Food-web models from different sites and/or points in time were compared quantitatively by calculating T .. with the R package “NetIndices” (Kones et al., 2009) for each of the 100 000 model solutions and subsequently summarized as mean ± standard deviation. A decrease in the difference of T .. between the food webs from outside and inside plough tracks (Δ T ..) over time was taken as a sign of ecosystem recovery following disturbance.

Linear inverse modeling is based on the principle of mass balance and various data sources (Vézina and Platt, 1988), i.e., faunal carbon stock and physiological constraints, that are implemented in the model, either as equalities or inequalities, and they are solved simultaneously. A food-web model with all compartments present in the food web, e.g., the PD 26 food web model outside plough tracks, consisted of 147 carbon flows with 14 mass balances, i.e., food-web compartments, and 76 data inequalities leading to a mathematically under-determined model (14 equalities vs. 147 unknown flows). Therefore, the linear inverse models (LIMs) were solved with the R package “LIM” (van Oevelen et al., 2010) in R (R-Core Team, 2017) following the likelihood approach (van Oevelen et al., 2010) to quantify means and standard deviations of each of the carbon flows from a set of 100 000 solutions. This set was sufficient to guarantee convergence of means and standard deviations within a 2.5 % deviation.

2.2 Data availability

Macrofauna, invertebrate megafauna, and fish density data (mean ± SD; ind. m−2) for the first four cruises (PD 0.1 to PD 7 ) were extracted from the original papers (Borowski and Thiel, 1998; Bluhm, 2001 annex 2.8; Borowski, 2001), and methodological details can be found in those papers. In brief, macrofaunal samples (> 500 µm size fraction) were collected with a 0.25 m−2 box corer (number of samples is reported in Table 1), and densities of invertebrate megafauna and fish were assessed on still photos and videos taken with a towed “Ocean Floor Observation System” (OFOS) underwater camera system (extent of total surveyed area is reported in Table 1). During the PD 26 cruise (R/V Sonne cruise SO242-2; Boetius, 2015), macrofauna were collected with a square 50 × 50 × 60 cm box corer (outside plough tracks: n=7; inside plough tracks: n=3), and the upper 5 cm of sediment were sieved on a 500 µm sieve (Greinert, 2015). All organisms retained on the sieve were preserved in 96 % un-denatured ethanol on board (Greinert, 2015) and were sorted and identified ashore under a stereomicroscope to the same taxonomic level as the previous cruises. Invertebrate megafauna and fish density during the PD 26 cruise were acquired by deploying the OFOS (Boetius, 2015). Every 20 s, the OFOS automatically took a picture from approximately 1.5 m above the seafloor (Boetius, 2015; Stratmann et al., 2018b) resulting in 1740 images of plough marks (inside plough tracks) and 6624 images from outside plough tracks (Boetius, 2015). A subset of 300 pictures from inside plough tracks (surface area: 1441 m2) and 300 pictures from the outside plough tracks (surface area: 1420 m2) were randomly selected from the original set of pictures and annotated using the open-source annotation software PAPARA(ZZ)I (Marcon and Purser, 2017). Invertebrate megafauna were identified to the same taxonomic levels as for the previous megafauna studies conducted within the DISCOL experimental area (DEA; Bluhm, 2001), whereas fishes were identified to genus using the Clarion-Clipperton Zone (CCZ) species atlas (http://www.ccfzatlas.com, last access: 14 February 2018).

The above-mentioned density data collected for macrofauna, invertebrate megafauna and fish were used to build food-web models to resolve carbon fluxes; hence, all faunal density data required conversion into carbon units before they could be used in the food-web model. Converting density data to carbon stocks was challenging in the current study, as few to no conversion factors for deep-sea fauna are available in the literature. Below, we describe the approach that we used to tackle this problem for macrofauna, invertebrate megafauna, and fish.

