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Porewater concentrations of dissolved oxygen and nutrientsThe sampling location and appearance of the microbial mats used in this study in cross section are shown in Fig. 1. Profound changes in dissolved oxygen concentration were observed over the diel cycle because of high rates of oxygenic photosynthesis in the daytime and oxygen-requiring respiration at night (Table 1). Briefly, Layer 1 was characterized by oxygen concentration fluctuations in the range of 200–800 µM. Layers 2 and 3 ranged from 0–1200 µM and 0–200 µM, respectively. Mat Layer 4 (3–4 mm below the surface) may contain some dissolved oxygen near noon on days when there is high solar irradiance but stays anoxic for most hours of most days. Layers 5–7 (4–7 mm from the surface) remain anoxic.Table 1 Oxygen concentrations throughout the first 4 mm of the mat measured at 100 µm resolution using microsensors, measured on 22 August, 2019.Full size tableConcentrations of ammonium (Table 1) reveal a pattern of increasing concentration with depth (34–124 µM) through the layers examined here. Nitrate concentrations ranged between 26–33 µM, with low variation across depths. The concentration of phosphate ranged between 3–6 µM, with the highest concentration detected in Layer 1 (0–1 mm from surface) at 5.5 µM.Analysis of genes and transcripts in mat layers by qPCR and RT-qPCRGene-copy number ranges for both DNA and cDNA across all layers for all genes examined are summarized as follows: Bacteria, 104−1010 per g mat and 101−105, per ng nucleic acid; Archaea, 106−108 and 102−104; nifH, 108−1011 and 104−107; archaeal-amoA, 104−105 and 2–3; bacterial-amoA, 104−107 and 3–335; Nitrospira-nxrB, 105−107 and 27–372; nosZ, 103−105 and 2–10; nirS, 105−107 and 33–1941; Planctomycetes-16S rRNA gene and cDNA of transcripts, 104−106 and 6–66 (Fig. 2, S1).Fig. 2: Vertical patterns in the abundance (DNA) and expression (cDNA) of Bacterial and Archaeal ribosomal and nitrogen cycling genes.Number of copies of DNA and cDNA genes recovered for Bacteria (A), Archaea (B), nifH (C), Archaeal-amoA (D), Bacterial-amoA (E), Nitrospira-nxrB (F), nosZ (G), nirS (H) and Planctomycetes-16S rRNA gene marker (anammox proxy) (I), per g of microbial mat, quantified by qPCR and RT-qPCR in hypersaline microbial mat profiles from different depths. P-values from Kruskal–Wallis test are overlain on each, and different letters indicate significantly different values for the given gene based on a Conover-Iman test p-value of  0.8, Table 2).Fig. 4: Non-metric multidimensional scaling (NMDS) plots of quantification of all nitrogen genes across all layers examined in this study.Genes associated with the following nitrogen transformations were examined: nitrogen fixation (nifH), nitrification (Bacterial-amoA, Archaeal-amoA, Nitrospira-nxrB), denitrification (nosZ, nirS) and Planctomycetes-16S rRNA gene marker (anammox proxy). The biotic data was standardized, and a sample resemblance matrix was generated using Bray-Curtis coefficient of similarity. In order to analyze the influence of abiotic variables (porewater nutrient and oxygen concentration) on the patterns of the biotic data, monotonic correlations of the abiotic variables were performed. In the plots, the distance between the samples’ points reflects their relative similarity, according to Bray-Curtis similarity matrices based on cDNA/DNA ratios of nitrogen genes examined. The vectors in panel A represent the cDNA/DNA ratios of nitrogen gene examined. In panel B, the vectors represent the environmental variables.Full size imageTable 2 (A) Spearman correlations coefficient (r) between the ratios of cDNA/DNA of nitrogen fixation (nifH), nitrification (Bacterial-amoA, Archaeal-amoA, Nitrospira-nxrB), denitrification (nosZ, nirS) and Planctomycetes-16S rRNA gene marker (anammox proxy) and oxygen, ammonium, nitrate and phosphate concentrations. (B) Spearman correlation p-value.Full size tablenifH, Bacterial-amoA and Archaeal-amoA were positively correlated with oxygen concentration (r ≥ 0.22, Table 2), while Nitrospira-nxrB was negatively correlated with oxygen (r = −0.68, Table 