Movement model.

Habitat-driven movements are, by definition, triggered by the need of individuals to find, and stay in, most suitable habitats. They are therefore expected to possess the following characteristics:

1. In the absence of any clear habitat gradient, the movement shall be close to a random walk (no preferred direction);
2. As habitat gradients increase, the movement shall become more directed and lead individuals towards more favorable areas;
3. The movement speed shall decrease with habitat suitability so that individuals move rapidly through poor habitats and slow down in favorable zones.

Movements with characteristics (i) to (iii) are, quite easily and efficiently, simulated using the biased random walk model proposed by Faugeras and Maury [17]: (1) where V_s(x,y,t,a) is the habitat-driven horizontal swimming velocity vector of an individual of age a at position (x, y) and time t, V_m is its maximum sustainable speed, h is a normalized habitat suitability index (0≤ h ≤1) and d is the unit vector pointing in the direction of movement: (2) where θ is the heading angle (relative to North). This angle is taken to be a realization of a stochastic variable having a von Mises distribution νM(μ, κ) with mean direction angle μ and concentration parameter κ. This distribution (Fig 1) is a circular analogue to the normal distribution. It converges to the uniform distribution as κ → 0 and tends to the point distribution concentrated in the mean direction μ as κ → ∞ (e.g. [20]).

The (1 − h) factor in Eq (1) guarantees that the swimming speed V_s (i.e. the norm of the velocity vector V_s) reaches its maximum value V_m in least suitable habitats (h = 0) and tends to zero in very favorable habitats (h →1) where individuals generally increase the time spent diving, searching for food, capturing and handling preys. Diving behavior however is not explicitly simulated.

The mean direction of movement is chosen to be the direction of the habitat gradient vector ∇h: (3)

Modeled movements thus follow, on average, that gradient and hence tend to maximize habitat suitability. In addition, the concentration parameter κ is taken to be proportional to the norm of ∇h: (4) where α is a scaling parameter. Accordingly, when ∥∇h∥ → 0, κ → 0 and the distribution of θ becomes uniform. On the contrary, large habitat gradients, and hence large κ values, yield strongly directed movement as the distribution of θ becomes strongly concentrated around the optimal direction θ_∇h.

Interestingly, the simple movement Eq (1) proves to be the Lagrangian equivalent of an Eulerian advection-diffusion equation in which advection and diffusion are strongly linked and governed by habitat values and their gradients [17], as in the SEAPODYM model [18].

Estimation of the maximum sustainable speed.

As implied by Eq (1), V_m is the speed at which a, likely fasting, animal will leave a very unfavorable area. It makes sense to assume that individuals escaping such areas will try to do so in the most energetically-efficient way, that is at a speed for which the amount of energy required to move one unit of distance, or work per meter (WPM), is minimum [21]. For an individual moving at speed V_s, the work per meter is directly related to the rate of energy expenditure per unit time, that is the metabolic rate (MR): (5)

In a fasting individual, MR is the sum of the resting metabolic rate (RMR) plus the energy expended per second to move against the hydrodynamic drag force [22]: (6) with ρ the sea water density, C_D the drag coefficient, S the surface of the turtle’s body and η is the overall efficiency coefficient of the flippers which includes their propeller efficiency and the aerobic efficiency of their muscles. Using Eq (6), Eq (5) can be rewritten: (7)

Differentiating Eq (7) with respect to V_s, the velocity that minimizes WPM is easily determined: (8)

This velocity can then be expressed as a function of size (L) using simple allometric relations. Noting M the mass of the individual and assuming that RMR scales with M^b while M scales with L^c and S scales with L², one obtains: (9) where v₀ is a scaling parameter that remains to be determined. This equation governs the evolution of V_m with size, or with age provided that a growth curve L(a)is known for the modeled species.

Habitat model.

Focusing on juvenile sea turtles looking for food and constrained by water temperatures, we express the habitat suitability index h as the product of a feeding habitat index (h_F) and a thermal habitat index (h_T) [18,19]: (10)

The feeding habitat suitability index, at a given place and time, is simply taken to be proportional to P(x,y,t) the local prey density (or a proxy of it), divided by the individual rate of food consumption F which varies with age (and species): (11)

Modulation of h_F by the rate of food consumption allows areas with relatively low abundance of preys to be favorable enough to support the foraging activity of young/small individuals while adults will seek richer areas.

