^{1}

^{2}

^{1}

^{1}

^{1}

^{1}

^{1}

^{1}

^{*}

^{2}

^{3}

^{*}

^{1}

^{2}

^{3}

Edited by: Mahmoud A. O. Dawood, Kafrelsheikh University, Egypt

Reviewed by: Ricardo Calado, University of Aveiro, Portugal; Nor Azman Kasan, Universiti Malaysia Terengganu, Malaysia

This article was submitted to Marine Fisheries, Aquaculture and Living Resources, a section of the journal Frontiers in Marine Science

This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner(s) are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

Seaweed aquaculture is a rapidly growing component of marine food production, but the capacity to control seaweed growth lacks behind that of land agriculture. Seaweed growth requires nutrients, acquired from dissolved pools through their fronds, and light, and, as such may also be density-dependent, but general relationships between seaweed growth, nutrient concentration and incident irradiance are not yet available. We used a dataset of 1729 experimental assessments of seaweed specific growth rates and density under various nutrient and irradiance levels retrieved from the published literature to examine the relationship between seaweed growth, density, irradiance, and nutrient concentration. This analysis confirmed strong density-dependence of seaweed specific growth rates, and further confirmed that nutrient and irradiance limitation strongly impose density-dependent seaweed growth. These findings demonstrate that nutrient and irradiance limitation modulate density-dependent seaweed growth, and can help maximize growth rates in seaweed aquaculture, a rapidly growing component of global aquaculture production, by manipulating stocking density where nutrients are scarce and/or underwater light penetration poor.

Plant stands typically show an upper, size-dependent limit to their abundance, which is expressed in the self-thinning law (

However, in contrast to terrestrial plants, which take up nutrients from the soil, seaweed take up nutrients from dissolved nutrient pools through their fronds. Indeed, nutrient uptake by macroalgae has also been reported to be size-dependent, specifically increasing with the surface to volume ratio (or decreasing with thickness) of the plants (

Understanding the regulation of seaweed growth has now gained particular importance, as seaweed aquaculture is a rapidly growing component of marine aquaculture (

Here we test the hypothesis that irradiance, nutrient limitation and density regulate seaweed growth. We do so through an analysis of the role of nutrients, density and irradiance in modulating the density-dependence of seaweed growth based on a comparative analysis of data on specific growth rates of seaweed across a range of densities under controlled nutrient conditions in the laboratory and aquaculture farms.

We searched the published literature for data on the density-dependence of seaweed growth under different nutrient levels. The search was based on the Web of Science^{®}, accessed in May 2019, using a combination of keywords including “seaweed and remediation,” “seaweed and bioremediation,” “seaweed and nitrogen removal,” and “seaweed and phosphorous removal.” These searches yielded a total of 164 papers reporting growth rates and biomass density for seaweed. We retrieved the growth rates, biomass density, concentration of the dominant forms of inorganic nutrients - ammonia, nitrate and phosphate – and incident irradiance, and recorded the taxa (chlorophyta, phaeophyta or rhodophyta). This generated a raw dataset containing a total of 1729 experimental assessments (^{–1} and biomass density (i.e., the seaweed biomass per unit habitat volume) to g FW L^{–1}. A total of 733 experimental assessments included data on specific growth rate and initial cultivation biomass density, while a total of 854 experimental assessments included data on seaweed specific growth rates and irradiance (

The density-dependence of specific seaweed growth (SGR, % d^{–1}) was described using a power law of the form SGR = a BD^{x}, where BD is the biomass density (BD, g FW L^{–1}) and x is the power exponent describing the scaling of SGR to BD. Similarly, the irradiance-dependence of specific seaweed growth (SGR, % d^{–1}) was described using a power law of the form SGR = a I^{x}, where I is the irradiance (I, μmol photon m^{–2} s^{–1}) and x is the power exponent describing the scaling of SGR to I. The relationship was fitted using model I linear regression on log_{10} transformed variables. The role of nutrients in modulating the density dependence of seaweed growth rate (log_{10} transformed) was then examined by fitting a general linear model including log_{10} transformed density, irradiance and nutrient (N, ammonia, nitrate or phosphate, mmol L^{–1}) concentrations as independent variables, yielding the equation log_{10} SGR = a + x_{1} log_{10} BD + x_{2} log_{10} I + x_{3} log_{10} N, which is equivalent, in arithmetic scale, to SGR = 10^{a} BD^{x1} I^{x2} N^{x3}, thereby involving interactions between density, irradiance and nutrient concentrations as covariates. All statistical analyses were conducted using JMP v. 10 software. The data supporting this study are available from the open access data repository PANGAEA (

