In order to address these questions, growth rates at different initial stocking densities and during different seasons were examined in small-scale culture experiments (“Density experiment”, “Seasonal growth experiment”). Using the results of these experiments, growth in culture was modelled over 1 year for different cultivation scenarios (different initial stocking densities and harvest densities). The aim of the modelling was to answer the following questions: (1) which initial stocking densities and which harvest densities have to be chosen to reach maximum annual yields? (2) What are the maximum annual yields? (3) How many harvests have to be performed in the different cultivation scenarios?
Location of the experimental farm
The cultivation experiments were conducted at premises of Kieler Meeresfarm GmbH & Co. KG at the northwestern shore of the Kiel Fjord in the western Baltic Sea. During the Density experiment in 2017, the experimental farm was located at 54.3758 N, 10.1620 E; later it had to be moved about 700 m along the shore to 54.3820 N, 10.1620 E, where the Seasonal growth experiment took place (see below). The moving of the farm was performed during a time when no experiments were conducted.
Fucus plants usually grow on hard substratum to which they are attached by a discoid holdfast. From the holdfast, a rigid stipe erects which carries the flattened fronds consisting of vegetative apices and, during the reproductive season, receptacles. In the western Baltic Sea, F. vesiculosus usually reaches sizes between 20 cm and 1 m and F. serratus between 50 cm and 1 m (own observation).
All experiments were conducted for both Fucus species in parallel. Fucus vesiculosus was collected from Kiel Holtenau (54.3690 N; 10.1541 E) and F. serratus from Bülk (54.4552 N; 10.1989 E). A sufficient number of individuals (> 5) was collected to achieve genotypically mixed experimental biomasses. The collected individuals were transported as whole plants in sea water to the experimental site where they were stored in buckets overnight. The next day, vegetative fronds of 3–10 cm (F. vesiculosus) and 5–15 cm (F. serratus) were cut from the plants and used for the start of the experimental cultures. The size range is typical for fronds found in the field when cut above the stipe. In order to ensure an even distribution of frond sizes and genotypes among the experimental units, a bulk of fronds was prepared from which random portions of the desired weight were taken to inoculate the experimental units. In a parallel experiment (results published in Meichssner et al. 2020), this method for the assembly of biomass yielded 4.5 ± 1.3 fronds per 10 g of experimental biomass with 43 ± 7 meristems for F. vesiculosus (N = 14 examined experimental units) and 3.4 ± 0.7 fronds per 10 g of experimental biomass with 15 ± 2 meristems for F. serratus (N = 9 examined experimental units). The maximum observed relative deviation of the normalized meristem number (meristems per 10 g biomass) from the mean was 27% for F. vesiculosus and 12% for F. serratus. Deviations of single replicates from the mean number of meristems seemed to have no significant impact on the growth behavior: no correlation was observed between the relative deviation of the normalized meristem number from the mean of the treatment group and the relative deviation of the relative daily growth rates, measured over the following 14 days, from the mean of the treatment group (see Supplementary material, Fig. S1). Thus, this method of assembling the experimental biomass is in our opinion close to aquacultural practice and allows for valid measurements of growth at the same time. The size difference between F. vesiculosus and F. serratus was accepted as no direct comparison between the species was intended.
Meichssner et al. (2021) have shown that low-fertility biomass from unattached Fucus populations is needed for successful long-term cultivation, because fertility-related biomass losses (degradation of receptacles after gamete shedding) are otherwise too strong. Unfortunately, the experiments for the present study were initiated before the results of Meichssner et al. (2021) were obtained. Therefore, the experiments presented here were still conducted with biomass originating from attached populations. However, as only fronds with vegetative apices were used and the experimental time was very short, i.e., only beginning receptacle initiation and no receptacle degradation did occur during the experiments, we consider the growth in these experiments as vegetative and thus comparable to the growth of biomass from unattached low-fertility populations.