Like all ectotherms, sea turtles can only perform in a limited range of body temperatures (T_b). Because of the high thermal conductivity of water, T_b is closely linked to the surrounding water temperature (T_w) so that sea turtles are forced to occupy a restricted range of water temperatures to avoid cold stunning or overheating. To model such a bounded thermal habitat we define 4 pivotal water temperatures: T₁<T₂<T₃<T₄ (Fig 2) where T₁ and T₄ are the critical temperatures below or above which an individual cannot survive for long while T₂ and T₃ are the lower and upper bounds of the thermal preferendum, that is the minimum and maximum water temperatures between which a sea turtle performs optimally or nearly so. The thermal habitat suitability index is then parameterized as: (12)

Of course, the pivotal water temperatures are species-dependent and can vary with mass, size or age. Note also that Eq (12) is formulated in such a way that when T_w reaches the critical values T₁ or T₄, h_T is close to zero but its gradient with respect to T_w remains significant. This ensures that individuals exposed to critical or near-critical temperatures will display vigorous movements directed towards more favorable thermal habitats.

Allometric relationships and movement model calibration.

For leatherbacks, we assume that RMR scales with M^0.831 [23] and use the growth curve and mass-length relationship of Jones et al. [24]: (13) (14) where L is the straight carapace length (SCL) in meters and M is in kilograms. These relationships imply b = 0.831 and c = 2.86, so that the relation defining the maximum sustainable speed Eq (9) reduces to: (15)

Interestingly, this expression indicates that V_m increases only slightly, and certainly less than linearly, with size. This probably holds true for all sea turtles species as, for simple scaling reasons, the value of c should always be close to 3 while the value of b proves to vary little between sea turtle species [23], remaining close to the generic value obtained for all reptiles (b = 0.83) [25].This is consistent with the results of Abecassis et al. [19] who show that, in juvenile loggerheads, V_m/L (i.e. the maximum sustainable speed expressed in body lengths per second) decreases markedly with size.

The calibration of the movement model finally requires the specification of v₀, the velocity scaling factor in Eq (15) and α, the factor controlling the concentration parameter in Eq (4). To estimate α, we simply hypothesize that, in the presence of a clear habitat gradient, an individual will systematically move into the half plane towards which ∇h points, that is in a direction that does not differ by more than 90° from the optimal direction given by ∇h. In practice, we decide that a clear habitat gradient exists whenever the norm of the habitat gradient is larger than its median value∇h_m. Since κ = 4 is the value of the heading concentration parameter of the von Mises distribution for which the probability of selecting movement directions deviating by more than 90° from the mean (optimal) direction becomes vanishingly small (see Fig 1), Eq (4) immediately yields α∇h_m = 4. Our simulations (see below) show that ∇h_m is close to 1.3 10⁻⁶. We therefore choose α = 3 10⁶.

In the absence of speed measurements in juvenile leatherbacks, the calibration of ν₀ can only rely on velocities measured in tracked adults. Based on growth curve Eq (13), simulated adults reach an SCL close to 1.4 m for which Eq (15) yields V_m ≈ ν₀ and Eq (1) accordingly implies: (16)

This shows that v₀ could readily be determined using either measurements of the maximum sustainable speed of adult leatherbacks or joint measurements of their swimming speed and habitat suitability. Unfortunately, a review of the literature on leatherback tracking experiments did not allow us to obtain such measurements. The most commonly reported speed estimate actually is the average speed, that is the mean speed computed over the complete trajectories of all turtles tracked in an experiment. Such average speeds typically range between 0.5 and 0.7 m/s [26–28]. Assuming that these average speeds are typical of an average habitat value (h = 0.5), Eq (16) indicates that v₀ shall be between 1 and 1.4 m/s. We accordingly select v₀ = 1.2 m/s. Simulation results (see below) show that with this choice of v₀, the simulated swimming velocities of less than 3-year old individuals range between 0 and 0.3 m/s, while over 10-year old individuals have swimming velocities varying typically between 0.2 and 0.8 m/s, their mean speed being close to 0.6 m/s.

Thermal habitat calibration.