2). Denitrification genes (nosZ, nirS) and Planctomycetes-16S rRNA genes were all positively correlated with ammonium (r ≥ 0.5) and orthophosphate (r ≥ 0.13) and negatively correlated with oxygen (r  > −0.70).Metagenome analysis of nitrogen cyclingA total number of 922 324 genes were identified; 1305 of these genes were annotated with KOs that are part of KEGG’s Nitrogen Metabolism pathway (Table S2, S3). A dendrogram based on Bray-Curtis similarities of normalized coverages of all recovered nitrogen metabolism genes is shown in Fig. 5A. Overall, the similarity between the layers was >75%. According to SIMPROF analysis, there was a significant difference in the N-related gene coverages (based on an alpha value of 0.05) between Layers 1-Layer 2, Layer 3, and Layer 4 (p = 0.001) and Layer 2-Layer 3, and Layer 4 (p = 0.001), but not between Layers 3 and Layer 4 (p = 1), where the similarity was >90%.Fig. 5: Functional nitrogen gene distribution based on metagenome analysis.A Cluster analysis illustrating the similarity of normalized coverages of all recovered nitrogen metabolism genes across the uppers 4 layers examined [(Layer 1 (0–1 mm from surface), Layer 2 (1–2 mm from surface), Layer 3 (2–3 mm from surface), Layer 4 (3–4 mm from surface)]. Red lines show non-significant differences, according to SIMPROF analysis (p  > 0.05). B The bar plots show the genes of the metabolic pathways in the nitrogen cycle identified in the mat, according metagenome analysis, with relative coverage of each nitrogen cycling gene across depths examined (Fraction of Depth Integrated Coverage, FDIC). 355 unique genes were recovered from KEGG’s Nitrogen Metabolism pathway: 60 annotated as involved in nitrogen fixation, 15 in assimilatory nitrate reduction, 38 in dissimilatory nitrate reduction to ammonia (DNRA), 52 in hydroxylamine dehydrogenase EC 1.7.2.6, 121 in hydroxylamine reductase, 69 in denitrification pathway. C Values of Nitrogen-focused Coverage per Million (N-CPM). The following enzymes perform nitrogen transformation in the mat: nitrogenase molybdenum-iron protein alpha chain (nifD), nitrogenase iron protein NifH, nitrogenase molybdenum-iron protein beta chain (nifK), hydroxylamine dehydrogenase EC 1.7.2.6 (hao), hydroxylamine reductase (hcp), nitrate reductase/nitrite oxidoreductase, alpha subunit (narG, narZ, nxrA), nitrate reductase/nitrite oxidoreductase, beta subunit (narH, narY, nxrB), nitrate reductase (cytochrome) (napA), nitrate reductase (cytochrome), electron transfer subunit (napB), nitrite reductase (NO-forming) / hydroxylamine reductase (nirS), nitrogenase molybdenum-iron protein beta chain (nirK), nitric oxide reductase subunit B (norB), nitric oxide reductase subunit C (norC), nitrous-oxide reductase (nosZ), nitrate reductase gamma subunit (narI, narV), cytochrome c nitrite reductase small subunit (nrfH), nitrite reductase (cytochrome c-552) (nrfA), ferredoxin-nitrite reductase (nirA), ferredoxin-nitrate reductase (narB), MFS transporter, NNP family, nitrate/nitrite transporter (NRT, nark, nrtP, nasA). D Nitrogen cycling genes recovered in this study and the transformation that they catalyze.Full size imageThe nitrogen fixation pathway was identified with nifD, nifH, and nifK genes (Fig. 5B, C, Table S4). Of the 60 genes detected in this metabolic pathway 17 genes were annotated as nifD, 22 genes as nifH, and 21 genes as nifK. The normalized coverage of these genes showed a decreasing trend with depth. Layer 1 was characterized by the highest values of Nitrogen-focused coverage per million (N-CPM, see Supplementary Text 1) of nifD, nifH, and nifK genes: 56264.7, 54934.2 and 60059.2, respectively. On average, the three genes involved in nitrogen fixation, nifD, nifH, and nifK, decreased with depth, (2.7-fold from Layer 1 to Layer 4, with a nearly 2-fold difference solely between Layer 1 and Layer 2).Genes involved in nitrate assimilation, annotated as nirA and narB which code for ferredoxin nitrate reductase, were 3 times as abundant in Layer 1 than Layer 2, but decreased less markedly from Layer 2 to Layers 3 and 4.Genes for dissimilatory nitrite reduction (nrfA, and nrfH) were 4 and 16 times more