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Research areaThe study was conducted in the Yunyang Experimental Station (108° 54′ E, 30° 55′ N; altitude of 700 m), Southwest University, Chongqing, China. The study area has a subtropical monsoon humid climate with an average annual sunshine duration of 1500 h, average annual temperature of 18.4 °C average annual rainfall of 1100.1 mm, and the rain period predominantly prolongs from June to September. Local soil type is clay loam in texture and Dystric Purple-Udic Cambosols according to the Chinese Soil Taxonomy (CRGCST 2001). Basic properties of 0–20 cm soil layer were as follows: pH 7.29, total N 0.94 g kg−1, total C 7.14 g kg−1, available N 37.45 mg kg−1, available P 2.36 mg kg−1, and available K 72.58 mg kg−1, respectively.The tested biochar was purchased from the Nanjing Qinfeng Straw Technology Co., Ltd. (Nanjing, China), which was made by pyrolysis of the rice (Oryza sativa L.) straw with limited oxygen supply at 500 °C for 2 h. Its properties were as follows: total N 0.61 g kg−1, total P 1.99 g kg−1, total K 27.15 g kg−1, total C 537.97 g kg−1 and pH 8.70.Experimental designA two-year filed experiment (2017–2019) was performed in a completely randomized design with twelve treatments in triplicates including two factors. The first factor was the application of biochar including B0 (0 t ha−1), B10 (10 t ha−1), B20 (20 t ha−1) and B40 (40 t ha−1); and the second factor is the application level N fertilizer including conventional rate (application amount by local farmers)-180 kg N ha−1 (N100), 80% of conventional rate-144 kg N ha−1 (N80) and 60% of conventional rate-108 kg N ha−1 (N60). The plot size was 3 m × 6 m with a border (0.5 m wide) between plots. Biochar was applied to soil only in the first year before the sowing of rapeseed. Each treatment plot received the same amount of potassium (90 kg K2O ha−1) and phosphorus (90 kg P2O5 ha−1). Further details of fertilizer application have been reported by Tian et al.24, being the same for the two-year experiment. Weed, pesticide, and pest management kept the same with the local farmers’ rapeseed management practices. Winter rapeseed (Sanxiayou No.5) was used in the experiment, which was sowed on 21 October 2017 and on 16 October 2018, respectively, and was harvested on 1 May in both years (2018 and 2019).Sampling and analysis of soil and cropCrop yieldRapeseed was hand-harvested when 70–80% of total seeds changed their color from green to black on 1 May 2019, and each plot was separately harvested for seed yield. Seed yield was calculated using 6% as standard seed moisture content.Soil indicesAfter the rapeseed harvest, soil samples were collected from all plots. Five sampling points were randomly selected within each plot. At each point, twenty soil cores of 2.5 cm diameter and 20.0 cm depth were taken in a 1 m radius of the point. All soil cores from each point were put in a plastic bag and thoroughly bulked, crumbled and mixed for physical, chemical and biological analyses. By dividing each soil sample into two subsamples, one subsample was ground, passed through a 2-mm sieve and was air-dried for the analyses of soil organic matter (SOM), total nitrogen (TN), total phosphorus (TP), total potassium (TK), alkali-hydrolyzale nitrogen (AN), available phosphorus (AP), available potassium (AK)25, particulate organic carbon (POC), water-soluble organic carbon (DOC), easily oxidized organic carbon (AOC)26, sucrase (SUC) and urease (URE)27, and another one was ground, passed through a 2-mm sieve and was stored in a refrigerator at − 20 °C for the analyses of structural and functional characteristics of soil microbial community28. At the same time, mixed soil samples (0–20 cm) from five points in each plot were taken using a shovel for soil aggregates analyses24.Drying method was used to determine soil water content (SWC); soil temperature (ST) was measured by temperature probe on the LI6400–09 (LI-COR Inc., Lincoln, NE); potassium dichromate oxidation method was used to determine SOM and DOC content; TN was measured by the Kjeldahl method; TP was determined by Mo-Sb colorimetric method; TK was determined by NaOH melting and analyzed using an atomic spectrophotometry; AN was determined by diffusion-absorption method; AP was quantified by colorimetric analysis following extraction of soil with 0.5 mol L−1 NaHCO3; AK was measured using 1.0 mol L−1 CH3COONH4 extraction; POC was determined by sodium hexametaphosphate dispersion method; AOC was measured by potassium permanganate oxidation method; SUC was measured by 3,5-dinitrosalicylic acid colorimetric determination method; URE was measured by phenol-sodium hypochlorite indophenol colorimetry method; amount of bacteria (B), fungi (F), actinomycetes (A), gram-positive bacteria (GP), gram-negative bacteria (GN) was measured by the Bligh–Dyer method; utilization of sugars (S), amino acids (AA), phenolic acids (PA), carboxylic acids (CA), amines (AM) and polymers (P) by microorganism was measured using commercial Biolog EcoPlate (Biolog Inc., CA, USA).Shannon index (H), Simpson index (D), and evenness index (E) were calculated by the following equations:$$ {text{AWCD}} = sum {(C_{i} – R_{i} )} /n $$$$ {text{H}} = – sum {P_{i} } (ln P_{i} )quad P_{i} = (C_{i} – R_{i} )/sum {(C_{i} – R_{i} } ) $$$$ {text{D}} = 1 – sum P _{i}^{2} $$$$ {text{E}} = {text{H}}/ln {text{S}} $$where n is the 31 carbon sources on the ECO board; Ci and Ri and are the optical density values of the microwell and the control well respectively; Pi is the ratio of the absorbance of a particular well i to the sums of absorbance of all 31well at 120 h; S is the number of color change holes, which represents the number of carbon source used by the microbial community; Average well color development (AWCD), representing the overall carbon substrate utilization potential of cultural microbial communities across all wells per plate.In order to investigate the aggregate structure, all bulk clod samples from each plot were carefully mixed and then gently sieved to pass through a 10-mm sieve. According to the wet-sieving and dry-sieving protocol, the