Black plastic baskets (BAUHAUS; Oase Pflanzkorb; edge length, 28 cm; volume, 14 L) were used for cultivation, which allowed for water inflow by holes of ca. 3 × 3 mm size (Fig. 1a). The baskets were covered with transparent plastic nettings to avoid the loss of culture material. Eight baskets were connected to packages of 3 × 3 baskets with the central position left empty. The packages were inserted into white boxes (glass fiber-reinforced plastic; shape, turned truncated pyramid; upper opening, 80 × 80 cm; basal area, 64 × 64 cm; height, ca. 40 cm) (Fig. 1b), which were deployed in the fjord using the gaps of a Jetfloat system (Jetfloat International) (double elements, 100 × 50 × 40 cm; single elements, 50 × 50 × 40 cm) (Fig. 1c). The white boxes had four side windows (35 × 37 cm) allowing for water inflow. Using this construction, the baskets were lowered to a depth of ca. 10 cm into the fjord, resulting in an 20 × 20 cm submerged cultivation area per basket. Six white boxes were available, yielding 48 baskets as experimental units. Experimental groups were distributed randomly in the white boxes; in addition, the position of the baskets within the white boxes was changed regularly to avoid position effects.
In all experiments, growth was measured as change in wet weight. All weights given in the following represent wet weights. For comparative purposes, the following dry matter contents can be assumed: F. vesiculosus, 21 ± 2% and F. serratus, 24 ± 1% (own pre-experiments). Wet weight measurements were performed with a lab scale (Kern EMB 1200) under wind protected conditions at the experimental site. Before weighing, the fronds were spun with a salad spinner for 15 s in portions of maximum 150 g to remove attached water.
Environmental data are provided for the Seasonal growth experiment. Water temperature within the cultivation baskets was logged every 60 min with a Hobo pendant data logger. Daily totals of photosynthetically active photon flux density (PPFD) were recorded in the Botanical Garden of Kiel University, 4.87 km from the experimental site as described in Pescheck and Bilger (2019) and Meichssner et al. (2020). The mesh used to cover the baskets reduced the incoming irradiance by 4 ± 2%. This mesh-related irradiance reduction increased to 12 ± 4% after 3–4 weeks when the mesh was colonized by microalgae. Nutrient data (concentrations of NO2−, NO3−, NH4+, PO43− in 1 m depth) from the Mönkeberg measurement station (ca. 3 km from the cultivation site within the Kiel Fjord: 54.3538 N; 10.1647 E) were kindly provided by LLUR (Landesamt für Landwirtschaft, Umwelt und ländliche Räume Schleswig–Holstein). Additional nutrient data (concentrations of NO2−, NO3−, NH4+, PO43− in 1 m depth) with a slightly higher temporal resolution were available from the Boknis Eck time series station (ca. 30 km from the cultivation site in the Kiel bay, 54.5167 N; 10.0333 E) (Lennartz et al. 2014). They were kindly provided by Kastriot Qelaj and Hermann Bange. Even though the actual concentrations at the experimental site might vary slightly from the concentrations measured at Mönkeberg and Boknis Eck, the data provide a good indication of the ambient nutrient dynamics, nutrient availabilities, and potentially limiting nutrient species. The environmental data are shown in the Supplementary material (Figs. S2 and S3, Tabs. S1 and S2).
Eight different initial stocking densities (40, 80, 100, 120, 140, 160, 180, 200 g basket−1, N = 3) were compared corresponding to 1, 2, 2.5, 3, 3.5, 4, 4.5, and 5 kg m−2. The experiment lasted from 24 May 2017 to 04 July 2017.
For all groups, relative daily growth rates (RDG) were calculated over the entire experimental time (41 days) by the following formula:
where RDG is the relative daily growth rate in percent day−1, Dt is the density at a given date in kg m−2, D0 is the initial stocking density in kg m−2, and t is the number of days between D0 and Dt.
