Individual-based modelling of shelled pteropods

Shelled pteropods are cosmopolitan, free-swimming organisms of biogeochemical and commercial importance. They are widely used as sentinel species for the overall response of marine ecosystems to environmental stressors associated with climate change and changes in ocean chemistry. However, currently we are unable to project the effects of climate change on shelled pteropods at the population level, due to the missing spatio-temporal characterization of the response of pteropods to environmental stressors, and the limited information on the pteropod life history and life cycle. In this study, we implement a shelled pteropod Individual-Based Model (IBM), i.e. we simulate a pteropod population as a set of discrete individuals over several generations, life stages (eggs, larvae, juveniles and adults) and as a function of temperature, food availability and aragonite saturation state. The model is able to provide an abundance signal that is consistent with the abundance signal measured in the temperate region. In addition, the modeled life stage progression matches the reported size spectrum across the year, with two major spawning periods in spring and fall, and maturation in March and September. Furthermore, our IBM correctly predicts the abundance maxima of younger, smaller and potentially more susceptible life stages in spring and winter. Thus, our model provides a tool for advancing our understanding of the response of pteropod populations to future environmental changes.


Introduction
In this study, we implement a shelled pteropod IBM using the life cycle with two genera-         The implementation of these processes is described below.

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Each one-day time-step, this function calculates the shell growth in four steps for each ptero-362 pod. First, we calculate the shell mass (M shell ) in mg CaCO 3 . Second, we calculate the shell 363 dissolution as a function of M shell and the Ω arag that pteropods experienced. Third, we calculate 364 the potential amount of CaCO 3 in mg that pteropods can produce as a function of their current 365 size, experienced temperature, and food availability. Finally, we calculate the growth or shell 366 repair based on the potential amount of CaCO 3 that can be produced and the amount that was 367 lost due to dissolution. 368 Figure 2. Structure of shell growth submodel divided into the four steps, and the attributes needed for each step. The shell mass step requires the pteropod size (L) and outputs the CaCO 3 mass of the shell (M S hell ). The potential growth requires L, M S hell , the temperature (T) and chlorophyll-a concentration (Chl-a) experienced by the pteropod and outputs the potential gain in shell mass g. The shell dissolution requires L, M S hell , and the aragonite saturation state (Ω arag ) that the pteropod experienced, and outputs the loss in shell mass l. The net growth step requires the g, l, and damage accumulated (Dam acc ) by the modeled pteropod. The final output of the net growth step is the updated L, and Dam acc .
Step 1 -Shell mass: We estimate the shell mass M shell in mg CaCO 3 as a function of the where DW is given in mg, and L is given in mm and non-dimensionalized. (2) Step 2 -Shell dissolution: The damage to the shell as a function of the Ω arag (l in mg

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The l is then calculated by multiplying M shell by ν: Step 3 -Potential growth: The amount of CaCO 3 that pteropods can produce (g in mg where Q 10 = 1.3 is the unitless temperature coefficient ( which is explained in detailed in section 2.8.

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The µ 0 , i.e. the size increase per day relative to the current size at T 0 , is calculated using the where L(t) is the size in mm at age t. S (t) parameterises the seasonal changes in pteropod growth. Step 4 -Net growth: We calculate the net amount of CaCO 3 (Net CaCO 3 ) that remains after 422 dissolution and calcification: (10) We then use Net CaCO 3 to calculate the effective change in shell mass ∆M shell and Dam acc : where an increase in shell mass only occurs if Net CaCO 3 is larger than the current Dam acc . Finally, 425 to find the size change, we add ∆M shell to the M shell (L) calculated in step 1 (eq. 2) and extract the 426 corresponding L. In our model, the pteropods die after reaching a maximum age, after releasing eggs, due to 520 exposure to corrosive waters, and due to other causes. We chose a maximum age of ten months Second, for each modeled pteropod we draw a pseudo-random number from a discrete uni- Fourth, we add ∆M to M and compare the pseudo-random number drawn at the beginning 540 with the corrected mortality coefficient. If the pseudo-random number is smaller than M + ∆M 541 then the modeled individual dies. Finally, we select the individuals with an age of ten months or 542 those that have released eggs and remove them from the population.   Between and within pteropod life stages, the β can vary by more than a factor of ten (e.g.

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In this study, we aim to (i) reproduce the pteropod abundance signal measured in the tem-   Table 3). Shortly after spawning, the individuals of the overwintering generation start to die 152-164 days after the 1st of January (Table 3). The eggs of the spring generation begin their transition to the larval, juvenile and adult stage between 100-110, 138-152, and 248-270 738 days after the 1st of January (Table 3). Upon reaching maturity, adults of the spring generation 739 begin to spawn the next overwintering generation at the earliest 257 days after the 1st of Jan-740 uary and at the latest 279 days after the 1st of January (Table 3). The spring generation then 741 disappears from the population 331-344 days after the 1st of January (Table 3)      geography along the western antarctic peninsula. Limnology and Oceanography 64 (S1).         Size of pteropods parameterised as a function of temperature and chlorophyll-a concentration under idealized temperature and food scarcity during winter. In black is the size of pteropods of the spring generation. In blue is the size of pteropods of the overwintering generation.
Table A.6. Outcome of the sensitivity analysis for the life stage and generation specific mortality rates, the number of eggs released per adult pteropod and spawning event, and the daily increase in the Egg Release Readiness (ERR) index after reaching maturity. The sensitivity was quantified using the Manhattan distance (L1) and the Pearson correlation (r) between the modeled pteropod abundance and the pteropod abundance reported in MAREDAT (Bednaršek et al., 2012a) between 30 • N and 60 • N. The sensitivity experiments were run under idealized conditions (section 2.5) with chosen parameters values increased/decreased by 10% individually. Under idealized conditions our IBM has L1 = 15.5 and r = 0.99.  daily increase in the Egg Release Readiness (ERR) index after reaching maturity. The red curve shows the modeled pteropod abundance without changing the aforementioned parameters, the blue/black curve shows the abundance after increasing/decreasing the parameter by 10%. Each modeled abundance was scaled to the interval between zero and one for comparison.
The pteropods were seeded randomly with repetition within the region shown in Figure          . The MAREDAT daily data was interpolated from monthly averaged and seasonally corrected abundance data found between 30 • and 60 • latitude in the Northern Hemisphere. The abundance data was scaled to the interval between zero and one. The spring pteropod abundance peak is shown in yellow. The Pearson correlation coefficient (r), Spearman correlation coefficient (ρ), the Manhattan distance (L1), and the proportion of modeled abundance outside of the measured abundance range ( f out ) between the MAREDAT data and the climatology are given at the top of the figure.