A unified theory for organic matter accumulation

Zakem, Emily J.; Cael, B. B.; Levine, Naomi M.

doi:10.1073/pnas.2016896118

A unified theory for organic matter accumulation

Emily J. Zakem https://orcid.org/0000-0001-6799-5063 zakem@usc.edu, B. B. Cael https://orcid.org/0000-0003-1317-5718, and Naomi M. Levine https://orcid.org/0000-0002-4963-0535Authors Info & Affiliations
Emily J. Zakem https://orcid.org/0000-0001-6799-5063 zakem@usc.edu，B. B. Cael https://orcid.org/0000-0003-1317-5718，和Naomi M. Levine https://orcid.org/0000-0002-4963-0535 作者信息和所属单位

Edited by David M. Karl, University of Hawaii at Manoa, Honolulu, HI, and approved December 30, 2020 (received for review August 9, 2020)
由大卫·M·卡尔（David M. Karl）编辑，夏威夷大学马诺阿分校（University of Hawaii at Manoa）批准，位于夏威夷檀香山市，2020年12月30日（接收审查日期为2020年8月9日）。

February 3, 2021

118 (6) e2016896118

https://doi.org/10.1073/pnas.2016896118

Commentary

February 23, 2021

Unifying chemical and biological perspectives of carbon accumulation in the environment

Daniel J. Repeta

Significance

Organic matter in the global ocean, soils, and sediments stores about five times more carbon than the atmosphere. Thus, the controls on the accumulation of organic matter are critical to global carbon cycling. However, we lack a quantitative understanding of these controls. This prevents meaningful descriptions of organic matter cycling in global climate models, which are required for understanding how changes in organic matter reservoirs provide feedbacks to past and present changes in climate. Currently, explanations for organic matter accumulation remain under debate, characterized by seemingly competing hypotheses. Here, we develop a quantitative framework for organic matter accumulation that unifies these hypotheses. The framework derives from the ecological dynamics of microorganisms, the dominant consumers of organic matter.
全球海洋、土壤和沉积物中的有机物贮存了大约比大气中的碳多五倍。因此，有机物积累的控制对于全球碳循环至关重要。然而，我们对这些控制缺乏定量的理解。这阻碍了对全球气候模型中有机物循环的有意义描述，而这些模型对于理解有机物储库的变化如何对过去和现在的气候变化提供反馈是必需的。目前，有关有机物积累的解释仍存在争议，表现为看似相互竞争的假设。在这里，我们建立了一个定量的有机物积累框架，将这些假设统一起来。该框架源于有机物的主要消费者微生物的生态动力学。

Abstract

Organic matter constitutes a key reservoir in global elemental cycles. However, our understanding of the dynamics of organic matter and its accumulation remains incomplete. Seemingly disparate hypotheses have been proposed to explain organic matter accumulation: the slow degradation of intrinsically recalcitrant substrates, the depletion to concentrations that inhibit microbial consumption, and a dependency on the consumption capabilities of nearby microbial populations. Here, using a mechanistic model, we develop a theoretical framework that explains how organic matter predictably accumulates in natural environments due to biochemical, ecological, and environmental factors. Our framework subsumes the previous hypotheses. Changes in the microbial community or the environment can move a class of organic matter from a state of functional recalcitrance to a state of depletion by microbial consumers. The model explains the vertical profile of dissolved organic carbon in the ocean and connects microbial activity at subannual timescales to organic matter turnover at millennial timescales. The threshold behavior of the model implies that organic matter accumulation may respond nonlinearly to changes in temperature and other factors, providing hypotheses for the observed correlations between organic carbon reservoirs and temperature in past earth climates.
有机物质构成全球元素循环中的关键储库。然而，我们对有机物质动态及其积累的理解仍然不完整。看似不相关的假设已被提出来解释有机物质的积累：内在难降解底物的缓慢降解、浓度降低以抑制微生物消耗，以及对附近微生物群落的消耗能力的依赖。在这里，我们使用一个机械模型，建立了一个理论框架，解释了有机物质在自然环境中如何由于生化、生态和环境因素而可预测地积累。我们的框架包含了以前的假设。微生物群落或环境的变化可以将一类有机物质从功能性难降解状态转变为被微生物消耗耗尽的状态。该模型解释了海洋中溶解有机碳的垂直分布，并将亚年时间尺度上的微生物活动与千年时间尺度上的有机物质周转联系起来。模型的阈值行为意味着有机物的积累可能对温度和其他因素的变化呈非线性响应，为过去地球气候中有机碳储量与温度之间的观察到的相关性提供了假设。

