 d, (dashed) 5 d, (dash-dotted) 1 month, and (dotted) continuously on an annual basis; and (teal) spawning events lasting 1 d every 10 d.The shaded area represents the 5 th to 95 th percentiles for the annual 1-d spawning events (gray) and 10-daily spawning events (pale teal).(b) As with (a), but for flux (based on groups, not cells).Note the different y scale.
frequency oceanographic variability, rather than being driven by genuine interannual oceanographic variability.
To summarize, although there is genuine interannual variability in the source strength and flux time series (reflecting the underlying oceanographic forcing, see Vogt-Vincent and Johnson 2023b), most variation in potential connectivity across annual spawning events is simply an artifact arising from low-frequency sampling of a signal dominated by highfrequency variability.
Most settling larvae are generated by a small minority of spawning events Although protracted spawning periods have been observed or inferred for some broadcast-spawning corals in the west Indian Ocean (e.g., Mangubhai and Harrison 2008), spawning is often short and synchronous, taking place over a few nights per year at most (e.g., Mangubhai et al. 2007;Sola et al. 2016).Since source strength is generally dominated by day-to-day variability, the fate of coral larvae generated by a spawning event is very sensitive to exact timing of spawning.
If source strength varied little between spawning events, we would expect roughly 50% of spawning events to account for 50% of settling larvae.In fact, SECoW predicts that half of all settling larvae were generated by only 13.3% of annual spawning events (the median across all reef cells, see Supplementary Material, Heading 4).However, this falls to below 4.0% for the decile of reefs with the greatest source strength variability and, for 47 reefs, this figure was less than 1%.In other words, for these reef sites, most settling larvae were generated by a once-in-a-century spawning event.Reefs the most unequal temporal distribution of source strength were almost always remote islands, including much of Seychelles and Mauritius (Fig. 8).The reefs with the most consistent year-to-year source strength were mostly along the path of the East Africa Coastal Current, due to the relatively continuous reef along the coast and predictable, consistent ocean currents.
This enormous predicted variance in settling likelihood is related to the theory of "sweepstakes reproductive success", and is expected to cause a significant reduction in the effective population size, and genetic variance amongst recruits (Hedgecock 1994).There is (equivocal) evidence for this from coral population genetics (Barfield et al. 2023), and metapopulation models suggest that high variance in reproductive success reduces population growth rates (Watson et al. 2012) and increases coral cover volatility (Barfield et al. 2023).
Some corals have been observed to "split spawn", that is, undergo multiple spawning events within a reproductive season, often (but not always) separated by a month (Willis et al. 1985).A previous modeling study based on the Great Barrier Reef found that split spawning separated by a month can significantly increase the reliability of larval supply (Hock et al. 2019), with similar results also found by Kough and Paris (2015).Our finding that a minority of spawning events generate most settling larvae supports this finding (in a very different and diverse oceanographic context), as a greater number of individual spawning events significantly increases the likelihood of a rare "high-impact" dispersal event.

