Modeling vitamin B1 transfer to consumers in the aquatic food web

Vitamin B1 is an essential exogenous micronutrient for animals. Mass death and reproductive failure in top aquatic consumers caused by vitamin B1 deficiency is an emerging conservation issue in Northern hemisphere aquatic ecosystems. We present for the first time a model that identifies conditions responsible for the constrained flow of vitamin B1 from unicellular organisms to planktivorous fishes. The flow of vitamin B1 through the food web is constrained under anthropogenic pressures of increased nutrient input and, driven by climatic change, increased light attenuation by dissolved substances transported to marine coastal systems. Fishing pressure on piscivorous fish, through increased abundance of planktivorous fish that overexploit mesozooplankton, may further constrain vitamin B1 flow from producers to consumers. We also found that key ecological contributors to the constrained flow of vitamin B1 are a low mesozooplankton biomass, picoalgae prevailing among primary producers and low fluctuations of population numbers of planktonic organisms.


Factors affecting mass-specific vitamin B 1 levels
We assume, that due to turnover rate of mitochondria and other cell structures, vitamin B 1 is degraded with a rate equal to the metabolic rate i.e. M R =0.001 [h -1 ] where M R is the fraction of vitamin B 1 in the cell degraded per hour. Bacteria and algae are assumed to synthesize and /or absorb dissolved vitamin B 1 with a rate twice of the assumed metabolic rate, i.e. the net rate of vitamin B 1 level increase is equal to the metabolic rate. Note that the predictions from our model do not change when the net rate of vitamin B 1 level in cells of microbes is set to 50% or 200% of metabolic rate M R (Fig. S1). The simulations starts from picomolar concentrations of vitamin B 1 in tissues of the modelled organisms but the predictions derived from our model also do not change when simulations start from maximal allowed levels of vitamin B 1 (Fig. S2). Hence, the model is robust in terms of changes regarding the assumed rate of vitamin B 1 synthesis/uptake as well as initial cellular concentrations of the vitamin ( Fig. S1-2).We used the following empirical estimates to set the maximal mass-specific concentration of vitamin B 1 [μmol·μmol -1 C]: bacteria 1.48e-7, picoalgae 1.48e-7, nanoalgae 1.18e-7 and microalgae 1.18e-7, 1.28e-7 for mesozooplakton 1,2 . Small planktivorous fish were allowed to contain at maximum 1.04e-10 [μmol· μmol -1 C] with average concentration of 6.41 -11 [μmol·μmol C -1 ] according to the vitamin B 1 content in clupeids of the Baltic Sea averaged data for sprat and herring reported by 3 . To recalculate the concentrations of vitamin B 1 in planktivorous fish we assumed carbon mass to constitute 12.5% of fresh body mass 4 . Due to a lack of empirical data on vitamin B 1 levels in protozoans, we set the maximal levels to 1.32e-7 [μmol·μmol -1 C] for nanoflagellates and 1.27e-7 [μmol·μmol -1 C] for ciliates by fitting a linear regression to the log-transformed data on mass specific vitamin B 1 content in other planktonic organisms. The assimilation rate in vitamin B 1 consumers was dependent on prey and predator biomass [μmol C·l -1 ], the assumed vitamin B 1 bioavailability (see below and in the main text) and the predators volume-specific clearance rates. The clearance rates were set to 1·10 -5 [h -1 ] for protozoans and mesozooplankton while three times lower specific clearance rate was assumed for clupeid fish 5,6 .

Vitamin B 1 bioavailability -sensitivity analysis of the model results
The bioavailability of vitamin B 1 determine the fraction of the compound loss during digestion process by consumers. Losses of water-soluble vitamin B 1 in fish during digestion can be very high and reach up to 98% 7 . In mammals bioavailability reaches up to 5% for water-soluble vitamin B 1 hydrochloride and up to ca. 20% for other vitamin B 1 analogues 8,9 . However, no data exist on vitamin B 1 bioavailability in protozoans or zooplankton. In the main text we report results for vitamin B 1 bioavailability of 15% i.e. 75% of the consumed vitamin B 1 is lost. In order to assess the effect of the assumed bioavailability levels on the model outcomes we run a sensitivity analysis. We ran calculations in the full space of model parameters i.e. abundance of planktivorous fish, nutrient input  Modelling vitamin B 1 transfer to consumers in the aquatic food web.
6 indicate scenarios with vitamin B 1 level in planktivorous fish lower than the average empirical estimate in 30% or more days.

Nutrient uptake by primary producers
The rate of nutrient uptake is a meaningful measure of competitive strength in marine and freshwater primary produces 10,11 . In previous studies of aquatic productivity, nutrient transport was modelled as constrained by the rate of the diffusion only cf. 5 . These studies assumed that algae cell is a perfect sink for nutrients and large cells are constrained by nutrient transport rate to a higher degree than small unicellular algae. In our model, consistent in approach with recent literature, nutrient affinity and nutrients-dependent growth rate scales with cell volume rather than its radius 10,11 . We modelled the rate of nutrient transport as allometrically dependent on cell volume using formulas for dependence of

Light attenuation and the effect of light on primary production
Light intensity in the model fluctuates in the annual and day-night cycle determined by day of year d, We use background attenuation coefficient k bg to model scenarios with variable degree of light attenuation by organic and inorganic substances dissolved in the water (see below). Modelling vitamin B 1 transfer to consumers in the aquatic food web.

The carbon production by an algae cell in our model
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Tested scenarios a.) Nutrient input
The degree to which nutrient concentrations and nutrient ratios constrain the growth rate of primary producers depends not only on the nutrient concentration in the water but also on the optimal stoichiometric composition of cells. Marine primary producers are highly variable with respect to their stoichiometric composition, with C:N:P ratio distributed around the Redfield ratio i.e. 106:16:1 21 .
Because our understanding of the adaptive component of this variability is poor 22,23 and to keep our model simple we assumed that primary producers are equally constrained by nitrogen and phosphorous availability. Hence, we assumed in our model that N:P ratio of algae cells and dissolved nutrients follows the Redfield ratio cf. 5 but we manipulated the level of nutrients available in the water at the beginning of simulation. We parameterized concentration of nitrate NO 3 and ammonium NH 4 + using data obtained at the Linnaeus Microbial Observatory (LMO) sampling site 24  ). We also rounded the precision of the nutrient concentration to two decimal places so it can be easily compared with levels measured in natural environments.

b.) Planktivorous fish abundance
We modelled population of planktivorous fish with body mass 4 g carbon body weight equivalent to ca. 32 g of fresh weight and ca. 15cm body length cf. 4 , which is an intermediate body size between Modelling vitamin B 1 transfer to consumers in the aquatic food web.
9 those for adult Baltic herring (Clupea harengus membras) and European sprat (Sprattus sprattus) see. 25,26 . We used the data on abundance of central Baltic population of herring and sprat in age 1+ in