Heterotrophic organisms consume organic matter (OM) for both energy and biomass synthesis. Their activities transform much of it back into the inorganic nutrients that fuel primary production. Residual OM accumulates as large reservoirs in the ocean, sediments, and soils. Together, these pools store about five times more carbon than the atmosphere and play a central role in global biogeochemistry (1). Therefore, the dynamics of OM cycling and accumulation are key to understanding how the carbon cycle changes with climate (1–3).
异养生物通过摄取有机物（OM）来获取能量和合成生物质。它们的活动将其中大部分转化为无机营养物，为初级生产提供能量。剩余的有机物在海洋、沉积物和土壤中积累形成大型储库。这些储库共储存了大约比大气中的碳多五倍，并在全球生物地球化学中起着核心作用（1）。因此，有机物循环和积累的动态对于理解碳循环如何随气候变化而变化至关重要（1-3）。

Standing stocks of OM comprise a heterogeneous mix of thousands of compounds, many of which are uncharacterized, with concentrations ranging over several orders of magnitude (4–7). Compounds are often conceptually described in terms of a degree of “lability” that correlates with consumption rates, such that labile compounds have low abundances and short residence times in the environment (8, 9). In most biogeochemical models, OM degradation is dictated by simple rate constants, rather than explicit consumption by dynamic microbial communities (10, 11). Though significant progress has been made on integrating OM cycling with microbial community dynamics (12–17), we still lack a mechanistic understanding of the ecological controls on OM and its accumulation.
OM的存量包括成千上万种化合物的异质混合物，其中许多化合物尚未被表征，浓度范围跨越几个数量级（4-7）。化合物通常以“可变性”程度的概念来描述，该程度与消耗速率相关，因此易变化的化合物在环境中的丰度较低，停留时间较短（8, 9）。在大多数生物地球化学模型中，OM的降解是由简单的速率常数决定的，而不是由动态微生物群落的明确消耗（10, 11）。尽管在将OM循环与微生物群落动态相结合方面取得了重大进展（12-17），但我们仍然缺乏对OM及其积累的生态控制机制的机械性理解。

Dissolved OM (DOM) cycling in the ocean has been studied for many decades, making this reservoir ideal for developing a mechanistic framework for OM accumulation. Three hypotheses have been invoked to explain DOM accumulation in the ocean: 1) “Recalcitrance”: Compounds may accumulate because they are relatively slowly degraded or resistant to further degradation by microorganisms (8, 9, 18, 19). This is consistent with observations, theory, and inferences of a wide range of consumption rates and compound ages in the ocean (20–25), as well as in sediments and soils (9–11, 26, 27). 2) “Dilution”: The accumulation may represent the sum of low concentrations of many organic compounds, each having been diluted by microbial consumption to a minimum amount (28). This is supported by evidence that concentrating apparently recalcitrant DOM from the deep ocean fuels microbial growth (29). Modeling efforts have reconciled observed carbon ages with this mechanism and have interpreted the minimum concentrations as resource subsistence concentrations—the minimum concentrations to which populations can deplete their required resources (17, 30). 3) “Dependency on ecosystem properties”: The accumulation may result from a mismatch between OM characteristics and the metabolic capability of the proximal microbial community (e.g., the substrate specificity of enzymes) (31–34). For example, the dispersal of microbial populations, which is controlled by the connectivity of the environment and which may manifest as a stochastic process (35), can allow for intermittent or sporadic OM consumption events (32, 34). In soils and sediments, some aspects of these hypotheses apply, while other processes also influence the accumulation of OM, such as diverse redox conditions and the physical and chemical dynamics of solid organic particles and mineral matrices.
海洋中的溶解有机物（DOM）循环已经研究了很多年，使得这个储库成为发展有机物积累机制的理想对象。有三个假设被提出来解释海洋中DOM的积累：1）“难降解性”：化合物可能积累是因为它们相对缓慢地被微生物降解或抵抗进一步降解（8, 9, 18, 19）。这与海洋中广泛的消耗速率和化合物年龄的观察、理论和推断（20-25），以及沉积物和土壤中的观察（9-11, 26, 27）是一致的。2）“稀释”：积累可能代表了许多有机化合物的低浓度之和，每个化合物都被微生物消耗稀释到最低限度（28）。这得到了浓缩深海中表现出难降解DOM的证据支持，这种DOM可以为微生物生长提供能量（29）。建模工作已经将观察到的碳年龄与这种机制相一致，并将最低浓度解释为资源维持浓度-种群可以耗尽其所需资源的最低浓度（17, 30）。 3）“对生态系统属性的依赖”：积累可能是由于有机物特性与近源微生物群落的代谢能力之间的不匹配（例如，酶的底物特异性）（31-34）。例如，微生物种群的扩散受环境的连通性控制，可能表现为随机过程（35），这可以导致间歇性或零星的有机物消耗事件（32, 34）。在土壤和沉积物中，这些假设的某些方面适用，同时其他过程也会影响有机物的积累，例如多样的氧化还原条件以及固体有机颗粒和矿物基质的物理和化学动力学。