The thermal habitat suitability index Eq (12) is characterized by 4 pivotal temperatures (T₁ to T₄) that define the range of water temperatures within which the modeled sea turtle species can maintain suitable body temperatures. Determination of the range of suitable body temperatures is thus requested before pivotal water temperatures can be specified.

Body temperatures measured in adult leatherbacks are typically in the range 24 to 28°C for individuals foraging in cold high-latitude areas [29,30] and 28 to 31°C for individuals tracked in the tropics [26,31]. Similar measurements are largely missing for hatchlings and juveniles. However, since hatchlings have a very small thermal inertia and little peripheral insulation, their body temperature has to be very close to the temperature of the water in which they are swimming. Hughes [32] analyzed ocean temperatures offshore several nesting beaches and concluded that leatherback hatchlings usually encounter waters between 25 and 31°C. A somewhat lower temperature of 24°C is also certainly suitable as it is the water temperature in which Jones et al. [24] successfully raised several leatherback hatchlings. We thus conclude that leatherbacks of all ages commonly experience body temperatures between 24 and 31°C. But does this range of observed body temperatures cover the whole range of suitable temperatures? The lowest suitable body temperature might actually be somewhat lower than 24°C, but not much. Indeed, the coagulation efficiency of leatherback’s blood decreases dramatically around 23°C [33] which suggests that such a low body temperature is not normally experienced [33,34]. We will accordingly assume that the lowest body temperature suitable for leatherbacks of all ages is 24°C.

On the contrary, the maximum suitable body temperature likely is well above 31°C: body temperatures reported in nesting females typically range between and 30.5 and 34.5°C [26,35–37] and hatchlings have an observed critical thermal maximum as high as 40.2°C [38], probably like adults [39]. The highest suitable body temperature shall thus be around 35°C or above. Such a high body temperature might be reached in the course of nesting activities but is probably never experienced at sea where water temperatures rarely exceed 30°C.

Assuming that leatherbacks never encounter unsuitably warm waters so that the condition T_w > T₃ is never met in Eq (12), we can just skip the specification of the upper pivotal water temperatures T₃ and T₄. The specification of T₁ and T₂, the lower pivotal water temperatures, is less simple. Indeed, thanks to various morphological, physiological and behavioral adaptations, leatherbacks are able to maintain T_b well above T_w [22,29,30,40,41] and the temperature gradient (T_b -T_w) that they can maintain proves to increase with their mass [40] and level of activity [41]. The evolution of this gradient is actually governed by the heat budget of the concerned individual. Based on the steady-state version of this budget, Bostrom et al. [41] deduce that, for a leatherback of mass M: (17) where d is a coefficient directly proportional to the individual’s metabolic heat production. The evolution of d with the metabolic rate (MR) can be made more explicit by rewriting Eq (17) under the form: (18) where d₀ is the value of d for a resting individual. Based on observations of quiescent captive juveniles, Bostrom et al. [41] estimated d₀ = 0.21. As 24°C is the assumed minimum suitable body temperature for leatherbacks of all ages/mass, Eq (18) implies that this value of T_b is obtained for: (19)

This equation provides the basis for estimating T₁ and T₂. Indeed, T₁ can be defined as the strictly minimum water temperature within which a most active individual is able to maintain T_b = 24°C while T₂ is the water temperature within which a resting individual will effortlessly obtain this same body temperature. Therefore: (20)

Then, the estimation of T₁ depends on the maximum value of the MR/RMR ratio that a leatherback can sustain. We expect this maximum value to be somewhere between 4 and 5 as nesting is often quoted as leatherbacks’ most strenuous activity, and metabolic rates measured in nesting females reach 4 to 5 times their RMR [40,41]. Such an estimate is consistent with the results of Peterson et al. [42] who analyzed the sustained metabolic rate (SMR) in a number of free ranging vertebrates. They observed that the SMR/RMR ratio is always smaller than 7 and, in most case, smaller than 5. In particular, this ratio remains below 5 in all surveyed ectothermic species (lizards).

We thus conservatively estimate that leatherback turtles can sustain metabolic rates up to 5 times their RMR so that the minimum water temperature (T₁) in which a (very) active individual will be able to maintain a minimum body temperature of 24°C is: (21)

Using Eqs (13) and (14) to express mass as a function of age, T₁ and T₂ can then readily be expressed as a function of age as needed: (22) (23)

It is worth noting that the minimum tolerated temperature (T_min) empirically determined by GAL for leatherbacks fits right in-between these two pivotal temperatures (Fig 3).