abundant in Layer 4 than Layer 1. Similarly, the nitrate/nitrite regulator protein genes narl and narV displayed a nearly inverse pattern, with Layer 1 having the least proportion of genes, a large increase from Layer 1 to Layer 2, and additional increases from Layer 2 to Layers 3 and Layer 4 (Fig. 5B, C, Table S4).Genes associated with nitrification were very poorly represented in the metagenome. No genes associated with ammonia oxidation (amoA) were detected. Genes associated with nitrite oxidation (nrxA, nrxB) that were detected are so closely related to denitrifier genes (narG, narZ, narH, narY) as to be annotated with the same KEGG KO models (K00370 representing narG, narZ, nxrA; and K00371 representing narH, narY, nxrB).The following genes involved in denitrification were detected: napA, napB, narG, narZ, narH, narY, narI, narV, nirK, nirS, norB, norC, and nosZ (Fig. 5B, C). The nitrate reduction metabolic pathway was represented by 4 genes encoding the nitrate reductase-nitrite oxidoreductase-alpha subunit (narG, narZ, nxrA genes), 6 genes encoding the nitrate reductase-nitrite oxidoreductase-beta subunit (narH, narY, nxrB genes), 31 genes encoding the nitrate reductase gamma subunit (narI, narV), 5 genes encoding the nitrate reductase -cytochrome electron transfer subunit (napB) and 7 genes encoding the nitrate reductase -cytochrome (napA) (Table S4). The N-CPM of nitrate reductase increased with depth, but with a similar proportion of those genes in Layers 3 and 4. With respect to nitrite reductase (nirk and nirS genes, 2 and 1 genes, respectively), no nirK genes were detected in Layer 1, where the highest N-CPM of nirS was recovered (Fig. 5B). In contrast, Layer 3 had no detected nirS and the highest N-CPM of nirK. Regarding nitric oxide reductase (norB and norC genes, 6 and 1 genes, respectively), the highest normalized coverage of norB was detected in Layer 3, while highest for norC was in Layer 1. Finally, nosZ (6 genes) was detected in all the layers, steadily decreasing in normalized coverage from the top layer to the deepest (Fig. 5B, C; Table S4).DNRA metabolism was represented by nrfA (26 genes) and nrfH (12 genes), and by narI, narV (31). Layer 1 was characterized by the lowest normalized coverage of narI, narV, nrfA, and nrfH genes (6880.2, 3724.6, and 284.6 N-CPM, respectively), while Layer 3 was characterized by the greatest coverage of narI, narV, nrfA, and nrfH genes (32760.5, 14417.9 and 4504.1, respectively; Fig. 5B, C; Table S4).Genes for hydroxylamine dehydrogenase EC 1.7.2.6 and hydroxylamine reductase (hao and hcp, respectively) were the most abundant nitrogen metabolism genes in the mat: hao having a cumulative N-CPM of ~150000 and hcp having a cumulative N-CPM of nearly 350,000 across the 4 depths (Fig. 5C). Both genes increased in abundance with depth; hcp increased two-fold between Layer 1 and Layer 2, and more gradually in Layer 3 and Layer 4. Hao exhibited a three-fold increase in relative abundance from Layer 1 to Layer 2 and remained relatively constant through Layer 3 and Layer 4 (Fig. 5B, C; Table S4). More

Nitrite oxidation rates in the ETNPWe sampled six stations in the ETNP OMZ with DO concentrations 1 µM at 100 m (Fig. 2A). Chlorophyll concentrations were also high in the upper water column (up to 5 mg m−3 at 20 m), with an SCM spanning 70–125 m (Fig. 2B). Nitrite oxidation displayed a local maximum at the base of the EZ at Station 1 (20–30 m), and then increased to higher levels ( >100 nmol L−1 day−1; Fig. 2C). This increase at 100 and 125 m corresponded with the overlap between the bottom of the SCM and the top of the SNM. Nitrite oxidation rates then reached higher values at 150 m within the SNM at Station 1. Stations 2 and 3 displayed similar nitrite oxidation rate profiles to each other, including elevated rates in the SCM (Fig. 2G, K). Nitrite oxidation rates were similar in magnitude, and peak values at the base of the EZ and in the OMZ were also similar (69–96 nmol L−1 day−1). Depth patterns tracked oceanographic differences across the three AMZ stations, as the depth of all features increased moving offshore from Stations 1 to 2 to 3. For