Measuring the carbon content of a macrofaunal specimen requires its complete combustion, which means that the specimen cannot be kept as a voucher. Macrofaunal samples collected for this study are part of the Biological Research Collection of Marine Invertebrates (Department of Biology & Centre for Environmental and Marine Studies, University of Aveiro, Portugal) and were therefore not sacrificed. Instead, we used the C conversion factors of macrofaunal specimens previously collected within the framework of a pulse-chase experiment in the CCZ (NE Pacific), in which a deep-sea benthic lander (3 incubation chambers, 20 × 20 × 20 cm each) was deployed at water depths between 4050 and 4200 m (Sweetman et al., 2018). The upper 5 cm of the sediment of the incubation chambers were sieved on a 500 µm sieve and preserved in 4 % buffered formaldehyde. Ashore, the samples were sorted and identified under a dissecting microscope, and the carbon content of individual freeze-dried, acidified specimens was determined with a Thermo Flash EA 1112 elemental analyzer (EA; Thermo Fisher Scientific, USA) to give the individual biomass in mmol C ind−1. Macrofaunal density data (ind. m−2) from all cruises were converted to macrofaunal carbon stocks (mmol C m−2) by multiplying each taxon-specific density (ind. m−2) with the mean, taxon-specific, individual biomass value for macrofauna (mmol C ind−1; Table 2). Subsequently, the carbon stock data of all taxa with the same feeding type (Table 2) were summed to calculate the carbon stock of each macrofaunal compartment (mmol C m−2; Supplement 2, Fig. 2).

The invertebrate megafaunal density data (ind. m−2) of the time series was converted to carbon stocks (mmol C m−2) by multiplying the taxon-specific density with a taxon-specific mean biomass per invertebrate megafaunal specimen (mmol C ind−1; Table 2). To determine this taxon-specific biomass per invertebrate megafaunal specimen, size measurements were used as follows. The “AUV Abyss” (Geomar Kiel) equipped with a Canon EOS 6D camera system with 8–15 mm f4 fisheye zoom lens and 24 LED arrays for lightning (Kwasnitschka et al., 2016) flew approximately 4.5 m above the seafloor at a speed of 1.5 m s−1 and took one picture every second (Greinert, 2015). Machine-vision processing was used to generate a photomosaic (Kwasnitschka et al., 2016). A subsample covering an area of 16 206 m2 of the mosaic was annotated using the web-based annotation software “BIIGLE 2.0” (Langenkämper et al., 2017). Lengths of all invertebrate megafaunal taxa for which data were available from previous cruises were measured using the approach presented in Durden et al. (2016). Briefly, depending on the taxon, either body length, the diameter of the disk, or the length of an arm was measured on the photo mosaic and converted into biomass per individual (g ind−1) using the relationship between measured body dimensions (mm) and preserved wet weight (g ind−1) (Durden et al., 2016). Subsequently, the preserved wet weight (g ind−1) was converted to fresh wet weight (g ind−1) using conversion factors from Durden et al. (2016) and to organic carbon (g C ind−1 and mmol C ind−1) using the taxon-specific conversion factors presented in Rowe (1983) (a detailed list with all conversion factors is presented in Supplement 2). For the taxa Cnidaria and Porifera, no conversion factors were available. Therefore, taxon-specific individual biomass values were extracted from a study from the CCZ (Tilot, 1992). The individual biomass of Hemichordata was calculated as the average biomass of an individual deep-sea invertebrate megafaunal organism (B, mmol C ind−1) at 4100 m depth following from the ratio of the regression for total biomass and abundance by Rex et al. (2006):

(1) B = 10 - 0.734 - 0.00039 × depth 10 - 0.245 - 0.00037 × depth .

Following the approach applied to the macrofauna dataset, individual carbon stocks of taxa with similar feeding types (Table 2) were summed to determine carbon stocks of invertebrate megafauna food-web compartments (mmol C m−2; Supplement 1; Fig. 2).

Individual biomass of fish was calculated using the allometric relationship for Ipnops agassizii:

(2) wet weight = a × length b ,

where a=0.0049 and b=3.03 (Froese et al., 2014; Froese and Pauly, 2017), as Ipnops sp. was the most abundant fish observed at the DEA (60 % of total fish density outside plough tracks and 40 % of total fish density inside plough tracks). The length (mm) of all Ipnops sp. specimens was measured on the annotated 600 pictures (300 pictures from outside plough tracks, 300 pictures from inside plough tracks) in PAPARA(ZZ)I (Marcon and Purser, 2017) using three laser points captured in each image (distance between laser points: 0.5 m; Boetius, 2015). The wet weight (g) was converted to dry weight and subsequently to carbon content (mmol C ind−1) using the taxon-specific conversion factors presented in Brey et al. (2010).