tested soil was fractionated into  > 5, 2 ~ 5, 1 ~ 2, 0.25 ~ 1 and  0.25} right)} }}{{sumnolimits_{{i = 1}}^{n} {(w_{i} )} }} times 100% $$$$ {text{D – MWD}}left( {{text{W – MWD}}} right) = sumlimits_{{i = 1}}^{n} {(bar{d}_{i} w_{i} )} $$$$ {text{D – GMD}}left( {{text{W – GMD}}} right) = exp left[ {frac{{sumlimits_{{i = 1}}^{n} {m_{i} ln bar{d}_{i} } }}{{sumlimits_{{i = 1}}^{n} {m_{i} } }}} right] $$where DR0.25 and WR0.25 are the proportion of  > 0.25 mm soil mechanical-stable aggregates and water-stable aggregates, respectively; D-MWD and W-MWD are the mean weight diameter of mechanical-stable aggregates and water-stable aggregates (mm), respectively; D-GMD and W-GMD are the mean geometric diameter of mechanical-stable aggregates and water-stable aggregates (mm), respectively; mi is mass in size fraction i; and wi is the proportion (%) of the total sample mass in size fraction i and di is mean diameter of size fraction i.Evaluation of soil fertilityGrey correlation analysisGrey correlation analysis refers to a method of quantitative description and comparison of a system’s development and change. The basic idea is to determine whether they are closely connected by determining the geometric similarity of the reference data column and several comparison data columns, which reflects the degree of correlation between the curves29. The grey relational coefficient ξi (k) can be expressed as follows:$$ xi (k) = frac{{mathop {min }limits_{i} mathop {min }limits_{k} left| {x_{0} (k) – x_{i} (k)} right| + rho mathop {max }limits_{i} mathop {max }limits_{k} left| {x_{0} (k) – x_{i} (k)} right|}}{{left| {x_{0} (k) – x_{i} (k)} right| + rho mathop {max }limits_{i} max left| {mathop {x_{0} (k)}limits_{k} – x_{i} (k)} right|}} $$$$ x_{i}^{k} = frac{{x_{i}^{k} }}{{mathop {max }limits_{i} x_{i}^{k} }} $$$$ gamma _{i} = frac{1}{n}sumlimits_{{k = i}}^{n} {xi _{i} } (k) $$$$ omega _{{i(gamma )}} = frac{1}{n}sumlimits_{{i = 1}}^{n} {gamma _{i} } $$$$ G_{i}^{k} = sumlimits_{{i = 1}}^{n} {left( {xi _{i} times omega _{{i(gamma )}} } right),quad k = 1,2,3, ldots ,n;quad i = 1,2,3, ldots ,n} $$where (x_{i}^{k}) The i trait observation value of treatment k; (mathop {max }limits_{i} x_{i}^{k}) The maximum value of the i trait in all treatments; (mathop {min }limits_{i} x_{i}^{k}) The minimum value of the i trait in all treatments; (mathop {min }limits_{i} mathop {min }limits_{k} left| {x_{0} (k) – x_{i} (k)} right|) Second level minimum difference; (mathop {max }limits_{i} mathop {max }limits_{k} left| {x_{0} (k) – x_{i} (k)} right|) Second level maximum difference; (rho) Resolution coefficient (0.5).Principal component analysisPrincipal component analysis refers to a multivariate statistical method that converts multiple indicators into several comprehensive indicators by the idea of dimensionality under the premise of losing little information. It simplifies the complexity in high-dimensional data while retaining trends and patterns30.Cluster analysisCluster analysis comprises a range of methods for classifying multivariate data into subgroups. Using the euclidean distance as a measure of the difference in the fertility of each treatment, the shortest distance method was used to systematically cluster according to the degree of intimacy and similarity of soil fertility levels. By organizing multivariate data into such subgroups, clustering can help reveal the characteristics of any structure or patterns present31.Statistical analysisCorrelation analysis was performed to assess the relationships between rapeseed yield and soil attributes. Grey correlation analysis and principal component analysis were performed to establish comprehensive score for soil fertility and the main soil factors affecting rapeseed yield. Cluster analysis was used to cluster the soil fertility of each treatment. All the statistical analyses were performed using Excel 2018 (Office Software, Inc., Beijing, China) and SPSS 17.0 (SPSS Inc., Chicago, Illinois, USA). The comparisons of treatment means were based on LSD test at the P  More

The cell modelGrowth rate of a cellThe growth rate of a bacteria cell depends on the acquisition of C (from the particle) and N (from the particle and through ({{rm{N}}}_{2}) fixation), as well as on metabolic expenses in terms of C.Uptake of C and NBacteria get C from glucose and both C and N from amino acids. The total amount of C available for the cell from monomers is (units of C per time)$${J}_{{rm{DOC}}}={f}_{{rm{G,C}}}J_{G}+{f}_{{rm{A}},{rm{C}}}{J}_{{rm{A}}},$$
(8)
and the amount of N available from monomer is (N per time)$${J}_{{rm{DON}}}={f}_{{rm{A}},{rm{N}}}{J}_{{rm{A}}},$$
(9)
where ({J}_{rm{G}}) and ({J}_{rm{A}}) are uptake rates of glucose and amino acids, ({f}_{rm{G,C}}) is the fraction of C in glucose, and ({f}_{rm{A,C}}) and ({f}_{rm{A,N}}) are fractions of C and N in amino acids.The rate of obtaining N through ({{rm{N}}}_{2}) fixation is:$${J}_{{{rm{N}}}_{2}}({{psi }})={{psi }}{M}_{{{rm{N}}}_{2}},$$
(10)
where ({psi },(0 < {{psi }} < 1)) regulates ({{rm{N}}}_{2}) fixation rate and fixation can happen at a maximum rate ({M}_{{{rm{N}}}_{2}}). ({{rm{N}}}_{2}) fixation is only limited by the maximum ({{rm{N}}}_{2}) fixation rate as dissolved dinitrogen (({{rm{N}}}_{2})) gas in seawater is assumed to be unlimited70.The total uptake of C and N from different sources becomes$${J}_{{rm{C}}}={J}_{{rm{DOC}}}$$ (11) $${J}_{{rm{N}}}({{psi }})={J}_{{rm{DON}}}+{J}_{{{rm{N}}}_{2}}({{psi }})$$ (12) CostsRespiratory costs of cellular processes together with ({{rm{N}}}_{2}) fixation and its associated ({{rm{O}}}_{2}) removal cost depend on the cellular ({{rm{O}}}_{2}) concentration. Two possible scenarios can be observed: Case 1: When ({O}_{2}) concentration is sufficient to maintain aerobic respiration Respiratory costs for bacterial cellular maintenance can be divided into two parts: one dependent on limiting substrates and the other one is independent of substrate concentration71. Here we consider only the basal respiratory cost ({R}_{rm{B}}{x}_{rm{B}}), which is independent of the limiting substrates and is assumed as proportional to the mass of the cell ({x}_{B}) (μg C). In