Settlement probability on a 30-m substrate patch.

<p>Depth-averaged settlement probabilities vs. current speed at three water column depths: m (A, D, G), m (B, E, H), and m (C, F, I). Includes settlement probabilities of larvae that dive in turbulence (A–C), larvae that sink passively in turbulence (D–F), and neutrally buoyant larvae (G–I). Symbols indicate substrate type: open circles, natural reef; closed circles, oyster shell; trianges, mud; , whelk shell.</p

Settlement probability of actively diving larvae.

<p>Depth-averaged settlement probability vs. current speed and reef patch length for larvae settling over natural reefs (A, C, E) and deposited oyster shell (B, D, F) in water depths of m (A–B), m (C–D), and m (E–F).</p

Biophysical Constraints on Optimal Patch Lengths for Settlement of a Reef-Building Bivalve

<div><p>Reef-building species form discrete patches atop soft sediments, and reef restoration often involves depositing solid material as a substrate for larval settlement and growth. There have been few theoretical efforts to optimize the physical characteristics of a restored reef patch to achieve high recruitment rates. The delivery of competent larvae to a reef patch is influenced by larval behavior and by physical habitat characteristics such as substrate roughness, patch length, current speed, and water depth. We used a spatial model, the “hitting-distance” model, to identify habitat characteristics that will jointly maximize both the settlement probability and the density of recruits on an oyster reef (<i>Crassostrea virginica</i>). Modeled larval behaviors were based on laboratory observations and included turbulence-induced diving, turbulence-induced passive sinking, and neutral buoyancy. Profiles of currents and turbulence were based on velocity profiles measured in coastal Virginia over four different substrates: natural oyster reefs, mud, and deposited oyster and whelk shell. Settlement probabilities were higher on larger patches, whereas average settler densities were higher on smaller patches. Larvae settled most successfully and had the smallest optimal patch length when diving over rough substrates in shallow water. Water depth was the greatest source of variability, followed by larval behavior, substrate roughness, and tidal current speed. This result suggests that the best way to maximize settlement on restored reefs is to construct patches of optimal length for the water depth, whereas substrate type is less important than expected. Although physical patch characteristics are easy to measure, uncertainty about larval behavior remains an obstacle for predicting settlement patterns. The mechanistic approach presented here could be combined with a spatially explicit metapopulation model to optimize the arrangement of reef patches in an estuary or region for greater sustainability of restored habitats.</p></div

Joint settlement probability of neutrally buoyant larvae.

<p>Joint settlement probability vs. reef patch length for larvae settling over natural reefs (A, C, E) and deposited oyster shell (B, D, F) in water depths of m (A–B), m (C–D), and m (E–F). Dashed lines indicate optimal patch lengths where joint settlement probability reaches a maximum .</p

Mean optimal patch lengths.

<p>Mean of tidally averaged A) optimal patch length and B) maximum joint settlement probability vs. water depth . Means are computed from tidally averaged values with peak tidal velocities cm s^-1. Results are shown for diving larvae, passively sinking larvae, and neutrally buoyant larvae on natural oyster reef and deposited oyster shell.</p

Joint settlement probability of actively diving larvae.

<p>Joint settlement probability vs. current speed and reef patch length for larvae settling over natural reefs (A, C, E) and deposited oyster shell (B, D, F) in water depths of m (A–B), m (C–D), and m (E–F). White dashed lines indicate optimal patch lengths at each current speed, and indicates the overall optimal patch length and current speed where joint settlement probability reaches a maximum .</p

Joint settlement probability of passively sinking larvae.

<p>Joint settlement probability vs. current speed and reef patch length for larvae settling over natural reefs (A, C, E) and deposited oyster shell (B, D, F) in water depths of m (A–B), m (C–D), and m (E–F). White dashed lines indicate optimal patch lengths at each current speed, indicates the overall optimal patch length and current speed where joint settlement probability reaches a maximum , and indicates second local maximum .</p

Photos of substrate patches.

<p>Sites where flow measurements were made <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0071506#pone.0071506-Whitman1" target="_blank">[12]</a>, including in order from bottom to top of image (A): oyster shell restoration, whelk shell restoration, mud, and oyster reef. Close-ups are oyster shell (B), whelk shell (C), oyster reef (D), and mud (E). Scale bar on images is 0.2 m.</p

Search strategy using bORNs or measurements of concentration.

<p>(A) Search strategy based on a pair of sensors. The searcher compares measurements of the time since the last odor arrival, Δ, or measurements of concentration, <i>C</i>, registered by left and right sensors and steers in the direction of the shorter time or higher concentration. (B) Example trajectory of bORN-based strategy (initial position is x = 150 cm, y = 0 cm). The searcher begins at the “start” point and stops at the “end” point. The trajectory is continuous, with decisions made at every dot. Points that end outside the plume indicate that the searcher backtracks to its previous position. (C, D) Mean and standard error for number of steps required for strategies based on measurements of concentration (blue) and time since last encounter (bORN strategy, red) as a function of starting location relative to the source.</p

Encoding and decoding time since the last odor encounter from a population of bORNs (experimental data from the spiny lobster <i>Panulirus argus</i>).

<p>(A) Electrophysiological recordings of spontaneous bursting from three bORNs with different intrinsic burst frequencies (left), and bursting pattern of a single bORN (right) stimulated with odor (blue marks). Trials aligned in order of increasing time since last burst (bottom to top). Note that bORN does not respond to stimulus when time since last burst is short (bottom 4 trials) and instead, continues to burst spontaneously, (B) Probability of bursting in response to odorant as a function of time since last burst <i>τ</i>. Blue points are electrophysiologial data; blue line is sigmoid fit to data. Red curve represents the probability that the bORN will go <i>τ</i> seconds before bursting spontaneously (1—CDF of spontaneous inter-burst interval). Together, these curves tune the bORN to be most sensitive to odors that arrive with a particular frequency. (C) Probability of bursting in response to a stimulus as a function of stimulus frequency for two bORNs tuned by different evoked and spontaneous burst functions. (D) Raster plot (upper) and burst histogram (lower) of a heterogeneous population of 210 bORNs constructed from multiple single-neuron electrophysiological recordings showing spontaneous bursting and responses to odor stimuli (blue marks). This reconstructed population of bORNs encodes time between two odor stimuli (20.7 s). (E) The time interval between odor stimuli can be decoded from the bursting pattern of a heterogeneous bORN population shown in (D) using a simple maximum likelihood procedure (decoded interval is 23.2 s). Data are from [<a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004682#pcbi.1004682.ref019" target="_blank">19</a>].</p