example, the SCM extended from 105 to 155 m at Station 2, while nitrite concentrations began to increase below 100 m; nitrite oxidation rates were elevated at 140 m and declined slightly with increasing depth (Fig. 2E–G). At Station 3, the SCM (120–180 m) and SNM ( >140 m) depths were deeper, and nitrite oxidation rates increased from 100 to 200 m (Fig. 2I–K).Fig. 2: Biogeochemical depth profiles.Profiles of A, E, I dissolved oxygen (solid lines) and nitrite (data points connected by dashed lines), B, F, J chlorophyll a, C, G, K nitrite oxidation rates, and D, H, L oxygen consumption rates (OCR; data presented as mean values of five independent replicates ±1 SD) show consistent variation across A–D Station 1, E–H Station 2, and I–L Station 3 (denoted by different colors). Black horizontal lines denote the depth of the oxygen minimum zone (OMZ), and shaded areas show the secondary chlorophyll maximum (SCM) at each station. Rates measured below the SCM should be considered potential rates (see main text). Maximum chlorophyll values at Station 1 plot off-axis.Full size imageIn contrast to these three AMZ stations (Stations 1–3), rate profiles at Stations 4–6 showed peaks at the base of the EZ followed by decreases with depth and lacked a pronounced rate increase within the OMZ (Supplementary Fig. 1). Parallel measurements of ammonia oxidation rates also showed this type of pattern at all stations (Supplementary Fig. 1). Subsurface maxima in ammonia oxidation tracked variations in the EZ across all six stations, but rates were not elevated in OMZ/AMZ waters—again contrasting with nitrite oxidation rate profiles at the AMZ stations. These data accord with earlier work in OMZs showing contrasting ammonia and nitrite oxidation rate profiles, and particularly high rates of nitrite oxidation in OMZ waters6,7,8,29,30,31.Initial DO concentrations for these measurements closely matched in situ values above the SCM (where DO concentrations are higher), and starting DO ranged from 260–1500 nM for measurements in and below the SCM. These DO concentrations are generally lower than those used for previous nitrite oxidation rate measurements in OMZs6,9, but similar to work examining the oxygen affinity of nitrite oxidation22 and overall oxygen consumption16,19. Elevated nitrite oxidation in the limited number of samples (n = 5) collected below the SCM ( >125 m at Station 1, >155 m at Station 2, and >180 m at Station 3)—where little to no DO is typically available—should be considered potential rates and could have a number of possible explanations discussed below. Within the SCM, our data support the idea that nitrite oxidation contributes to ‘cryptic’ oxygen cycling15—i.e., that DO produced via oxygenic photosynthesis is rapidly consumed.Oxygen consumption via nitrite oxidationWe determined the contribution of nitrite oxidation to overall oxygen consumption via parallel measurements of OCRs using in situ optical sensor spots—which are noninvasive, provide nearly identical results as other low-level measurement approaches32, are the only effective means of achieving substantial replication, and for which sensitivity increases as DO decreases32,33. Decreases in DO were measured in both nitrite and ammonia oxidation rate sample bottles, as well as in three additional replicates, to leverage statistical power for increased sensitivity to low-level DO consumption (see “Methods”). Water column OCR profiles at all stations showed exponential declines with depth and decreasing DO concentrations (Fig. 2D, H, L and Supplementary Fig. 1). Rates were highest in the upper water column and declined sharply within the upper portion of the OMZ above the SCM. The majority of measurements within the SCM—where DO may be produced via photosynthesis—were 100 s of nmol L−1 day−1, with an overall range of 160–1380 nmol L−1 day−1. Below the SCM, DO would be available more rarely (e.g., ref. 16), and OCR measurements represent potential rates should oxygen be supplied; OCR ranged from 120 to 390 nmol L−1 day−1. OCR also tracked variations in DO across stations, with progressively steeper declines in OCR with depth from Station 6 to Station 