order to solubilize particles, particle-attached bacteria produce ectoenzymes that cleave bonds to make molecules small enough to be transported across the bacterial cell membrane. Cleavage is represented by a biomass-specific ectoenzyme production cost ({R}_{rm{E}})72. The metabolic costs associated with the uptake of hydrolysis products and intracellular processing are assumed to be proportional to the uptake (({J}_{i})): ({R}_{{rm{G}}}{J}_{{rm{G}}}) and ({R}_{{rm{A}}}{J}_{{rm{A}}}) where the ({R}_{i})’s are costs per unit of resource uptake. In a similar way, the metabolic cost of ({{rm{N}}}_{2}) fixation is assumed as proportional to the ({{rm{N}}}_{2}) fixation rate: ({R}_{{{rm{N}}}_{2}}{rho }_{{rm{CN}},{rm{B}}}{J}_{{{rm{N}}}_{2}}), where ({rho }_{{rm{CN}},{rm{B}}}) is the bacterial C:N ratio. If we define all the above costs as direct costs, then the total direct respiratory cost becomes$${R}_{{rm{D}}}({{psi }})={R}_{{rm{B}}}{x}_{{rm{B}}}+{R}_{{rm{E}}}{x}_{{rm{B}}}+{R}_{{rm{G}}}{J}_{{rm{G}}}+{R}_{{rm{A}}}{J}_{{rm{A}}}+{R}_{{{rm{N}}}_{2}}{rho }_{{rm{CN}},{rm{B}}}{J}_{{{rm{N}}}_{2}}({{psi }}).$$ (13) Indirect costs related to ({{rm{N}}}_{2}) fixation arises from the removal of ({{rm{O}}}_{2}) from the cell and the production/replenishment of nitrogenase as the enzyme is damaged by ({{rm{O}}}_{2}). The cell can remove ({{rm{O}}}_{2}) either by increasing respiration73 or by increasing the production of nitrogenase enzyme itself74. Here we consider only the process of ({{rm{O}}}_{2}) removal by increasing respiration. To calculate this indirect cost, the concentration of ({{rm{O}}}_{2}) present in the cell needs to be estimated.Since the time scale of ({{rm{O}}}_{2}) concentration inside a cell is short, we have assumed a pseudo steady state inside the cell; the ({{rm{O}}}_{2}) diffusion rate inside a cell is always balanced by the respiration rate14, which can be expressed as$${rho }_{{rm{CO}}}{F}_{{{rm{O}}}_{2}}={R}_{{rm{D}}}left({{psi }}right).$$ (14) Here ({rho }_{{rm{CO}}}) is the conversion factor of respiratory ({{rm{O}}}_{2}) to C equivalents and ({F}_{{{rm{O}}}_{2}}) is the actual ({{rm{O}}}_{2}) diffusion rate into a cell from the particle and can be calculated as$${F}_{{{rm{O}}}_{2}}=4{rm{pi }}{r}_{{rm{B}}}{K}_{{{rm{O}}}_{2}}left({X}_{{{rm{O}}}_{2}}-{X}_{{{rm{O}}}_{2},{rm{C}}}right),$$ (15) where ({r}_{{rm{B}}}) is the cell radius, ({X}_{{{rm{O}}}_{2}}) is the local ({{rm{O}}}_{2}) concentration inside the particle, ({X}_{rm{{O}}_{2},{rm{C}}}) is the cellular ({{rm{O}}}_{2}) concentration, and ({K}_{{{rm{O}}}_{2}}) is the effective diffusion coefficient of ({{rm{O}}}_{2}) over cell membrane layers. The effective diffusion coefficient can be calculated according to Inomura et al.14 in terms of diffusion coefficient inside particles (({bar{D}}_{{{rm{O}}}_{2}})), the diffusivity of cell membrane layers relative to water (({varepsilon }_{{rm{m}}})), the radius of cellular cytoplasm (({r}_{{rm{C}}})), and the thickness of cell membrane layers (({L}_{{rm{m}}})) as$${K}_{{{rm{O}}}_{2}}={bar{D}}_{{{rm{O}}}_{2}}frac{{varepsilon }_{{rm{m}}}({r}_{{rm{C}}}+{L}_{{rm{m}}})}{{varepsilon }_{{rm{m}}}{r}_{{rm{C}}}+{L}_{{rm{m}}}}.$$ (16) The apparent diffusivity inside particles (({bar{D}}_{{{rm{O}}}_{2}})) is considered as a fraction ({f}_{{{rm{O}}}_{2}}) of the diffusion coefficient in seawater (({D}_{{{rm{O}}}_{2}}))$${bar{D}}_{{{rm{O}}}_{2}}={f}_{{{rm{O}}}_{2}}{D}_{{{rm{O}}}_{2}}.$$ (17) Combining (14) and (15) gives the cellular ({{rm{O}}}_{2}) concentration ({X}_{{rm{O}}_{2},{rm{C}}}) as$${X}_{{{rm{O}}}_{2},{rm{C}}}={{max }}left[0,{X}_{{{rm{O}}}_{2}}-frac{{R}_{{rm{D}}}left({{psi }}right)}{4{rm{pi }}{r}_{{rm{B}}}{K}_{{{rm{O}}}_{2}}{rho }_{{rm{CO}}}}right].$$ (18) If there is excess ({{rm{O}}}_{2}) present in the cell after respiration (({X}_{{rm{O}}_{2},{rm{C}}} , > , 0)), then the indirect cost of removing the excess ({{rm{O}}}_{2}) to be able to perform ({{rm{N}}}_{2}) fixation can be written as$${R}_{{{rm{O}}}_{2}}left({{psi }}right)=Hleft({{psi }}right){rho }_{{rm{CO}}}4{rm{pi }}{r}_{{rm{B}}}{K}_{{{rm{O}}}_{2}}{X}_{rm{{O}}_{2},{rm{C}}},$$
(19)
where (H({{psi }})) is the Heaviside function:$$Hleft({{psi }}right)=left{begin{array}{cc}0,&{rm{if}}{,}{{psi }}=0\ 1, &{rm{if}}{,}{{psi }} , > , 0end{array}right..$$
(20)
Therefore, the total aerobic respiratory cost becomes:$${R}_{{rm{tot}},{rm{A}}}left({{psi }}right)={R}_{{rm{D}}}left({{psi }}right)+{R}_{{{rm{O}}}_{2}}left({{psi }}right).$$
(21)

Case 2: Anaerobic respiration
When available ({{rm{O}}}_{2}) is insufficient to maintain aerobic respiration (({R}_{{rm{tot}}}left({{psi }}right) , > , {rho }_{{rm{CO}}}{F}_{{{rm{O}}}_{2},{{max }}})), cells use ({{{rm{NO}}}_{3}}^{-}) and ({{{rm{SO}}}_{4}}^{2-}) for respiration. The potential ({{{rm{NO}}}_{3}}^{-}) uptake, ({J}_{{{rm{NO}}}_{3},{rm{pot}}}), is$${J}_{{{rm{NO}}}_{3},{rm{pot}}}={M}_{{{rm{NO}}}_{3}}frac{{A}_{{{rm{NO}}}_{3}}{X}_{{{rm{NO}}}_{3}}}{{A}_{{{rm{NO}}}_{3}}{X}_{{{rm{NO}}}_{3}}+{M}_{{{rm{NO}}}_{3}}},$$
(22)
where ({M}_{{{rm{NO}}}_{3}}) and ({A}_{{{rm{NO}}}_{3}}) are maximum uptake rate and affinity for ({{{rm{NO}}}_{3}}^{-}) uptake, respectively. However, the actual rate of ({{{rm{NO}}}_{3}}^{-}) uptake, ({J}_{{{rm{NO}}}_{3}}), is determined by cellular respiration and can be written as$${J}_{{{rm{NO}}}_{3}}={{min }}left({J}_{{{rm{NO}}}_{3},{rm{pot}}},{{max }}left(0,frac{{R}_{{rm{tot}},{rm{A}}}left({{psi }}right)-{rho }_{{rm{CO}}}{F}_{{{rm{O}}}_{2},{{max }}}}{{rho }_{{rm{C}}{{rm{NO}}}_{3}}}right)right),$$
(23)
where ({rho }_{{rm{C}}{{rm{NO}}}_{3}}) is the conversion factor of respiratory ({{{rm{NO}}}_{3}}^{-}) to C equivalents and the maximum ({{rm{O}}}_{2}) diffusion rate into a cell ({F}_{{{rm{O}}}_{2},{{max }}}) can be obtained by making cellular ({{rm{O}}}_{2}) concentration ({X}_{{{rm{O}}}_{2},{rm{c}}}) zero in (15) as$${F}_{{{rm{O}}}_{2},{{max }}}=4{rm{pi }}{r}_{{rm{B}}}{K}_{{{rm{O}}}_{2}}{X}_{{{rm{O}}}_{2}},$$
(24)
Further, in the absence of sufficient ({{{rm{NO}}}_{3}}^{-}), the cell uses ({{{rm{SO}}}_{4}}^{2-}) as an electron acceptor for respiration. Since the average concentration of ({{{rm{SO}}}_{4}}^{2-}) in seawater is 29 mmol L−1 75, ({{{rm{SO}}}_{4}}^{2-}) is a nonlimiting nutrient for cell growth and the potential uptake rate of ({{{rm{SO}}}_{4}}^{2-}) is mainly governed by the maximum uptake rate as$${J}_{{{rm{SO}}}_{4},{rm{pot}}}={M}_{{{rm{SO}}}_{4}},$$