Here, we investigate why OM accumulates using a stochastic model that simulates the complex dynamics of microbial OM consumption. We find that the mechanisms underlying each of the three above hypotheses come into play simultaneously in the model. We develop a quantitative definition of functional recalcitrance that depends on both the microbial community and the environmental context, in addition to substrate characteristics. We demonstrate the model’s ability to explain the accumulation of DOM in the ocean. Furthermore, because it is grounded in basic principles of microbial ecology, we suggest that this framework can also extend to soil and sediment environments. Finally, the threshold behavior of the recalcitrance indicator suggests nonlinear OM responses to changes in the environment.
在这里，我们使用一种模拟微生物有机物消耗复杂动力学的随机模型来研究为什么有机物（OM）会积累。我们发现，在模型中，上述三个假设背后的机制同时发挥作用。我们提出了一个定量的功能难降解性的定义，该定义取决于微生物群落、环境背景和底物特性。我们展示了该模型能够解释海洋中溶解有机物（DOM）的积累。此外，由于该模型基于微生物生态学的基本原理，我们认为这个框架也可以扩展到土壤和沉积环境。最后，难降解性指标的阈值行为表明有机物对环境变化的响应是非线性的。

A Mechanistic Model of OM Consumption.

We develop a model of OM consumption by microbial populations using established forms of equations for microbial growth and respiration (12, 36, 37). The model resolves multiple pools of OM (

n = 1,000

) that are supplied stochastically and consumed by one or more microbial populations (

n = 1,000

or

2,000

; Eqs. 4–6 and Fig. 1). Stochastic supply captures the variable nature of the release of organic compounds, which is a function of complex biological dynamics (e.g., exudation, lysis, and grazing). We represent the net impact of each complex OM–microbe interaction [e.g., hydrolysis, enzymatic rates, cellular allocation of enzyme, and free energy released by OM oxidation (16, 32, 33, 38)] with a simplified set of parameters: maximum uptake rate, half-saturation concentration, and biomass yield (Materials and Methods). To include the impact of variable community composition, we modulate the OM consumption by each population over time according to its stochastically assigned probability of presence. We vary the degree of “specialists” (consuming a single OM pool) vs. “generalists” (consuming multiple OM pools), incorporating a penalty that increases with the number of pools consumed to represent a tradeoff among the strategies. We vary both the number of pools consumed by each population and the number of consumers of each pool (Fig. 1; SI Appendix, Fig. S1). Population loss rates are proportional to biomass according to both quadratic and linear mortality parameters, simulating predation, viral lysis, senescence, and maintenance demand.
我们使用已建立的微生物生长和呼吸方程式的形式，开发了一个微生物群体对有机物（OM）消耗的模型（12、36、37）。该模型解决了多个供应随机的OM池（

n = 1,000

），这些池被一个或多个微生物群体（

n = 1,000

或

2,000

；方程式4-6和图1）消耗。随机供应捕捉到了有机化合物释放的变化性质，这是复杂生物动力学的一个函数（例如，分泌、溶解和捕食）。我们用一组简化的参数来表示每个复杂的OM-微生物相互作用的净影响（例如，水解、酶速率、酶的细胞分配和OM氧化释放的自由能）：最大摄取速率、半饱和浓度和生物量产率（材料和方法）。为了包括可变的群落组成的影响，我们根据其随机分配的存在概率，随时间调节每个群体对OM的消耗。我们改变了“专家”（只消耗单个OM池）与 “综合型”（消耗多个OM池），引入一个随着消耗池数量增加而增加的惩罚，以代表不同策略之间的权衡。我们同时改变每个种群消耗的池数量和每个池的消费者数量（图1；附录图S1）。种群损失率根据二次和线性死亡参数与生物量成比例，模拟捕食、病毒裂解、衰老和维持需求。

Fig. 1.