We have now completed the parameterization of the thermal habitat suitability index. This index is shown in Fig 4 for leatherbacks of various ages. As expected for hatchlings, this index falls almost immediately down to zero in water temperatures below 24°C. For larger/older individuals, markedly colder waters remain suitable, but the suitability index becomes very small so that modeled individuals will tend to move out of these cold waters.

Feeding habitat calibration.

The definition of the feeding habitat suitability index Eq (11) is based on the local prey density (P) and the individual rate of food consumption F(a). In the absence of synoptic estimates of the distribution of jellyfish, the main diet of leatherbacks, we follow Saba et al [43] and use satellite-derived estimates of the net primary production (NPP) as a proxy for P.

The rate of leatherback’s food consumption has been estimated by Jones et al. [44]. This estimate is expressed in kilograms of jellyfish consumed per year and must thus be rescaled to account for the fact that NPP is used as a proxy for P instead of jellyfish density. To do so, we first define F₀(a), a normalized and nondimensionalised version of the Jones et al [44] estimate of the rate of food consumption: (24) where f₀ = 0.094 so that F₀(a)→1 when a →+∞ (Fig 5).

The actual rate of food consumption is then given by: (25) where P₀ is a scaling factor expressed in the same units as P, the prey field or its proxy (in this case, NPP). The feeding habitat suitability index Eq (11) thus finally reads: (26)

This expression thus clearly shows that P₀ is the threshold value of NPP above which the adults’ habitat suitability reaches its maximum value (h_F = 1). Estimation of that parameter is probably the most uncertain part of the model’s calibration. One could simply decide that h_F = 1 for the maximum NPP value encountered in the North Pacific. However, this would yield a very high P₀ value, only encountered in the richest coastal areas where the accuracy of satellite-derived NPP estimates is, unfortunately, the weakest [45]. Furthermore, known favorable pelagic foraging areas (such as the North Pacific Transition Zone) have much weaker NPP levels than most productive coastal areas. They would thus only have a weak suitability index if P₀ was set at a high coastal NPP value. We therefore set the value of P₀ at the level corresponding to the 90^th percentile of the NPP distribution in the North-Pacific. With this choice, P₀ = 55 mmol C m² day^-1. This is well below the high NPP values measured in coastal regions and typically in the range of the NPP values found in productive pelagic areas of the North Pacific [46].

Seasonal migrations.

Seasonal migrations are commonly observed in both juvenile and adult chelonid sea turtles, e.g. [55–57]. They are known to occur in sub-adult and adult leatherbacks [58,59] and are thus expected in juvenile leatherbacks. Such migrations cannot be generated by the passive drift mechanism but naturally appear when habitat-driven movements are added. The S2 animation clearly shows that, as soon as active turtles reach the middle latitudes, they undertake north-south migrations following the seasonal movements of the habitat suitability index. Two conditions need to be met to trigger a complete seasonal migration cycle. The first one is that juveniles need to have reached latitudes where wintertime water temperatures fall below the lower bound of their thermal preferendum (T₂). In that case, the thermal habitat suitability gradient leads simulated individuals to retreat southward towards warmer waters. The second condition is that turtles must move back north as the water warms up during spring. This is achieved when simulated juveniles reach an age at which their food requirements are large enough to create a foraging habitat gradient that leads them towards richer foraging grounds, generally found northward.

The need to move south to escape cold waters first appears in the Kuroshio individuals, at the end of the second year of simulation (note that, at that time, these individuals are only 1-year old, as they were born between June and November of the first simulation year). Unfortunately many of these individuals appear to be unable to swim fast enough to avoid overly cold waters (see the discussion about mortality in the next section). The need to move north in search for better foraging grounds appears later, mostly during the fourth year of simulation, when seasonal migrations become fully visible in the S2 animation.

The NECC individuals remain longer in warmer and sufficiently productive waters and initiate seasonal migrations only when they reach the colder waters of the NPTZ. This typically happens when they are 3 up to 6-year old.

Simulated habitat-driven movements, and the resulting seasonal migrations, also clearly shape the northern boundary of the dispersal area. In the passive dispersal simulation, this boundary is very diffuse and situated roughly between 40 and 50°N (Fig 6a). In the active dispersal simulation, a more clear-cut boundary is observed around 40°N (Fig 6b). This is the latitude above which the water temperature falls below T₂ towards the end of the fall and leads active turtles to undertake their southward wintertime migration.

Cold-induced mortality.

The pivotal water temperature T₁ being defined as the temperature below which a turtle cannot survive long, we will accordingly assume that a simulated turtle dies if it experiences T_w <T₁ during 10 days or more. A simple analysis of the water temperatures encountered along the trajectories of all active and passive turtle thus immediately reveals when and where cold-induced mortality occurs. The very first deaths actually occur at the end of the second year of simulation (Fig 9), that is when the first (both active and passive) Kuroshio individuals arrive offshore Japan in wintertime. During that first winter spent at mid-latitudes, death is diagnosed for 16% of the passive individuals and 10% of the active ones. The difference between the passive and active cases is even larger during the next winter: another 29% of the passive individuals, but only 6% of the active ones, die from hypothermia. During the following winters, an additional 25% of the passive individuals, but only 3% of the active ones suffer cold-induced mortality. This indicates that, after about 3 years, most active individuals are sufficiently cold-resistant and powerful swimmers to efficiently exploit the rich waters found in the northern part of the NPTZ during summer and fall and then rapidly retreat southward as winter arrives and water temperature drops down. At the end of the simulation, the cumulative mortality reaches 70% in passive individuals but only 19.3% in active turtles. This clearly shows that simulated habitat-driven movements, and seasonal migration in particular, are very efficient at limiting, but not completely suppressing, cold-induced mortality.

Death events in passive turtles are widely dispersed in the North Pacific (Fig 10a). Young (a ≤ 3 yr) passive turtles die from hypothermia generally north of 25°N and west of the dateline. These are mostly Kuroshio individuals. Older, more cold-resistant, passive individuals are observed to die mostly above 35°N and east of the dateline. Death events in active turtles are much less dispersed. They mostly occur offshore Japan, in 2- to 3-year-old Kuroshio individuals. (Fig 10b). Somewhat older individuals are also observed to die further east offshore Japan and in the Sea of Japan.

The link between cold-induced mortality in active turtles and their initial dispersal pathway (Kuroshio or NECC) is easily highlighted by analyzing their mortality as a function of the easternmost longitude reached south of 10°N, that is when simulated turtles (possibly) circulate into the NECC. Turtles that do not drift further east than 140°E have a mortality rate approaching 50% (Fig 11). These are the Kuroshio individuals plus some individuals that circulate only briefly into the NECC. Turtles that circulate further east into the NECC have much lower mortality rates, well below 10% for the individuals drifting east of 170°E. This decrease in the mortality rate is clearly related to the age at which individuals enter the colder mid-latitude waters. Kuroshio individuals reach 30°N at a mean age between one and two. Individuals that drift past 170°E are typically 3- to 4-year-old when they reach that latitude. By then they are more cold-resistant and sufficiently powerful swimmers to escape overly cold waters when needed.

North Pacific crossing time.

GAL defined the North Pacific crossing time (PCT) as the age at which simulated individuals first reach the longitude of 140°W and showed that passive turtles emerging from Jamursba-Medi can reach that longitude within 5 to 6 years. However, in doing so, all of them encounter water temperatures below their minimum tolerated temperature (T_min) and thus likely die. Furthermore GAL noted that the presence of 5 to 6-year old leatherbacks in the eastern North Pacific is unlikely as all leatherbacks incidentally caught east of 150°W by the Hawaii-based longline fleet are large individuals (SCL>1.3m), likely older than 10 years. GAL thus concluded that (a) Jamursba-Medi hatchlings are unlikely to achieve a fast, purely passive, crossing of the North Pacific Ocean and (b) a slower crossing, lasting over 10 years or more, would be more consistent with observations. GAL then argued that an active dispersal scenario involving active seasonal north-south migrations could generate such a slower crossing of the North Pacific basin. Indeed, individuals retreating each winter towards the center of the subtropical gyre would encounter weaker eastward currents and would thus cross the North Pacific basin more slowly. A detailed analysis of our passive and active simulations actually reveals that, besides the weaker eastward currents encountered by seasonally-migrating individuals, another more important mechanism explains why active turtles likely cross the Pacific more slowly than the passive ones.