1.These OCR results are similar to the limited previous measurements that have been conducted in OMZ regions, with some key differences. In particular, they are consistent with previous measurements of rapid DO consumption in the SCM, with OCR rates ranging from 482 to 1520 nmol-O2 L−1 day−1 in the ETSP, and from 55 to 418 nmol-O2  L−1 day−1 in the ETNP15. Earlier OCR measurements conducted in the ETNP near Stations 1 and 3 (across a wide range of DO values) likewise ranged from 420 to 828 nmol L−1 day−1 in the SCM near Station 1, and from 101 to 269 nmol L−1 day−1 in the SCM near Station 3 (ref. 16). Above the SCM, previous OCR measurements in the ETNP spanned 2260 to 662 nmol L−1 day−1 from the EZ to the edge of the OMZ; these values are lower than our measurements at 44 and 67 m depth at Station 2, but in line with our remaining measurements above the SCM. OCR reached 1610 nmol L−1 day−1 in the SCM in Namibian shelf waters and 200–400 nmol L−1 day−1 in the SCM off Peru18. Kalvelage et al.18 furthermore observed sharp decreases with depth in the ETSP, with rates declining from >1000 nmol L−1 day−1 above the SCM.This pattern of declining OCR with increasing depth and decreasing DO was also evident in our dataset and contrasted with that of nitrite oxidation rates, which were notably elevated in the SCM at the AMZ stations (Fig. 2). We directly compared nitrite oxidation rates with OCR, assuming that each mole of nitrite is oxidized using ½ mole of O2 (ref. 5). We found that nitrite oxidation systematically increased as a proportion of overall OCR at lower DO levels (Fig. 3A, B). Nitrite oxidation was responsible for up to 69% of OCR at Station 1, although most values were closer to 10–40% at Stations 2 and 3 (Fig. 3A, B). In contrast, ammonia oxidation contributed 100 s of nM represent potential rates. For OMZ edge samples, OCR values in the µM range were higher than observed in profiles—most likely due to the effects of bubbling19, which could physically break down the organic matter present in higher concentrations at these depths (Table 1). Throughout all experiments, rate magnitudes in the 100 s of nM DO concentration range (11–820 nmol L−1 day−1) were similar to profile measurements (Fig. 2), as well as to previous measurements in OMZs15,16,18,19 (see above).DO concentrations were also continuously monitored in a subset of experimental bottles, and DO consumption was consistently linear (see “Methods”). The few exceptions occurred in several experiments conducted at DO concentrations More

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Model speciesThe American lobster Homarus americanus, is a crustacean found in temperate regions across the Northwest Atlantic Ocean. It is a highly valuable fishery species, caught off the coast of Eastern Canada and Northeast USA. For the past decade, they have been the most valuable single-species fishery in all of Canada and the US30,48. In Canada, catch was estimated at 104,000 tonnes and 14% of all of Canada’s total marine fisheries catch in 2019. However, their landed value was almost $1.6 billion and 44% of the Canada’s total marine fisheries landed value, and over 49% of the landed value from Canada’s Atlantic coast fisheries30,49. Canada’s Atlantic marine fisheries provide employment to over 40,000 people in primary harvesting and processing sectors, and supports many rural populations30.Dynamic bioclimate envelope modelWe used a dynamic bioclimate envelope model (DBEM)31,50 to assess spatial and temporal changes in the abundance and fisheries catch under different scenarios of climate change and fishing pressure. The model infers the environmental preference of the modelled species51, and simulates future changes in biomass and maximum catch potential. Notably, the DBEM integrates growth models52, ecophysiological models53, advection–diffusion models54, and surplus production population dynamics models55 to determine ocean change effects on species distribution, abundance, and catch. Since H. americanus is primarily a benthic invertebrate, we used values at sea floor for environmental variables in our model. However, they also have a pelagic larval phase and we used surface environmental variables to model this life stage.Initial distribution and abundanceThe DBEM uses an initial species distribution determined using a rule-based algorithm56,57,58. This algorithm determines species’ distribution range base on a series of geographic constraints, including latitudinal range, depth range, occurring ocean basins, and published or expert provided ‘bounding box’. It assumes that the relative abundance of the species distributes along gradients within these geographic limits with the centroid of the range having the highest relative abundance (Palomares et al. 2016). Species distributions are mapped on a global grid with a resolution of 0.5° longitude by 0.5° latitude cells with values representing relative abundance. Historical reconstructed catch data (http://www.seaaroundus.org)59 was used to estimate the global abundance and distributed accordingly with relative abundance values60. These catch data are based on various government and non-government reports, primary and grey literature, and also mapped on a 0.5° longitude by 0.5° latitude grid.The initial species distribution is then overlaid on climatologies of historical environmental conditions (e.g. temperature, salinity, oxygen, pH) simulated from outputs of Earth system models (e.g. Bopp et al. 2013; Dunne et al. 2013). The DBEM assumes that species distribution is in equilibrium with the average historical environmental condition (1971–2000 average) and abundance in cells are assumed to be at carrying capacity.Modelling individual growthGrowth is modelled using a derived von Bertalanffy growth model to incorporate how environmental stressors affects body size of lobsters31,32,61. We model the following important life history parameters as a function of relative changes in temperature, oxygen content [O2], and pH [H+]. Growth rate (dB/dt) is dependent on weight-specific anabolic and catabolic rates:$$frac{dB}{{dt}} = H_{i,t} W^{d} – k_{i,t} W$$
(1)
where H and k represent the coefficients for oxygen supply (anabolism) and oxygen demand for maintenance metabolism (catabolism), respectively, for cell i at time t. Body weight is scaled to anabolism with the exponent d  40 ppt), mixoeuhaline ( > 29 ppt), polyhaline ( > 18 ppt), mesophaline ( > 5 ppt), oligohaline ( > 0 ppt)—and SAssoc is the association of the species with each salinity class; and Icei is the sea ice % area coverage in a cell and IceP is the ice-dependency of the species. For H. americanus, they are not specifically associated with any habitat and thus only restricted by depth parameters. However, they are limited to mixoeuhaline and polyhaline salinities62.The TPP was estimated using the initial predicted relative abundance (described above) overlaid with the inputs of earth system models of initial environmental conditions. The relative weight for each temperature class z of the temperature preference profile was calculated as (TPP_{z} = R_{z} /sum R_{z}), where Rz is the relative abundance in each temperature class.A fuzzy logic model was used to model the movement between neighbouring cells based on differences in habitat suitability50. Emigration into a cell is favoured if habitat suitability is higher than surrounding cells, and immigration out of a cell is favoured if habitat suitability is lower than surrounding cells.We estimated larval production as 30% of spawning population biomass for each cell i, while larval mortality was 0.85 day−1 and settlement rate was 0.15 day−1—these values were chosen based on the sensitivity testing of these parameters50.Larval dispersal is modelled using an advection–diffusion54 and a larval duration model based on temperature66, such that abundance Ai,t in each cell is numerically solved for using the equation:$$frac{{partial A_{i,t} }}{partial t} = frac{partial }{partial x}left( {D_{i,t} frac{{partial A_{i,t} }}{partial x}} right) + frac{partial }{partial y}left( {D_{i,t} frac{{partial A_{i,t} }}{partial y}} right) – frac{partial }{partial y}left( {u cdot A_{i,t} } right) – frac{partial }{partial y}left( {v cdot A_{i,t} } right) – lambda cdot A_{i,t}$$
(16)