Specific growth rates ranged from below detection limit to very fast rates of 54.6% d^{–1}, with an average (±SE) of 6.40 ± 0.18% d^{–1} (median 4.51% d^{–1}), and the biomass density ranged from 0.04 to 25 g FW L^{–1}, with an average (±SE) of 3.43 ± 0.11 g FW L^{–1} (median 2.0 g FW L^{–1}) (^{–1} for seaweed density in the data set corresponds, assuming a density of 1, to an occupation of 0.2% of the available volume by seaweed biomass. This is similar to results derived from examination of the size-dependence of the maximum abundance of aquatic organisms in culture, which indicates that they can occupy, at maximum density, 0.1% of the available volume regardless of whether they are photosynthetic organisms or animals (

Specific seaweed growth declined with biomass density (^{–1.44 (±0.18)} (^{–1} at BD less than 0.2 g FW L^{–1} to <1% day^{–1} at BD >8 g FW L^{–1}. SGR increased with incident irradiance as described by the power law SGR = I ^{1.72 (±0.18)} (^{–1} at I < 100 μm photon m^{–2} s^{–1} to average values of 100% day^{–1} at I > 10,000 μm photon m^{–2} s^{–1}.

The relationship between specific growth rate (SGR) and biomass density (BD) for seaweed growing under experimental or culture conditions. The closed symbols show the mean values for BD bins of 0.1 g FW L^{–1}, for BD < 1 g FW L^{–1}, and intervals of 1 g FW L^{–1} for greater values, and the insert shows the raw values. The fitted power law for the binned and raw data are SGR = 17.4 BD^{–1.44 ± 0.18} (^{2} = 0.51, ^{–0.21 ± 0.03} (^{2} = 0.06,

The relationship between SGR and irradiance (I) for seaweed growing under experimental or culture conditions. The closed symbols show the mean values for BD bins of 0.1 g FW L^{–1}, for BD < 1 g FW L^{–1}, and intervals of 1 g FW L^{–1} for greater values, and the insert shows the raw values. The fitted power law for the binned and raw data are SGR = 2.0 × 10^{–7} I ^{1.72 ± 0.18} (^{2} = 0.60, ^{–0.41 ± 0.03} (^{2} = 0.15,

General linear models showed that the SGR yielded the fitted equation:

Where nitrate has units of μmol L^{–1} (^{2} = 0.39, ^{–1}) was

(^{2} = 0.33,

The general model with phosphate concentrations did not yield a significant effect for phosphate (

These relationships show that seaweed growth rate for any given density increases as the ^{1/3} power of irradiance and increases much faster with increasing nitrogen when this is supplied as ammonium compared to nitrate (

The fitted relationships between SGR and BD for seaweed growing under experimental or culture conditions under different irradiance (I), ammonia (NH_{4}^{+}), and nitrate (NO_{3}^{–}) concentrations. The solid lines correspond to the fitted general linear models log_{10} SGR = –0.03–0.51 (±0.04) log_{10} BD + 0.08 (±0.02) log_{10} NO_{3} + 0.30 (±0.05) log_{10} I (^{2} = 0.39, _{10} SGR = –0.37–0.37 (±0.04) log_{10} BD + 0.17 (±0.03) log_{10} NH_{4} + 0.30 (±0.05) log_{10} I (^{2} = 0.33, ^{–2} s^{–1}, respectively, which are the 2.5, 50, and 97.5% quantiles of the irradiance data. _{3}^{–}), under low, medium and high irradiance, respectively; _{4}^{+}), under low, medium and high irradiance, respectively.

These results confirm that the density-dependence of seaweed growth rate is imposed by nitrogen and light limitation, with seaweed growing under high nutrient supply and incoming irradiance able to sustain high growth rates, even when occupying 2% of the available space (^{–1} even at high biomass density (3 g FW L^{–1} or 3% of available space,

The results presented explain the high yield of seaweed in the intensive farms that have proliferated along much of the coast of China, where eutrophication leads to very high nutrient concentrations exceeding 127 μmol NH_{4} and 2.21 μmol PO_{4} along much of the coast of China (

Whereas light limitation, resulting from self-shading, will impose an ultimate limit to seaweed growth with increasing biomass density (

The results presented here can help predict potential seaweed yields in aquaculture, given incident irradiance and nutrient concentrations, and also inform how density can be managed to achieve maximum growth where nutrient concentrations and or light maybe limiting. Because space is rarely a constraint in seaweed aquaculture (e.g.,

The datasets generated for this study are available on request to the corresponding author.

CD, SA, JW, and XX conceived and designed the comparative analysis. XX, FL, YY, YP, and KL generated the datasets. CD and XX wrote the manuscript. All authors analyzed, interpreted the results and edited the manuscript.

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

The Supplementary Material for this article can be found online at: