Integrated monitoring of mola mola behaviour in space and time

Over the last decade, ocean sunfish movements have been monitored worldwide using various satellite tracking methods. This study reports the near-real time monitoring of finescale (< 10 m) behaviour of sunfish. The study was conducted in southern Portugal in May 2014 and involved satellite tags and underwater and surface robotic vehicles to measure both the movements and the contextual environment of the fish. A total of four individuals were tracked using custom-made GPS satellite tags providing geolocation estimates of fine-scale resolution. These accurate positions further informed sunfish areas of restricted search (ARS), which were directly correlated to steep thermal frontal zones. Simultaneously, and for two different occasions, an Autonomous Underwater Vehicle (AUV) videorecorded the path of the tracked fish and detected buoyant particles in the water column. Importantly, the densities of these particles were also directly correlated to steep thermal gradients. Thus, both sunfish foraging behaviour (ARS) and possibly prey densities, were found to be influenced by analogous environmental conditions. In addition, the dynamic structure of the water transited by the tracked individuals was described by a Lagrangian modelling approach. The model informed the distribution of zooplankton in the region, both horizontally and in the water column, and the resultant simulated densities positively correlated with sunfish ARS behaviour estimator (r(s) = 0.184, p < 0.001). The model also revealed that tracked fish opportunistically displace with respect to subsurface current flow. Thus, we show how physical forcing and current structure provide a rationale for a predator's finescale behaviour observed over a two weeks in May 2014

Higher order paracontrolled calculus

61 pagesInternational audienceWe develop in this work a general version of paracontrolled calculus that allows to treat analytically within this paradigm some singular partial differential equations with the same efficiency as regularity structures, with the benefit that there is no need to introduce the algebraic apparatus inherent to the latter theory. This work deals with the analytic side of the story and offers a toolkit for the study of such equations, under the form of a number of continuity results for some operators. We illustrate the efficiency of this elementary approach on the example of the generalised parabolic Anderson model equation $$(\partial_t + L) u = f(u)\zeta$$ for a spacial 'noise' $\zeta$ of Hölder regularity $\alpha-2$, with $\frac{2}{5}< \alpha \leq \frac{2}{3}$, and the generalized KPZ equation $$(\partial_t + L) u = f(u)\zeta + g(u)(\partial u)^2,$$ in the relatively mild case where $\frac{1}{2}<\alpha\leq \frac{2}{3}$

Heat semigroup and singular PDEs: With an Appendix by F. Bernicot and D. Frey

New appendix.International audienceWe provide in this work a semigroup approach to the study of singular PDEs, in the line of the paracontrolled approach developed recently by Gubinelli, Imkeller and Perkowski. Starting from a heat semigroup, we develop a functional calculus and introduce a paraproduct based on the semigroup, for which commutator estimates and Schauder estimates are proved, together with their paracontrolled extensions. This machinery allows us to investigate singular PDEs in potentially unbounded Riemannian manifolds under mild geometric conditions. As an illustration, we study the generalized parabolic Anderson model equation and prove, under mild geometric conditions, its well-posed character, in small time on a potentially unbounded 2-dimensional Riemannian manifold, for an equation driven by a coloured noise, and for all times for the linear parabolic Anderson model equation in 2-dimensional unbounded manifolds. This machinery can be extended to an even more singular setting and deal with Sobolev spaces rather than Hölder spaces

Comparison between the seal (red lines) and the nearest Keops Oxygen-Depth profiles (black lines).

<p>A gap between the profiles appears in the Oceanic Mixed Layer (OML). The letters a,b & c correspond to the profiles located in the <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132681#pone.0132681.g002" target="_blank">Fig 2</a>.</p

Distribution of surface oxygen in the physical context of the Southern Ocean.

<p>a) In 2010, the more oxygenated waters were mainly located south to the Fawn Through Current (FTC), also called the surface expression of the Polar Front and here symbolized by the 0.5°C isotherm. b) In 2011, the surface waters North to the Subantarctic Front (SAF) were low oxygenated compared to surface waters located South to the Polar Front. Within the Polar Frontal Zone (PFZ), no clear pattern appears in the distribution of dissolved oxygen regarding to the main physical structures.</p

Vertical sections of oxygen and temperature records along each trajectory.

<p>Respectively, a) and a’) Individual #1 b) and b’) Individual #2 c) and c’) Individual #3 d) and d’) Individual #4 e) and e’) Individual #5. (See Figs <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132681#pone.0132681.g001" target="_blank">1</a>, <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132681#pone.0132681.g007" target="_blank">7</a> & <a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0132681#pone.0132681.g009" target="_blank">9</a> for the location of each section).</p

Distribution of surface Apparent Oxygen Utilization in the biological context of the Southern Ocean in 2011.

<p>The AOU values indicate that the most oxygenated surface waters (i.e. the lowest AOU) within the PFZ and north to the SAF were related to the higher chlorophyll-a concentrations. No relation was observed in 2010.</p

Relationship between the AOU values along the seal tracks and the mean concentration of Chl-a extracted under each location recorded in 2011.

<p>The higher the concentration in Chl-a, the lower the values of AOU. The black line represents the significant linear regression: <i>y</i> = −6.4<i>x</i> + 23.7, p < 0.001.</p

Temporal drift of the seal oxygen sensors.

<p>Deep oxygen values (> 400 m) as a function of time showing a constant decrease in oxygen value that start after approximately 30 days at sea. Red lines represent fitting curves.</p

Location of oxygen profiles recorded by Kerguelen elephant seals and the ship survey Keops2.

<p>The seal profiles were obtained during the post-breeding foraging trip of 5 females. The individual #1 was equipped in October 2010. The 4 other females (#2 to #5) were equipped in October 2011. Blue dots correspond to the Keops2 stations (Keops St). The Keops survey was conducted in October and November 2011. Isobaths are illustrated in light gray.</p