High-frequency oceanographic variability introduces considerable uncertainty to inter-reef connectivity predictions
Time-mean potential connectivity matrices are widely used to explain genetic connectivity (e.g., Foster et al. 2012;Padr on et al. 2018).However, given the enormous variability in potential connectivity, it is pertinent to consider the uncertainty oceanographic variability may introduce into these predictions.
For this purpose, we consider the backward cumulated multistep implicit connectivity, hereon implicit connectivity for brevity, defined by Ser-Giacomi et al. (2021).For a pair of nodes (reef groups) i and j, the implicit connectivity for n steps gives the probability that a pair of random walks terminating at i and j passed through the same node within n steps.If post-settlement processes are neglected and steps of a random walk are interpreted as gene flow, the implicit connectivity may reflect the degree of shared ancestry for a pair of reefs over a given number of (Legrand et al. 2022), with 1 indicating definite shared ancestry, and 0 indicating zero shared ancestry.We extract 100 random time-slices from the full flux matrix, and compute the implicit connectivity between all pairs of reef groups across 100 steps, assuming spawning occurs 1 d per year during the northwest monsoon.We repeat this for 1000 different random subsets of the full flux matrix, to generate a large set of possible dispersal histories, sampling across the range of stochastic oceanographic variability.This is shown in Fig. 9 for a random subset of sites.The implicit connectivity computed from the time-mean flux matrix (black points in Fig. 9) is rarely close to the median implicit connectivity (white points) across the 1000 realizations, and ordering implicit connectivity using the time-mean flux matrix would result in a completely different ranking to most implicit connectivity estimates based on time-varying flux matrices.In almost all cases, the 5 th to 95 th percentiles range for implicit connectivity is considerable.This uncertainty is related to stochastic turbulence in the ocean, thereby imposing fundamental limitations on what we can infer about genetic connectivity between site pairs from physical larval dispersal (before even considering uncertainty in biological parameters).
For example, based on the time-mean potential connectivity matrix, high implicit connectivity (and therefore low genetic differentiation) would be expected for the pair of sites marked with an asterisk in Fig. 9.If the genetic differentiation between these sites were in fact observed to be high, this could be interpreted as overprinting of the physical connectivity signal by, for instance, selection.This may be correct but, as is clear from Fig. 9, high genetic differentiation is, in fact, entirely consistent with the uncertainty in implicit connectivity introduced by oceanographic variability.It is therefore not clear how much insight can be gained by, for instance, tuning biophysical models to best fit observed genetic differentiation (Legrand et al. 2022), particularly when implicit connectivity uncertainty can span orders of magnitude when computed over fewer steps (Supplementary Fig. S7).
For demographic connectivity (e.g., considering the role larval dispersal may play in driving recovery after mass-mortality events), the larval flux over a smaller number of spawning events is more relevant than the implicit connectivity.Summed over 10 spawning events, the total number of larvae transported between pairs of sites may vary over many orders of magnitude due to stochastic oceanographic variability (Supplementary Fig. S8), again introducing fundamental and uncertainty to what we can predict about demographic connectivity between reefs.We therefore argue that studies generating potential connectivity data to inform marine management efforts should discuss (and publish) data on dispersal variability rather than just the time-mean dispersal matrix (or the mean seasonal cycle).It is also questionable whether a time-mean dispersal matrix should be used to explain recent inferred gene flow (e.g., Padr on et al. 2018), when model-data mismatch (or agreement) could simply be due to stochastic variability.
In contrast, uncertainty in the timing of spawning within monsoons introduces little additional uncertainty to long-term connectivity predictions (Supplementary Fig. S9).Spawning in the southwest Indian Ocean tends to occur during the northwest monsoon (e.g., Baird et al. 2021;Koester et al. 2021) so, in the absence of any better constraints, metrics averaged over the northwest monsoon will capture the first-order patterns of long-term potential connectivity for corals in this region.

Conclusions
Coral reef potential connectivity is highly complex, with time-mean and seasonal signals often drowned out by highmagnitude, high-frequency variability.However, we have demonstrated that there is some order within this complexity.
Within the southwest Indian Ocean, there are relatively robust oceanographic and geographic predictors of highfrequency variability in potential connectivity between reefs.This variability is most extreme at remote islands and atolls, and suppressed along near-shore reefs, particularly where ocean currents tend to trap larvae against the coast.These patterns will provide marine practitioners with an initial indication of how significant high-frequency variability in potential connectivity may be at sites of interest.Where high-frequency variability is dominant, connectivity over ecological timescales will be subject to considerable uncertainty.Even with excellent data assimilation (which is rarely available at fine scales relevant for larval dispersal), day-to-day potential connectivity variability is chaotic and stochastic.The uncertainty introduced by this variability is rarely fully acknowledged in the literature, but it is essential for sensibly interpreting larval dispersal simulations.
Since most settling larvae are generated by a small minority of spawning events, studies simulating only a small number of spawning events may significantly underestimate long-term potential connectivity, particularly at remote islands.This may have particularly important consequences for predicting genetic connectivity, in which rare but "high-impact" dispersal events may play a disproportionately important role.Reasonably characterizing the potential connectivity of a relatively sparse network of reefs therefore requires many spawning events, ideally over multiple decades.If this is not possible (for instance, due to the costs associated with running a high-resolution hydrodynamical model), simulating many spawning events over a smaller number of years likely gives a better indication of potential connectivity variability than simulating a smaller number of spawning events over a larger number of years.Neglecting this will severely under-represent uncertainty in potential connectivity from the dispersal model.However, even with many simulated spawning events, the time-mean (or seasonal) connectivity matrix alone may be of limited utility for many ecological applications, since the actual potential connectivity over years and even decades may deviate massively from the long-term average.Furthermore, due to uncertainty introduced by oceanographic variability, we would argue that, over sub-evolutionary timescales, it is impossible to obtain anything more than first-order constraints on the importance of individual connections between reefs through marine dispersal.
Since the autocorrelation timescale for potential connectivity at most reefs is on the order of a few days, protracted spawning eliminates most variability associated with source strength, and some variability associated with the strength of individual connections.This suggests that the larval supply associated with broadcasting corals that spawn infrequently over a short duration is likely to be highly irregular, inconsistent, and unpredictable, in comparison to corals carrying out split-spawning, asynchronous and protracted spawning, or continuous larval release by some brooding corals.In contrast, although constraints on spawning duration are therefore critical to reasonably characterize the variability of coral reef connectivity, the timing of spawning onset appears to be of lesser importance.In the monsoon-dominated southwest Indian Ocean, long-term potential connectivity patterns are relatively consistent within monsoons.
We expect that these results will also apply to oceanographically and geographically analogous reef systems outside of the Indian Ocean.For example, remote coral islands influenced by equatorial currents-such as Seychelles-are abundant throughout the Pacific, and linear reef systems along the path of major western boundary currents-such as the coasts of Kenya and Tanzania-are also found in Florida and southern Japan.Despite the strong influence of the monsoons on surface circulation in our study region (which is unique to the Indian Ocean and some Southeast Asian seas), our results demonstrate that, at most reefs, day-to-day variability in potential connectivity is greater in magnitude than the mean connectivity, the seasonal cycle, and interannual variability.Other reef taxa, including many algae, echinoderms, mollusks and crustaceans, also generate long-lived and weakly or non-swimming propagules (Kingsford et al. 2002;Shanks 2009), and may therefore experience similar dispersal variability to the broadcast-spawning corals we investigated here.