(25)
where ({M}_{{{rm{SO}}}_{4}}) is the maximum uptake rate for ({{{rm{SO}}}_{4}}^{2-}) uptake. The actual rate of ({{{rm{SO}}}_{4}}^{2-}) uptake, ({J}_{{{rm{SO}}}_{4}}), can be written as$${J}_{{{rm{SO}}}_{4}}={{min }}left({J}_{{{rm{SO}}}_{4},{rm{pot}}},{{max }}left(0,frac{{R}_{{rm{tot}},{rm{A}}}left({{psi }}right)-{rho }_{{rm{CO}}}{F}_{{{rm{O}}}_{2},{{max }}}-{rho }_{{rm{CN}}{{rm{O}}}_{3}}{F}_{{{rm{NO}}}_{3},{rm{pot}}}}{{rho }_{{rm{C}}{{rm{SO}}}_{4}}}right)right),$$
(26)
where ({rho }_{{rm{C}}{{rm{SO}}}_{4}}) is the conversion factor of respiratory ({{{rm{SO}}}_{4}}^{2-}) to C equivalents.According to formulations (23) and (26), ({{{rm{NO}}}_{3}}^{-}) and ({{{rm{SO}}}_{4}}^{2-}) uptake occurs only when the diffusive flux of ({{rm{O}}}_{2}), and both ({{rm{O}}}_{2}) and ({{{rm{NO}}}_{3}}^{-}) are insufficient to maintain respiration(.) Moreover, the uptake rates of ({{{rm{NO}}}_{3}}^{-}) and ({{{rm{SO}}}_{4}}^{2-}) are regulated according to the cells’ requirements.Uptakes of ({{{rm{NO}}}_{3}}^{-}) and ({{{rm{SO}}}_{4}}^{2-}) incur extra metabolic costs ({R}_{{{rm{NO}}}_{3}}{rho }_{{rm{C}}{{rm{NO}}}_{3}}{J}_{{{rm{NO}}}_{3}}) and ({R}_{{{rm{SO}}}_{4}}{rho }_{{rm{C}}{{rm{SO}}}_{4}}{J}_{{{rm{SO}}}_{4}}), where ({R}_{{{rm{NO}}}_{3}}) and ({R}_{{{rm{SO}}}_{4}}) are costs per unit of ({{{rm{NO}}}_{3}}^{-}) and ({{{rm{SO}}}_{4}}^{2-}) uptake. The total respiratory cost can be written as$${R}_{{rm{tot}}}left({{psi }}right)={R}_{{rm{tot}},{rm{A}}}left({{psi }}right)+{R}_{{{rm{NO}}}_{3}}{rho }_{{rm{C}}{{rm{NO}}}_{3}}{J}_{{{rm{NO}}}_{3}}+{R}_{{{rm{SO}}}_{4}}{rho }_{{rm{C}}{{rm{SO}}}_{4}}{J}_{{{rm{SO}}}_{4}}.$$
(27)
Synthesis and growth rateThe assimilated C and N are combined to synthesize new structure. The synthesis rate is constrained by the limiting resource (Liebig’s law of the minimum) and by available electron acceptors such that the total flux of C available for growth ({J}_{{rm{tot}}}) (μg C d−1) is:$${J}_{{rm{tot}}}left({{psi }}right)={{min }}left[{J}_{{rm{C}}}-{R}_{{rm{tot}}}left({{psi }}right),{rho }_{{rm{CN,B}}}{J}_{{rm{N}}}left({{psi }}right),{rho }_{{rm{CO}}}{F}_{{{rm{O}}}_{2}}+{rho }_{{rm{C}}{{rm{NO}}}_{3}}{J}_{{{rm{NO}}}_{3}}+{rho }_{{rm{C}}{{rm{SO}}}_{4}}{J}_{{{rm{SO}}}_{4}}right].$$
(28)
Here, the total available C for growth is ({J}_{{rm{C}}}-{R}_{{rm{tot}}}({{psi }})), the C required to synthesize biomass from N source is ({rho }_{{rm{CN}},B}{J}_{rm{N}}), and the C equivalent inflow rate of electron acceptors to the cell is ({rho }_{{rm{CO}}}{F}_{{rm{O}}_{2}}+{rho }_{{rm{C}}{{rm{NO}}}_{3}}{J}_{{{rm{NO}}}_{3}}+{rho }_{{rm{C}}{{rm{SO}}}_{4}}{J}_{{{rm{SO}}}_{4}}). We assume that excess C or N is released from the cell instantaneously.Synthesis is not explicitly limited by a maximum synthesis capacity; synthesis is constrained by the C and N uptake in the functional responses (Eqs. 34 and 35). The division rate (mu) of the cell (d−1) is the total flux of C available for growth divided by the C mass of the cell (({x}_{rm{B}})):$$mu ({{psi }})={J}_{{rm{tot}}}({{psi }})/{x}_{rm{B}}.$$
(29)
The resulting division rate, (mu), is a measure of the bacterial fitness and we assume that the cell regulates its ({{rm{N}}}_{2}) fixation rate depending on the environmental conditions to gain additional N while maximizing its growth rate. The optimal value of the parameter regulating ({{rm{N}}}_{2}) fixation ({{psi }}) ((0le {{psi }}le 1)) then becomes:$${{{psi }}}^{ast }={{arg }}mathop{{{max }}}limits_{{{psi }}}{mu ({{psi }})},$$
(30)
and the corresponding optimal division rate becomes$${mu }^{ast }=mu left({{{psi }}}^{ast }right).$$
(31)
The particle modelWe consider a sinking particle of radius ({r}_{{rm{P}}}) (cm) and volume ({V}_{{rm{P}}}) (cm3) (Supplementary Fig. S1). The particle contains facultative nitrogen-fixing bacterial population (B(r)) (cells L−1), polysaccharides ({C}_{{rm{P}}}(r)) (μg G L−1), and polypeptides ({P}_{{rm{P}}}(r)) (μg A L−1) at a radial distance (r) (cm) from the center of the particle, where G and A stand for glucose and amino acids. We assume that only fractions ({f}_{{rm{C}}}) and ({f}_{{rm{P}}}) of these polymers are labile (({C}_{{rm{L}}}(r)={f}_{{rm{C}}}{C}_{{rm{P}}}(r),) ({P}_{{rm{L}}}(r)={f}_{{rm{P}}}{P}_{{rm{P}}}(r))), i.e., accessible by bacteria. Bacterial enzymatic hydrolysis converts the labile polysaccharides and polypeptides into monosaccharides (glucose) ((G) μg G L−1) and amino acids ((A) μg A L−1) that are efficiently taken up by bacteria. Moreover, the particle contains ({{rm{O}}}_{2}), ({{{rm{NO}}}_{3}}^{-}), and ({{{rm{SO}}}_{4}}^{2-}) with concentrations ({X}_{{{rm{O}}}_{2}}(r)) (μmol O2 L−1), ({X}_{{{rm{NO}}}_{3}}(r)) (μmol NO3 L−1), and ({X}_{{{rm{SO}}}_{4}}(r)) (μmol SO4 L−1). Glucose and amino acids diffuse out of the particle whereas ({{rm{O}}}_{2}) and ({{{rm{NO}}}_{3}}^{-}) diffuse into the particle from the surrounding environment. Due to the high concentration of ({{{rm{SO}}}_{4}}^{2-}) in ocean waters, we assume that ({{{rm{SO}}}_{4}}^{2-}) is not diffusion limited inside particles, its uptake is limited by the maximum uptake capacity due to physical constraint. The interactions between particle, cells, and the surrounding environment are explained in Supplementary Fig. S1 and equations are provided in Table 1 of the main text.We assume that labile polysaccharide (({C}_{{rm{L}}})) and polypeptide (({P}_{{rm{L}}})) are hydrolyzed into glucose and amino acids at rates ({J}_{{rm{C}}}) and ({J}_{{rm{P}}}) with the following functional form$${J}_{{rm{C}}}={h}_{{rm{C}}}frac{{A}_{{rm{C}}}{C}_{{rm{L}}}}{{h}_{{rm{C}}}+{A}_{{rm{C}}}{C}_{{rm{L}}}}$$
(32)
$${J}_{{rm{P}}}={h}_{{rm{P}}}frac{{A}_{{rm{P}}}{P}_{{rm{L}}}}{{h}_{{rm{P}}}+{A}_{{rm{P}}}{P}_{{rm{L}}}}$$
(33)
where ({h}_{{rm{C}}}) and ({h}_{{rm{P}}}) are maximum hydrolysis rates of the carbohydrate and peptide pool, and ({A}_{{rm{C}}}) and ({A}_{{rm{P}}}) are respective affinities. ({J}_{{rm{G}}}) and ({J}_{{rm{A}}}) represent uptake of glucose and amino acids:$${J}_{{rm{G}}}={M}_{{rm{G}}}frac{{A}_{{rm{G}}}G}{{A}_{{rm{G}}}G+{M}_{{rm{G}}}}$$
(34)
$${J}_{{rm{A}}}={M}_{{rm{A}}}frac{{A}_{{rm{A}}}A}{{A}_{{rm{A}}}A+{M}_{{rm{A}}}}$$
(35)
where ({M}_{{rm{G}}}) and ({M}_{{rm{A}}}) are maximum uptake rates of glucose and amino acids, whereas ({A}_{{rm{G}}}) and ({A}_{{rm{A}}}) are corresponding affinities. Hydrolyzed monomers diffuse out of the particle at a rate ({D}_{{rm{M}}}).({mu }^{ast }) is the optimal division rate of cells (Eq. 31) and ({m}_{rm{B}}) represents the mortality rate (including predation) of bacteria. ({F}_{{{rm{O}}}_{2}}) and ({J}_{{{rm{NO}}}_{3}}) represent the diffusive flux of ({{rm{O}}}_{2}) and the consumption rate of ({{{rm{NO}}}_{3}}^{-}), respectively, through the bacterial cell membrane. ({bar{D}}_{{{rm{O}}}_{2}}) and ({bar{D}}_{{{rm{NO}}}_{3}}) are diffusion coefficients of ({{rm{O}}}_{2}) and ({{{rm{NO}}}_{3}}^{-}) inside the particle.At the center of the particle ((r=0)) the gradient of all quantities vanishes:$${left.frac{partial G}{partial r}right|}_{r=0}={left.frac{partial A}{partial r}right|}_{r=0}={left.frac{partial {X}_{{{rm{O}}}_{2}}}{partial r}right|}_{r=0}={left.frac{partial {X}_{{rm{N}}{{rm{O}}}_{3}}}{partial r}right|}_{r=0}=0$$
(36)
At the surface of the particle ((r={r}_{{rm{P}}})) concentrations are determined by the surrounding environment:$${left.Gright|}_{r={r}_{{rm{P}}}}={G}_{infty },{left.Aright|}_{r={r}_{{rm{P}}}}={A}_{infty },{left.{X}_{{{rm{O}}}_{2}}right|}_{r={r}_{{rm{P}}}}={X}_{{{rm{O}}}_{2},infty },{left.{X}_{{{rm{NO}}}_{3}}right|}_{r={r}_{{rm{P}}}}={X}_{{{rm{NO}}}_{3},infty }$$
(37)
where ({G}_{infty },) ({A}_{infty ,}) ({X}_{{{rm{O}}}_{2},infty }) and ({X}_{{{rm{NO}}}_{3},infty }) are concentrations of glucose, amino acids, ({{rm{O}}}_{2}), and ({{{rm{NO}}}_{3}}^{-}) in the environment.Calculation of total N2 fixation rateThe total amount of fixed ({{rm{N}}}_{2}) in a specific size class of particle, ({{rm{N}}}_{{rm{fix}},{rm{P}}}) (({rm{mu }})g N particle−1), is calculated as$${{rm{N}}}_{{rm{fix}},{rm{P}}}=int int 4pi {{r}_{{rm{B}}}}^{2}B{J}_{{{rm{N}}}_{2}}{rm{d}}{r}_{{rm{P}}}{rm{dz}},$$
(38)
where ({r}_{{rm{P}}}) (cm) is the particle radius and z (m) represents the water column depth.({{rm{N}}}_{2}) fixation rate per unit volume of water, ({{rm{N}}}_{{rm{fix}},{rm{V}}}left(tright)) (({rm{mu }}{rm{mol}}) N m−3 d−1), is calculated as$${{rm{N}}}_{{rm{fix}},{rm{V}}}=int int 4pi {{r}_{{rm{B}}}}^{2}rho B{J}_{{{rm{N}}}_{2}}n(x){rm{d}}{r}_{{rm{P}}}{rm{d}}x,$$
(39)
Here (x) (cm) represents the size range (radius) of particles, (rho) is the fraction of diazotrophs of the total heterotrophic bacteria, and (n(x)) (number of particles per unit volume of water per size increment) is the size spectrum of particles that is most commonly approximated by a power law distribution of the form$$n(x)={n}_{0}{(2x)}^{xi }$$
(40)
where ({n}_{0}) is a constant that controls total particle abundance and the slope (xi) represents the relative concentration of small to large particles: the steeper the slope, the greater the proportion of smaller particles and the flatter the slope, and the greater the proportion of larger particles34.Depth-integrated ({{rm{N}}}_{2}) fixation rate, ({{rm{N}}}_{{rm{fix}},{rm{D}}}) (({rm{mu }}{rm{mol}}) N m−2 d−1), can be obtained by$${{rm{N}}}_{{rm{fix}},{rm{D}}}left(tright)=int {{rm{N}}}_{{rm{fix}},{rm{V}}}{rm{d}}z.$$
(41)
Assumptions and simplification in the modeling approachAccording to our current model formulation, the particle size remains constant while sinking. However, in nature, particle size is dynamic due to processes like bacterial remineralization, aggregation, and disaggregation. We neglect these complications to keep the model simple and to focus on revealing the coupling between particle-associated environmental conditions and ({{rm{N}}}_{2}) fixation by heterotrophic bacteria. These factors can, however, possibly be incorporated by using in situ data or by using the relationship between carbon content and the diameter of particles48 and including terms for aggregation and disaggregation55.Our model represents a population of facultative heterotrophic diazotrophs that grow at a rate similar to other heterotrophic bacteria but the whole community initiates ({{rm{N}}}_{2}) fixation when conditions become suitable. However, under natural conditions, diazotrophs may only constitute a fraction of the bacterial community, and their proliferation may be gradual21, presumably affected by multiple factors. In such case, our approach will overestimate diazotroph cell concentration and consequently the ({{rm{N}}}_{2}) fixation rate.For simplicity, our approach includes only aerobic respiration, ({{{rm{NO}}}_{3}}^{-}) and ({{{rm{SO}}}_{4}}^{2-}) respiration, although many additional aerobic and anaerobic processes likely occur on particles (e.g Klawonn et al.19). To our knowledge, a complete picture of such processes, their interactions and effects on particle biochemistry is unavailable. For example, we have assumed that when ({{rm{O}}}_{2}) and ({{{rm{NO}}}_{3}}^{-}) are insufficient to maintain respiration, heterotrophic bacteria start reducing ({{{rm{SO}}}_{4}}^{2-}). However, ({{{rm{SO}}}_{4}}^{2-}) reduction has been detected only with a significant lag after the occurrence of anaerobic conditions, suggesting it as a slow adapted process76, whereas we assume it to be instantaneous. On the other hand, the lag may not be real but due to a so called cryptic sulfur cycle, where ({{{rm{SO}}}_{4}}^{2-}) reduction is accompanied by concurrent sulfide oxidation effectively masking sulfide production77. Hopefully, future insights into interactions between diverse aerobic and anaerobic microbial processes can refine our modelling approach and fine-tune predictions of biochemistry in marine particles.Procedure of numerically obtaining optimal N2 fixation rateTo avoid making the optimization in Eq. (30) at every time step during the simulation, a lookup table of ({mu }^{ast }) (Eq. 31) over realistic ranges of the four resources (glucose, amino acids, ({{rm{O}}}_{2}), and ({{{rm{NO}}}_{3}}^{-})) and the parameter determining ({{rm{N}}}_{2}) fixation rate (({{psi }})) was created at the beginning of the simulation.The effects of temperature on N2 fixation rateTo examine the role of temperature variation on ({{rm{N}}}_{2}) fixation rate in sinking particles, we consider hydrolysis of polysaccharide and polypeptide, uptake of glucose and amino acids, uptake of ({{{rm{NO}}}_{3}}^{-}), respiration, and diffusion dependent on temperature. Apart from diffusion, all other processes are multiplied by a factor ({Q}_{10}) that represents the factorial increase in rates with ({10}^{0})C temperature increase. The rate (R) at a given temperature (T) is then$$R={R}_{{rm{ref}}}{{Q}_{10}}^{(T-{T}_{{rm{ref}}})/10}.$$