In addition, the yield (Y) in kg m-2 was calculated:
Fitting of the data from the Density experiment was performed with the program Qtiplot using the Levenberg–Marquardt method (Kelley 1999). There are at least three reasonable options for the fitting of RDG–D0 relationships: first, a fit equation derived from the traditional yield–density equation for land plants (Li et al. 2016) (see Supplementary material), which assumes that the maximum RDG at x = 0 is approached in a steep manner and the minimum RDG at high densities in a rather asymptotic manner; second, a linear fit equation; third, a sigmoidal fit equation assuming that the highest RDGs at low densities as well as the lowest RDGs at high densities are approached in an asymptotic manner. All three options yielded similar R2 values (F. vesiculosus, 0.92–0.93; F. serratus; linear fit equation, 0.81; fit equation derived from traditional yield density equation and sigmoidal fit equation, 0.85). A sigmoidal fit equation seemed in our opinion most appropriate, due to the following reasons: (i) RDGs at very low densities are expected to be rather equal as competition for light, nutrients etc. becomes irrelevant at very low densities (own observation). (ii) RDGs from 3.5 to 5 kg m−2 were not significantly different for both Fucus species (Tukey’s HSD for all possible group comparisons between 3.5 and 5 kg m−2: p > 0.05). This corresponds to a sigmoidal approximation towards a theoretical infinite density. (iii) The RDG cannot be 0% day−1 or lower at a theoretical infinite density and should asymptotically approach a minimum at high densities. Therefore, we decided to use a sigmoidal Boltzmann fit equation for the RDG–D0 relationship:
where A1 represents the initial value, i.e., the fitted maximum RDG at the minimum density, and A2 represents the final value, i.e., the fitted minimum RDG at the maximum density. x0 is the turning point, i.e., the density at which the change in RDG is highest; dx is the time constant; it can be used to calculate the slope at x0 by the following formula: slope = (A1 − A2)/4dx. Especially the parameters A1 and A2 adopted unrealistic values because the available data points did not include very low and very high densities, respectively, and thus did not allow for a precise fitting of a wide density range. This was accepted since the fit was only used to represent the experimentally tested culture-relevant densities which were later included in the modelling (see below). The RDGs at these densities were well represented by the fit (Fig. 2).
For fitting the yield–density relationship, we used an equation deduced from the fit equation for the RDG (Eq. 3). For this purpose, Eq. 3 was inserted into the following Eq. 4, which describes the calculation of the yield from the RDG:
In case of the Density experiment, t = 41 days. The resulting fit equation for the yield–density relationship was
In this case, the parameters (A1, A2, x0, dx) do not relate to any specific growth features of the cultivated seaweed anymore.
The fit equations for the RDG–D0 relationship and yield–D0 relationship based on a traditional equation for land plants (see above) are shown in the Supplementary material.
Seasonal growth experiment
Growth was measured over 1 year (15 December 2018 to 15 December 2019) in eight periods of ca. 1.5 months each. The cultures of each period (N = 3) were started with 20 g fronds basket−1 (i.e., 0.5 kg m−2). The relative daily growth rates over the 1.5 months were calculated by Eq. 1.
Modelling of annual yield
Annual yield was modelled in Microsoft Excel for the period 15 December 2018 to 15 December 2019 (parallel to the Seasonal growth experiment). To create model scenarios, initial stocking densities (1–4.75 kg m−2, intervals of 0.25 kg m−2) and harvest densities (1.25–5 kg m−2, intervals of 0.25 kg m−2) were defined. For every possible combination of initial stocking density and harvest density, the annual yield as well as the required number of harvests was modelled. For this purpose, the density for each single day of the year was modelled using the following formula:
where mDt is the modelled density at a given day, Dt-1 is the density of the day before, and mRDGt-1 is the relative daily growth rate for Dt-1, which was calculated by inserting Dt-1 as “D0” into Eq. 3. z is a seasonal correction factor, which corrects mRDGt-1 for the growth rate of the specific period of the year. It was calculated as the ratio of the RDG measured during each specific period of the year in the Seasonal growth experiment and the RDG measured during period 4, which is the time when the Density experiment was conducted in 2017.
If mDt reached the defined harvest density, the density of the next day was set to the defined initial stocking density, which was considered as harvest. The annual yield was then calculated by the following formula:
where dDh is the defined harvest density, dD0 is the defined initial stocking density, and mD365 is the modelled density of day 365 of the modelled year.
Statistical analysis was performed with R (R Core Team 2013). For the Density experiment and the Seasonal growth experiment, the RDGs of the groups were compared by one-way ANOVA and post-hoc Tukey’s HSD test (in part to validate the used fitting method in the Density experiment, see above). Normality of residuals was tested by Shapiro–Wilk test and homogeneity of residuals by Fligner’s test.