Schematic of the OM consumption model. Multiple OM pools $C$ and microbial populations $B$ are resolved. The parameter values dictating the supply of each OM pool, the interaction between each pool and the microbial population (uptake kinetics and yield), and the loss of biomass (to viral lysis, grazing, senescence, and cell maintenance) are assigned stochastically. Here, we show an illustrative example where the fluxes dictated by these parameter values are represented with different widths of arrows. The supply and the presence or absence of each population vary stochastically over time in the model according to assigned probabilities.
OM消耗模型的示意图。解析了多个OM池 $C$ 和微生物群落 $B$ 。随机分配了参数值，用于决定每个OM池的供应、每个池与微生物群落之间的相互作用（摄取动力学和产量），以及生物量的损失（病毒裂解、捕食、衰老和细胞维持）。在这里，我们展示了一个说明性的例子，其中由这些参数值决定的通量用不同宽度的箭头表示。根据分配的概率，模型中的供应和每个群落的存在与否会随时间随机变化。

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Because we expect the values of these growth and mortality parameters to vary widely among organisms and substrates, we sample all parameter values from uniform distributions over wide, plausible ranges (Table 1; SI Appendix, SI Text 1). We numerically integrate the equations forward in time, allowing the concentrations of OM pools to emerge from the ecological interactions. The dynamics presented here are robust across the parameter space, variations in the model structure, and variations in the number of OM pools and populations (SI Appendix, SI Text 2 and 3 and Figs. S2–S7). Sequential transformation of one OM pool to another due to incomplete oxidation gives qualitatively similar solutions (SI Appendix, SI Text 2), although this may increase compound age (17). We present results from simulations integrated for 10 y (Fig. 2).
由于我们预计这些生长和死亡参数的值在不同的生物和底物之间会有很大的变化，我们从广泛的、合理的范围内的均匀分布中抽样所有参数值（表1；附录SI，附录SI文本1）。我们通过数值积分将方程向前推进，允许有机物池的浓度从生态相互作用中出现。这里呈现的动态在参数空间、模型结构的变化以及有机物池和种群数量的变化下是稳健的（附录SI，附录SI文本2和3以及图S2-S7）。由于不完全氧化导致一个有机物池逐渐转化为另一个有机物池，解决方案在定性上是相似的（附录SI，附录SI文本2），尽管这可能会增加化合物的年龄（17）。我们展示了经过10年积分的模拟结果（图2）。

Table 1.

Parameters and their distributions for the OM microbial consumption model

Parameter	Symbol	Value (range)	Units
Number of OM pools*	$n$	1,000
Number of populations^†	$m$	1,000 and 2,000
Probability of presence	$P$	0 to 1
Total OM supply (all pools)	$σ_{T}$	0.1	$μ$ M $\cdot d^{- 1}$
Potential supply (each pool)	$σ$	$σ_{T} n^{- 1}$	$μ$ M $\cdot d^{- 1}$
Probability of supply	$q$	0 to 1
Maximum specific uptake rate	$ρ^{max}$	$1 0^{- 2} - 1 0^{2}$ ^‡	$d^{- 1}$
Half-saturation concentration	$k$	$ρ^{max} {(1 0^{0} - 1 0^{2})}^{- 1}$ ^‡	$μ$ M
Yield (growth efficiency)	$y$	0 to 0.5	mol $\cdot$ mol⁻1
Quadratic mortality rate	$m^{q}$	0.1 to 1	( $μ$ M $\cdot$ d)⁻1
Linear mortality rate	m^l	0 to 0.01	$d^{- 1}$
Loss rate	$L$	$m^{q} B + m^{l}$	$d^{- 1}$

Parameter values are assigned stochastically according to uniform distributions over the indicated ranges.
参数值根据指定范围内的均匀分布随机分配。

*

Here, we illustrate two 10-member ensembles with 1,000 OM pools in each individual model, giving a total of 10⁴ pools per ensemble. See SI Appendix, Fig. S3 for an individual model with 10⁴ pools.
这里，我们展示了两个由每个模型中的1,000个OM池组成的10成员集合，每个集合共有10个 ⁴ 池。有关包含10个 ⁴ 池的单个模型，请参见SI附录，图S3。

†

The community consumption matrix dictates which populations consume each pool (SI Appendix, Fig. S1). See SI Appendix, Figs. S4–S7 for variations, including variations in the ratio of populations to pools from 2:1 to 1:1,000.
社区消费矩阵决定了哪些人口消费每个资源池（见附录SI，图S1）。请参阅附录SI，图S4-S7以了解不同的变化，包括人口与资源池的比例从2:1到1:1,000的变化。

‡

Varied over a log rather than a linear range.