(42)
Here the reference rate ({R}_{{rm{ref}}}) is defined as the rate at the reference temperature ({T}_{{rm{ref}}}.) We set the reference temperature ({T}_{{rm{ref}}}) at room temperature of 20 °C. The effect of temperature on the diffusion coefficient D for glucose, amino acids, ({{rm{O}}}_{2}), and ({{{rm{NO}}}_{3}}^{-}) is described by Walden’s rule:$$D={D}_{{rm{ref}}}{eta }_{{rm{ref}}}T/(eta {T}_{{rm{ref}}})$$
(43)
where (eta) is the viscosity of water at the given temperature (T), and ({D}_{{rm{ref}}}) and ({eta }_{{rm{ref}}}) are diffusion coefficient and viscosity at ({T}_{{rm{ref}}}).({Q}_{10}) values for different enzyme classes responsible for hydrolysis (({Q}_{10,{rm{h}}})) lie within the range 1.1–2.978. Here, we have chosen ({Q}_{10,{rm{h}}}=2) for hydrolysis from the middle of the prescribed range. The ({Q}_{10}) values for uptake affinities (({Q}_{10,{rm{A}}})) are taken as 1.579. ({Q}_{10,{rm{R}}}=2) is chosen for all parameters related to respiration (({R}_{{rm{B}}}), ({R}_{{rm{E}}}), ({R}_{{rm{G}}}), ({R}_{{rm{A}}}), ({R}_{{{rm{N}}}_{2}}), ({R}_{{{rm{NO}}}_{3}}), ({R}_{{{rm{SO}}}_{4}}))80. ({R}_{{rm{ref}}}) and ({D}_{{rm{ref}}}) are the values of (R)’s and (D)’s provided in Table S1. The reference viscosity (({eta }_{{rm{ref}}})) and viscosities ((eta)) at different temperatures are taken from Jumars et al.80. More

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System overviewTo address the open-set novel species detection problem, our system leverages a two-step image recognition process. Given an image of a mosquito specimen, the first step uses CNNs trained for species classification to extract relevant features from the image. The second step is a novelty detection algorithm, which evaluates the features extracted by the CNNs in order to detect whether the mosquito is a member of one of the sixteen species known to the CNNs of the system. The second step consists of two stages of machine learning algorithms (tier II and tier III) that evaluate the features generated in step one to separate known species from unknown species. Tier II components evaluate the features directly and are trained using known and unknown species. Tier III evaluates the answers provided by the tier II components to determine the final answer, and is trained using known species, unknown species used for training tier II components, and still more unknown species not seen by previous components. If the mosquito is determined by tier III not to be a member of one of the known species, it is classified as an unknown species, novel to the CNNs. This detection algorithm is tested on truly novel mosquito species, never seen by the system in training, as well as the species used in training. If a mosquito is recognized by the system as belonging to one of the sixteen known species (i.e. not novel), the image proceeds to species classification with one of the CNNs used to extract features.Unknown detection accuracyIn distinguishing between unknown species and known species, the algorithm achieved an average accuracy of 89.50 ± 5.63% and 87.71 ± 2.57%, average sensitivity of 92.18 ± 6.34% and 94.09 ± 2.52%, and specificity of 80.79 ± 7.32% and 75.82 ± 4.65%, micro-averaged and macro-averaged respectively, evaluated over twenty-five-fold validation (Table 1). Here, micro-average refers to the metric calculated without regard to species, such that each image sample has an equal weight, considered an image sample level metric. Macro-average refers to the metric first calculated within a species, then averaged between all species within the relevant class (known or unknown). Macro-average can be considered a species level metric, or a species normalized metric. Macro-averages tend to be lower than the micro-averages when species with higher sample sizes have the highest metrics, whereas micro-averages are lower when species with lower sample sizes have the highest metrics. Cross validation by mixing up which species were known and unknown produced variable sample sizes in each iteration, because each species had a different number of samples in the generated image dataset. Further sample size variation occurred as a result of addressing class imbalance in the training set. The mean number of samples varied for each of the 25 iterations because of the mix-up in data partitioning for cross-validation (see Table 1 for generalized metrics; see Supplementary Table 1, Datafolds for detailed sampling data).Table 1 Micro- and macro-averaged metrics of the novelty detection algorithm on the test set using 50-fold validation.Full size tableDifferences within the unknown species dictated by algorithm structureThe fundamental aim of novelty detection is to determine if the CNN in question is familiar with the species, or class, shown in the image. CNNs are designed to identify visually distinguishable classes, or categories. In our open-set problem, the distinction between known and unknown species is arbitrary from a visual perspective; it is only a product of the available data. However, the known or unknown status of a specimen is a determinable product of the feature layer outputs, or features, produced by the CNN’s visual processing of the image. Thus, we take a tiered approach, where CNNs trained on a specific set of species extract a specimen’s features, and independent classifiers trained on a wider set of species analyze the features produced by the CNNs to assess whether the CNNs are familiar with