Using the PCT definition of GAL, we observe that the number of individuals reaching the longitude of 140°W indeed peaks at 5–6 years for passive turtles and much later (12–13 years) for active turtles (Fig 12). In addition, passive turtles with a short PCT prove to suffer massive cold-induced mortality, as previously observed by GAL. Actually, all passive turtles with a PCT shorter than 6 years die in the GAL simulation while a few of them survive in our passive dispersal simulation. This is simply due to the fact that our cold-induced mortality criterion is less stringent than the one used by GAL (i.e. T₁ < T_min, see Fig 3).

Interestingly also, we observe that about one third of our passive turtles cross the Pacific in more than 6 years and have a significantly lower mortality rate than those with a shorter PCT. On the contrary, the mortality rate of active turtles bears no apparent correlation with the PCT. This difference in the mortality rates is easily understood looking at the speed at which passive and active turtles with different PCT move towards higher latitudes and thus encounter cold waters.

Passive turtles with different PCT display markedly different trajectories (Fig 13a). Those with the shortest crossing time are clearly Kuroshio individuals: they have the fastest northward progression and hence the highest cold-induced mortality rate. They reach 35°N, the mean latitude of the Kuroshio, within 2 years and then circulate rapidly into this mighty eastward current towards the other side of the Pacific. Passive turtles with a longer crossing time progress more slowly towards North and are thus more cold-resistant when entering cold mid-latitude waters. Their crossing time is longer mostly because they reach 35°N later (and more to the East) than the Kuroshio individuals. They thus encounter weaker eastward currents and therefore take longer to cross the Pacific.

On the contrary, groups of active turtles with different crossing times prove to have very similar trajectories (Fig 13b). They thus visit similar latitudes at similar times and accordingly have similar cold-induced mortality rates.

We finally have to explain why the PCT of active turtles is, on average, much longer than that of passive turtles. To do so, let us concentrate on the two most numerous groups: the group of passive turtles with a PCT of 6 years and the group of active turtles with a PCT of 13 years. As the swimming velocities are initially very small, the mean trajectories of the active and passive groups remain close to each other during their two first years of life. At the end of this period, the mean positions of the two groups are close to (25°N, 148°E). From there, both groups have to cover a distance towards East of about 6600 km before reaching 140°W. The passive group does that in 4 years, the active one in 11 years. To cover that distance, the passive group is pushed by currents having a mean zonal (eastward) component u_c = 0.052 m/s. As expected, this is almost exactly the speed needed to cover 6600km in 4 years. For the reason explained by GAL, the active group experiences a weaker mean eastward current speed: u_c = 0.039 m/s. At such a speed however, this group would cover the distance of 6600 km in 5.4 years and would thus have a PCT of 7.4 years, not 11 years! The missing part of the puzzle is that active turtles actually swim (on average) towards west, at a mean zonal speed u_s = -0.02 m/s. Their zonal speed on the ground (u_g = u_c + u_s) is thus only 0.019 m/s, which is indeed the speed needed to cover 6600 km in 11 years.

This, possibly surprising, result must be properly interpreted: that active turtles have a mean westward swimming speed of -0.02 m/s does not imply that they permanently swim against the dominant eastward flow. They actually swim faster (daily mean V_s = 0.42±0.23 m/s) but in all directions (Fig 14). The distribution of their heading angles however is clearly skewed towards west so that the resulting mean value of u_s is negative (i.e. westward). The origin of this westward bias in swimming velocities is analyzed in the next section.

Habitat gradients and swimming speeds.

Simulated habitat-driven swimming velocities being directed towards more favorable habitats, these velocities shall be westward if better habitats are found to the west. This is indeed the case in the 30-to-40°N latitude band within which active turtles cross the Pacific. Productivity triggered by the highly turbulent Kuroshio extension current is specially high offshore Japan and more generally in the western part of the NPTZ (Fig 7c and 7d). Active turtles crossing the Pacific Ocean thus encounter favorable feeding conditions in the western part of the basin before moving through progressively poorer areas of the central and eastern Pacific. Fig 15a confirms that the foraging habitat suitability index (h_F) is maximum to the west of the basin, decreases steadily through the central and eastern Pacific and finally increases again when active turtles reach the productive California current region. The total habitat suitability index (h) displays similar longitudinal variations as the thermal habitat suitability index (h_T) proves to vary little with longitude, except off California where colder waters induce a decrease in h_T). In agreement with these zonal variations of h and its gradient, the mean value of u_s remains close to zero in the westernmost part of the basin (Fig 15b). It becomes clearly negative in a broad longitude band between 170°E and 150°W and then comes back to zero near 135°W, before finally changing sign when the zonal habitat gradient also changes sign and leads active turtles to swim towards the rich Californian feeding grounds.