while adult dispersal is similarly modelled,$$frac{{partial A_{i,t} }}{partial t} = frac{partial }{partial x}left( {D_{i,t} frac{{partial A_{i,t} }}{partial x}} right) + frac{partial }{partial y}left( {D_{i,t} frac{{partial A_{i,t} }}{partial y}} right)$$
(17)
Advection was modelled for larval dispersal using parameters u and v for horizontal (east–west) and vertical (north–south) directions for surface current velocity (m2 s−1), respectively, between neighbouring cells x and y in the east–west and north–south direction, respectively. Instantaneous rate of larval mortality, ML, and settlement, SL was integrated into Eq. (16), where (lambda = 1 – e^{{ – left( {M_{L} + S_{L} } right)}}). The coefficient Di,t is the diffusion parameter:$$D_{i,t} = frac{{D_{i,0} cdot m}}{{1 + e^{{(tau cdot P_{i,t} cdot rho_{i,t} )}} }}$$
(18)
and$$rho_{i,t} = 1 – frac{{emptyset_{i,t} }}{{left( {C_{i,t} /overline{W}_{i,t} } right)}}$$
(19)
where Di,0 is the initial diffusion coefficient and a function of the spatial grid size (GR): (D_{i,0} = left( {1.1 times 10^{4} } right) cdot GR cdot 1.33). Parameters m and (tau)—both set at 2 in the model—determine the curvature of the functional relationship between D, P, and (rho)50. Parameter (rho_{i,t}) represents density-dependent factors and a function of population density (number of individuals), (emptyset_{i,t}), carrying capacity ((C_{i,t})), and mean body weight ((overline{W}_{i,t})) in each cell i.Models of ocean acidification effectsThe DBEM operates to model larval dispersal using advection–diffusion models. Survival is calculated at each time step (biweekly) based on a static annual survival rate. We recently tested a simple linear relationship between survival rate and pH, represented by percent changes in the survival rate given a change in pH32. We used parameters derived from previous experimental studies, where they observed a ~ 15% increase in mortality in larval and juvenile stages37 from a doubling of hydrogen ion concentration.We explore the OA effects by modelling variations in life stage-specific sensitivities to OA. Larvae, juveniles, and adults are modelled based on size classes, and the weight at maturity determines the size at which juveniles transition into adults65. Therefore, impacts of OA on survival can be modelled for various size classes. We model the effects of OA on the three major life history stages—larval, juvenile, and adult—and use a correlative approach to link changes in ocean acidity with changes in survival.The length transition matrix (Eqs. (8) and (9)) is split up into 40 length size classes, divided evenly from 0 to (l_{infty ,i,t}). We assume larvae transition from the pelagic phase to the growth transition matrix, and enter as the ‘larval’ stage for only the first size class. Next, juvenile size classes comprise all size classes below the length at maturity, lmat, as determined in Eq. (12), and lobster in any size classes greater are considered adults. While our models do not incorporate lobster-specific life cycle traits (i.e. transitioning between larval stages then to juvenile stages), we use more general models that can be broadly applied to many species.Modelling effects on survivalOA effects can be modelled as relative changes in survival rate for all life stages in Table 2. In other words, percent changes in acidity (i.e. hydrogen ion concentration) from baseline initial conditions results in a percent change in baseline survival rate. We use a model structure similar to that of previous work we have done32:$$Surv_{t} = Surv_{init} *left[ {1 + left( {p*left( {frac{{left[ {H^{ + } } right]_{t} }}{{left[ {H^{ + } } right]_{init} }} – 1} right)^{w} } right)} right]$$
(20)