the species in question. The novelty detection algorithm consists of three tiers, hereafter referred to as Tier I, II, and III, intended to determine if the specimen being analyzed is from a closed set of species known to the CNN:Tier I: two CNNs used to extract features from the images.Tier II: a set of classifiers, such as SVMs, random forests, and neural networks, which independently process the features from Tier I CNNs to distinguish a specimen as either known or unknown species.Tier III: soft voting of the Tier II classifications, with a clustering algorithm, in this case a Gaussian Mixture Model (GMM), which is used to make determinations in the case of unconfident predictions.The tiered architecture necessitated partitioning of groups of species between the tiers, and an overview of the structure is summarized in Fig. 2A. The training schema resulted in three populations of unknown species: set U1, consisting of species used to train Tier I, also made available for training subsequent Tiers II and III; set U2, consisting of additional species unknown to the CNNs used to train Tiers II and III; and set N, consisting of species used only for testing (see Fig. 2B). Species known to the CNNs are referred to as set K. It is critical to measure the difference between these species sets, as any of the species may be encountered in the wild. U1 achieved 97.85 ± 2.81% micro-averaged accuracy and 97.34 ± 3.52% macro-averaged accuracy; U2 achieved 97.05 ± 1.94% micro-averaged accuracy and 97.30 ± 1.41% macro-averaged accuracy; N achieved 80.83 ± 19.91% micro-averaged accuracy and 88.72 ± 5.42% macro-averaged accuracy. The K set achieved 80.79 ± 7.32% micro-averaged accuracy and 75.83 ± 5.42% macro-averaged accuracy (see Table 2). The test set sample sizes for each of the twenty five folds are as follows, (formatted [K-taxa,K-samples;U1-taxa,U1-samples;U2-taxa,U2-samples;N-taxa,N-samples]): [16,683;8,51;10,536;13,456], [16,673;8,51;9,537;13,485], [16,673;8,51;8,523;13,508], [16,673;8,46;6,159;11,869], [16,694;8,51;7,483;10,548], [15,409;9,62;11,2906;8,546], [15,456;9,62;9,2458;12,1024], [15,456;10,67;13,2359;9,1115], [15,456;9,62;8,3189;12,306], [15,456;10,67;10,2874;10,601], [16,543;10,56;12,1450;10,1052], [16,484;9,52;11,2141;10,312], [16,492;10,54;11,2185;12,263], [16,512;8,45;15,2292;10,189], [16,480;9,49;9,1652;13,790], [16,442;9,44;11,1253;11,665], [16,494;10,54;14,1727;10,228], [16,442;9,55;13,1803;10,96], [16,538;10,60;8,1509;9,502], [16,489;10,60;13,1764;9,184], [16,462;8,47;13,1415;11,452], [16,437;8,54;9,1548;11,320], [16,447;8,55;11,654;10,1193], [16,547;8,44;9,1437;11,531], [16,548;7,52;7,1464;11,499]. See Supplementary Table 1, Datafolds for more detailed sample information.Figure 2The novelty detection architecture was designed with three tiers to assess whether the CNNs were familiar with the species shown in each image. (A) Tier I consisted of two CNNs used as feature extractors. Tier II consisted of initial classifiers making an initial determination about whether the specimen is known or unknown by analyzing the features of one of the Tier I CNNs, and the logits in the case of the wide and deep neural network (WDNN). In this figure, SVM refers to a support vector machine, and RF refers to a random forest. Tier III makes the final classification, first with soft voting of the Tier II outputs, then sending high confidence predictions as the final output and low confidence predictions to a Gaussian Mixture Model (GMM) to serve as the arbiter for low confidence predictions. (B) Data partitioning for training each component of the architecture is summarized: Tier I is trained on the K set of species, known to the algorithm; Tier I open-set CNN is also trained on the U1 set of species, the first set of unknown species used in training; Tier II is trained on K set, U1 set, and the U2 set of species, the second set of unknown species used in training; Tier III is trained on the same species and data-split as Tier II. Data-split ratios were variable for each species over each iteration (Xs,m where s represents a species, m represents a fold, and X is a percentage of the data devoted to training) for Tiers II and III; Xs,m was adjusted to manage class imbalance within genus across known and unknown classes. Testing was performed on each of the K, U1, and U2 sets, as well as the N set, the final set of unknown species reserved for testing the algorithm, such that it is tested on previously unseen taxa, replicating the plausible scenario to be encountered in deployment of CNNs for species classification. Over the twenty-five folds, each known species was considered unknown for at least five folds and included as novel for at least one-fold.Full size imageTable 2 Accuracy metrics for the known, unknown, and novel unknown species sets over twenty-five-fold validation.Full size tableSubsequent species classificationFollowing the novelty detection algorithm, species identified as known are sent for species classification to the closed-set Xception model used in Tier I of the novelty detection algorithm. Figure 3A shows the species classification results independently over the five folds of Tier I, which achieved a micro-averaged accuracy 97.04 ± 0.87% and a macro F1-score of 96.64 ± 0.96%. Figure 3B shows the species classification cascaded with the novelty detection methods where all unknown species are grouped into a single unknown class alongside the known classes in an aggregated mean confusion matrix over the twenty-five folds of the full methods, yielding a micro-averaged accuracy of 89.07 ± 5.58%, and a macro F1-score of 79.74 ± 3.65%. The confusion matrix is normalized by species and shows the average classification accuracy and error distribution. The independent accuracy for classifying a single species ranged from 72.44 ± 13.83% (Culex salinarius) to 100 ± 0% (Aedes dorsalis, Psorophora cyanescens), and 15 of the 20 species maintained an average sensitivity above 95%. Test set sample size for each species were as follows (formatted as species, [fold1,fold2,fold3,fold4,fold5]): Ae. aegypti: [127,0,133,132,126]; Ae. albopictus: [103,90,0,99,102]; Ae. dorsalis: [43,41,42,0,41]; Ae. japonicus: [162,159,154,156,0]; Ae. sollicitans: [57,0,60,58,60]; Ae. taeniorhynchus: [0,25,27,25,24]; Ae. vexans: [50,48,0,46,49]; An. coustani: [29,21,18,0,22]; An. crucians s.l.: [56,58,61,61,0]; An. freeborni: [87,0,77,79,80]; An. funestus s.l.: [158, 174,0,173,175]; An. gambiae s.l.: [182,178,178,0,166]; An. punctipennis: [0,36,31,34,33]; An. quadrimaculatus: [0,28,28,28,30]; Cx. erraticus: [47,47,44,49,0]; Cx. pipiens s.l.: [212,0,218,219,205]; Cx. salinarius: [25,26,0,26,25]; Ps. columbiae: [66,59,67,0, 64]; Ps. cyanescens: [0,55,56,54,56]; Ps. ferox: [40,31,41,34,0].Figure 3Mean normalized confusion matrices for species classification shows the distribution of error within species. The species classification in these confusion matrices was performed by the Tier I CNN, the closed-set Xception model. The confusion matrix conveys the ground truth of the sample horizontally, labels on the left, and the prediction of the full methods vertically, labels on the bottom. Accurate classification is across the diagonal, where ground truth and prediction match, and all other cells on the matrix describe the error. Sixteen species were known for a given fold, and 51 species were considered unknown for a given fold, with each of the twenty known species considered unknown for one fold. (A) The species classification independent of novelty detection shows an average accuracy of 97.04 ± 0.87% and a macro F1-score of 96.64 ± 0.96%, calculated over the five folds of Tier I classifiers, trained and tested over an average of 7174.8 and 1544.6 samples. Of the error, 73.5% occurred with species of the same genus as the true species. (B) The species classification as a subsequent step after novelty detection yielded 89.07 ± 5.58% average accuracy, and a macro F1-score of 79.74 ± 3.65% trained and tested on an average of 7174.8 and 519.44 samples, evaluated over the twenty-five folds of the novelty detection methods. First, a sample was sent to the novelty detection algorithm. If the sample was predicted to be known to the species classifier, which was the closed-set Xception algorithm used in Tier I, then the sample was sent to the algorithm for classification.Full size imageMany of the species which were a part of the unknown datasets had enough data to perform preliminary classification experiments. Thirty-nine of the 67 species had more than 40 image samples. Species classification on these 39 species yielded an unweighted accuracy of 93.06 ± 0.50% and a macro F1-score of 85.07 ± 1.81% (see Fig. 4A). The average F1-score for any one species was plotted against the number of specimens representing the samples in the species, which elucidates the relationship between the training data available and the accuracy (see Fig. 4B). No species with more than 100 specimens produced an F1-score below 93%.Figure 4Species classification across 39 species shows the strength of CNNs for generalized mosquito classification, and elucidates a guideline for the number of specimens required for confident classification. Classification achieved unweighted accuracy of 93.06 ± 0.50% and a macro F1-score of 85.07 ± 1.81%, trained, validated, and tested over an average of 9080, 1945, and 1945 samples over five folds. (A) The majority of the error in this confusion matrix shows confusion between species of the same genera. Some of the confusion outside of genera is more intuitive from an entomologist perspective, such as the 10.2% of Deinocerites cancer samples classified as Culex spp. Other errors are less intuitive, such as the 28.61% of Culiseta incidens samples classified as Aedes atlanticus. (B) This plot of average F1-score of a species against the number of specimens which made up the samples available for training and testing shows the relationship between the available data for a given specimen and classification accuracy. When following the database development methods described in this work, a general guideline of 100 specimens’ worth of data can be extrapolated as a requirement for confident mosquito species classification.Full size imageTest set sample size for each species in the 39 species closed-set classification were as follows (formatted as species, [fold1,fold2,fold3,fold4, fold5]): Ae. aegypti: [131,127,127,124,133]; Ae. albopictus: [99,99,107,97,95]; Ae. atlanticus: [15,13,14,14,15]; Ae. canadensis: [17,21,21,21,20]; Ae. dorsalis: [42,41,43,40,43]; Ae. flavescens: [13,14,14,14,14]; Ae. infirmatus: [17,15,19,18,16]; Ae. japonicus: [155,153,151,160,150]; Ae. nigromaculis: [6,6,5,5,5]; Ae. sollicitans: [63,61,58,57,60]; Ae. taeniorhynchus: [30,25,27,25,25]; Ae. triseriatus s.l.: [14,16,17,14,13]; Ae. trivittatus: [28,24,25,24,23]; Ae. vexans: [46,58,57,51,50]; An. coustani: [25,32,27,33,27]; An. crucians s.l.: [64,57,60,59,62]; An. freeborni s.l.: [85,77,82,74,89]; An. funestus s.l.: [181,187,166,175,161]; An. gambiae s.l.: [191,182,178,185,194]; An. pseudopunctipennis: [10,8,12,9,9]; An. punctipennis: [32,28,38,32,32]; An. quadrimaculatus: [30,33,26,37,35]; Coquillettidia perturbans: [31,29,30,32,35]; Cx. coronator: [10,9,10,11,10]; Cx. erraticus: [48,51,49,53,50]; Cx. nigripalpus: [14,14,13,13,13]; Cx. pipiens s.l.: [205,203,216,208,216]; Cx. restuans: [12,13,12,14,12]; Cx. salinarius: [24,25,24,23,24]; Cus. incidens: [9,9,9,9,8]; Cus. inornata: [9,9,8,9,9]; Deinocerites cancer: [10,10,10,10,9]; De. sp. Cuba-1: [16,14,15,14,15]; Mansonia titillans: [15,16,15,14,13]; Ps. ciliata: [29,26,24,23,28]; Ps. columbiae: [62,59,63,60,61]; Ps. cyanescens: [55,54,57,55,55]; Ps. ferox: [32,48,31,36,34]; Ps. pygmaea: [24,25,25,24,25].Comparison to alternative methodsSome intuitive simplifications of our methods, along with some common direct methods for novel species detection, are compared to our full methods. All compared methods were found to be statistically different from the full methods using McNemar’s test. The compared methods tested, along with their macro F1-score, standard deviation, and p-value as compared to the full methods, were as follows: (1) soft voting of all Tier II component outputs, without a GMM arbiter (86.87 ± 3.11%, p  More