Spatial density distribution.

The spatial density distribution of juvenile sea turtles is a critically needed information to locate high use areas and evaluate risks of interactions with fisheries. A simple way of obtaining density maps from individual tracking experiments is to bin daily positions (or “turtle days”) in regular boxes and then use the number of turtle days per box as an estimate of the turtle density [60,61]. This is actually only a proxy of the turtle density as the number of turtle days per box increases not only with the local density of turtles but also with the residence time of each turtle in the box.

Using the daily positions generated by our passive and active dispersal simulations, the number of turtle days per 1°x1° boxes is easily computed. Even if the passive and active dispersal patterns are broadly similar (Fig 6), the corresponding density maps are strikingly different (Fig 16). Pushed by (on average) faster eastward currents and not forced to converge towards favorable habitats, passive turtles disperse widely in the North Pacific and rapidly cross it. Low turtle densities are thus recorded almost everywhere in the basin, except in the easternmost part of the subtropical gyre where the convergence of Ekman currents tend to aggregate passive turtles, just like passive plastic debris [60]. On the contrary, active turtles target favorable habitats and follow them seasonally. They thus gather in the same latitude band in the same season. This latitude band oscillates typically between 25 and 40°N (see Fig 13b) so that the turtle density is especially high between these two latitudes. In that latitude band also, the density clearly increases from west to east. The relatively low densities in the western part of the basin are due to the fact that simulated individuals are still widely dispersed in latitude. NECC individuals only progressively reach 25°N, sometimes at longitudes as far east as 170 to 180°E. However, once most individual are gathered in the 25 to 40°N latitude band, the number of turtle days keeps increasing towards East. This is mostly due to the fact the mean zonal velocity on the ground (u_g) decreases nearly steadily towards east (Fig 15b) and causes simulated turtles to stay longer in each longitude box. The density distribution finally changes shape at about 135°W, where the mean swimming speed changes direction and becomes westward. From there active turtles start spreading along the coast of California and Baja California.

Although no juvenile leatherback tracking data are available to validate the simulated density map, we note that Briscoe et al. [61] recently produced a comparable map for juvenile loggerheads tracked in the North Pacific. Interestingly, their density distribution displays some similarity with ours. In particular, loggerhead trajectories are also concentrated in the 30 to 40°N latitude band and residence times are especially high in the central part of the basin (180°W to 160°W).

Food availability, growth and energy accumulation.

As discussed in the previous section, active turtles initiate their crossing of the Pacific in the productive waters found in the western part of the NPTZ. They then transit through the less-productive central and eastern North Pacific before finally entering the rich waters of the California current system. Model results accordingly indicate that the NPP encountered by active turtles during their 3 first years of life is, on average, more than sufficient to meet their daily food requirements, i.e. NPP > F(a) (Fig 17). During the next 4 year, that is when active turtles move between 150°W and 180°, NPP is only marginally (seasonally) sufficient. NPP then becomes insufficient to fully meet the food requirements of the simulated individuals crossing the eastern part of the basin. Slower growth and increased starvation-induced mortality is thus expected in this area. Finally, NPP increases markedly as active turtles get into the California current region (at about 130°W) where high productivity allows larger/older individuals to fulfill their food requirements. This likely signals the beginning of a period of energy accumulation after which the first reproductive migration might occur. If this was the case, sexual maturity would be reached after about 15 years, the mean time needed for active turtles to reach 130°W.

A similar analysis of the NPP encountered by passive turtles shows that (a) passive turtles which cross the Pacific without encountering lethal temperatures experience generally lower NPP values than active turtles and (b) their food requirements are no longer met after the age of 7. Death through starvation is thus likely. This reinforces the idea that passive dispersal across the North Pacific basin is definitely not a viable hypothesis for juvenile western Pacific leatherbacks.