Table 2 Scenario settings explored with model projections.Full size tableSurv is the survival rate per year and used here as an example but can be applied to other life histories affected by OA (e.g. growth, reproduction). Survival rate in year t is derived from the initial (init) survival rate and the relative change in [H+] between year t and initial [H+] conditions. Note that in our previous model, p represents the point value of the percent change effect size with a doubling of [H+]. This model utilizes single point effect size estimates that have no underlying assumed relationship between acidity and survival. In our model, we used an exponent value, w, equal to 1, which assumes a linear relationship32.Fishing pressureFishing mortality was assumed to be at maximum sustainable yield (MSY), which is the theoretical maximum biomass that can be sustainably removed from the population indefinitely. MSY is calculated using a Gordon Schaefer population growth model67:$$MSY = frac{{B_{infty } cdot r}}{4}$$where B∞ is the population carrying capacity and r is the intrinsic population growth rate. We use this measure of MSY as a proxy for the maximum catch potential (MCP) into the future, thus we assume that fisheries management are optimized and operate at MSY.Furthermore, the fishing mortality rate, Fi,t—i.e. the annual proportion at which biomass is taken from the current population biomass—in each cell i at time t at MSY can be calculated as:$$F_{MSY,i,t} = frac{r}{2}$$The fishing mortality rate was adjusted to explore scenarios of reduced fishing pressure and interactions with climate change and OA on the population dynamics of lobster. Any reductions in fishing pressure began in 2010 to represent how changes in fishing implemented now could change the state of lobster populations with the added stressors of climate change.Fishing size limitsFishing size limits were set to represent management scenarios and to observe their effects on lobster populations and size distribution of the population. We set four scenarios of minimum body size restrictions of lobster catch: no limit, canner small ( > 0.5 lb, 220 g), canner large ( > 0.75 lb, 320), and market ( > 1 lb, 430 g). Canner lobsters are smaller lobsters that are often sold at a cheaper price. They range from 0.5 to 1 lb, and are largely caught in Northumberland Strait where size limits are currently set lower due to warmer waters and smaller size at maturity44. For these scenarios of fishing size limits, we continue to assume catch is at maximum sustainable yield. Therefore, the same catch biomass (calculated using fishing mortality rate, F) will be the same for the various size limit restrictions, and more biomass will be taken from upper size classes where size limits are implemented. The no size limit results in fishing mortality to all size classes (including undersized lobsters).Climate change scenariosWe use outputs from three Earth system models for projections of various future climate change outcomes: NOAA’s Geophysical Fluid Dynamics Laboratory (GFDL-ESM), Institute Pierre Simon Laplace Climate Modelling Centre (IPSL-ESM), and Max Planck Institute for Meteorology (MPI-ESM)68. These models are included in the Coupled Model Intercomparisons Projection Phase 5 (CMIP5). We used two Representative Concentration Pathways (RCPs)69 which are greenhouse gas (GHG) concentration trajectories derived to reflect possible combinations of various socioeconomic assumptions, RCP 2.6 and RCP 8.5. The number associated with RCPs represent the radiative forcing values by the year 2100 based on greenhouse gas concentrations. RCP 2.6 corresponds with a low climate change scenario and assumes immediate mitigation of GHG emissions where annual emissions peak by mid-decade (year 2025) but is reduced considerably. This scenario is more in line with the 2015 Paris Agreement to limit warming to + 1.5 °C relative to other emissions scenarios applied in most CMIP5 Earth system models. Conversely, RCP 8.5 corresponds to a high climate change scenario and our current trajectory where we continue to use fossil fuels, have little to no change to switch to renewable energy sources, and GHG emissions continue to increase with no implementation of any mitigation action. We chose these three Earth system models as they provide sea surface and bottom layers and the full range of environmental variables required by the DBEM (i.e. sea temperature, dissolved oxygen, primary production, pH, current advection, salinity, sea ice extent) for both RCP scenarios2.All statistical analyses and figures were generated using the programming software R v4.0.370. More