Fig. 1 .
Fig. 1.The model domain investigated in this study, colored by the time-mean surface current speed from WINDS.Model cells containing coral reef are shaded in red.Also shown is a schematic representation of the major ocean currents in the region during the northwest monsoon (the main season for coral spawning), namely the South Equatorial Current (SEC), Northeast Madagascar Current (NEMC), Southeast Madagascar Current (SEMC), East Africa Coastal Current (EACC), and South Equatorial Countercurrent (SECC).Flow in the Mozambique Channel (MC) is dominated by eddies.

Fig. 2 .
Fig. 2. (a) Variance fraction of unfiltered (daily) source strength explained by low-pass filtered source strength, as a function of the low-pass filter cut-off period, expressed as deciles across the 8088 reef cells.Also shown in dashed lines are examples of three particular reef cells, dominated by low-frequency variability (Tanga), high-frequency variability (Rémire Island), and a mixture (Mahé).Animations giving further insight into variability at these three sites, as well as Bassas da India, a particularly remote reef in the south Mozambique Channel, can be found in Supplementary Animations S1-S4.(b) Source strength power spectral density for the three example reef cells using Welch's method.(c-e) Three years of the full source strength time series for the three example reef cells.The numbers in brackets in subplot titles refer to the 1-d lagged autocorrelation (see Methods section).

Fig. 3 .
Fig. 3. One-day lagged autocorrelation, r 1d , for the source strength time series of individual reef cells.The corresponding figure for the full domain is provided in the Supplementary Material (Fig. S4) but, for clarity, this figure focuses on six subregions: (a) north Tanzania; (b) Seychelles, excluding the Aldabra and Farquhar Groups; (c) the Chagos Archipelago; (d) the Quirimbas Archipelago, Mozambique; (e) the Comoro Islands, including Banc du Geyser; and (f) north Madagascar.Background shading represents the mean current speed, with arrows representing the mean current velocity.GCB, Great Chagos Bank.

Fig. 4 .
Fig. 4. Histograms for the 1-d lagged autocorrelation of source strength for individual reef cells (r 1d ), as a function of a predictor variable.The predictor variable plotted is the variable with the highest R 2 value from ordinary least-squares regression with r 1d .

Fig. 5 .
Fig. 5. (a) Correlation of ocean current monthly mean speed (colors) and direction (arrows) with PC1 from the source strength matrix.(b) Seasonal cycle of PC1, with the total range for monthly means across all years (1993-2019) shaded.

Fig. 6 .
Fig. 6.Close-up views of selected reefs from Fig. 5: (a) north Tanzania; (b) Seychelles, excluding the Aldabra and Farquhar Groups; (c) the Chagos Archipelago; (d) the Quirimbas Archipelago, Mozambique; (e) the Comoro Islands, including Banc du Geyser; and (f) north Madagascar.Colors represent the correlation of monthly mean source strength with PC1.The background is shaded by the correlation between ocean current monthly mean speed and PC1 as in Fig. 5 but, for clarity, we show the magnitude only, in greyscale.Arrows show mean current velocities during minimum (January [northwest monsoon], black) and maximum (August [southeast monsoon], white) PC1.

Fig. 8 .
Fig. 8. Percentage of years contributing half of settling larvae (colors), shown for the lowest and highest decile of reef cells only.Marker size is scaled by the mean source strength, and do not represent the physical size of reef cells.

Fig. 9 .
Fig. 9. (Backward) cumulated multistep implicit connectivity (CMIC) over 100 dispersal events.The teal bars show the 5 th to 95 th percentiles of CMIC (shared ancestry) across 1000 random realizations, and the white points represent the median.The black points represent the CMIC obtained from the time-mean potential connectivity matrix.