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Fig. 2.

Simulated concentrations from the stochastic OM consumption model. (A) The modeled OM concentrations $C$ and associated diagnostic $C^{*}$ , the subsistence concentrations of the microbial consumers (Eq. 2 and *SI Appendix*, Eq. **S18**), against recalcitrance indicator $Q$ (Eq. 3). The $Q = 1$ threshold (gray dashed line) delineates the functionally recalcitrant (accumulating) and functionally labile (equilibrated) OM. We illustrate compiled results from two model versions, each resolving 1,000 OM pools: one with only 1,000 specialist microbial populations, and one with the specialists and an additional 1,000 generalist populations, which consume varying numbers of OM pools. We compile 10 simulations of each model version so that 10,000 OM concentrations underlie the illustrated statistics. The red and light red dots indicate the binned means for the two compilations. The red and light red bars (for the model solutions) and the light blue shaded area (for diagnostic $C^{*}$ ) indicate the 16th and 84th percentiles (equivalent to one SD for a Gaussian distribution). The gray dots indicate the 20,000 individual OM concentrations from both compilations combined. (B) The normalized frequencies of the concentrations and their contributions to total carbon in the model (for the version with both specialists and generalists). Frequencies are split at $Q \approx 1$ (cutoff at 1.01).
随机OM消耗模型中的模拟浓度。（A）模拟的OM浓度 $C$ 和相关的诊断 $C^{*}$ ，微生物消费者的维持浓度（方程2和SI附录，方程S18），与难降解指标 $Q$ （方程3）相对比。灰色虚线标示功能上难降解（积累）和功能上易降解（平衡）的OM的阈值。我们展示了两个模型版本的编译结果，每个版本解析了1,000个OM池：一个只有1,000个专业微生物种群，另一个有专业种群和额外的1,000个广义种群，它们消耗不同数量的OM池。我们编译了每个模型版本的10个模拟，以便在所示统计数据下有10,000个OM浓度。红色和浅红色的点表示两个编译的分组均值。红色和浅红色的条形图（用于模型解决方案）和浅蓝色阴影区域（用于诊断 $C^{*}$ ）表示第16和第84百分位数（相当于高斯分布的一个标准差）。灰色点表示来自两个编译的20,000个个体OM浓度的组合。（B）模型中浓度的归一化频率及其对总碳的贡献（适用于同时包含专家和普通物种的版本）。频率在 $Q \approx 1$ 处分割（截断值为1.01）。

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The solutions reveal a bimodal distribution of OM concentrations (Fig. 2), implying a set of qualitatively distinct controls on OM accumulation. Whether or not the bimodality is discernible depends on the parameter distributions (SI Appendix, Fig. S13), as well as other sources and sinks not included in the model (e.g., photolysis). In the simple model, the majority of pools are depleted to relatively low concentrations (

10^{- 4}

to 1

μ

M C), while a subset accumulates to substantially higher concentrations (0.1 to 10

μ

M C). The latter accumulated pools comprise the bulk of total carbon content (Fig. 2B).
解决方案显示有机质浓度呈双峰分布（图2），暗示着对有机质积累有一组定性不同的控制因素。双峰性是否可辨取决于参数分布（附录SI，图S13），以及模型中未包括的其他来源和汇（例如光解作用）。在简单模型中，大多数池的浓度较低（

10^{- 4}

至1

μ

M C），而一部分池的浓度积累到较高水平（0.1至10

μ

M C）。后者积累的池占据了总碳含量的大部分（图2B）。

Diagnosing Functional Recalcitrance.

We evaluate whether each OM pool equilibrates or accumulates in the model. Equilibration indicates that the pool can sustain a microbial population in the given environment, and we classify that pool as “functionally labile.” Otherwise, the pool accumulates in the environment, and we classify that pool as “functionally recalcitrant.” For example, we describe the population dynamics of specialist population

j

, subsisting solely on OM pool

i

, as (Materials and Methods):
我们评估每个有机质（OM）池在模型中是否达到平衡或累积。平衡表示该池能够在给定环境中维持微生物群落，我们将该池分类为“功能易降解”。否则，该池在环境中累积，我们将该池分类为“功能难降解”。例如，我们描述了专门群体

j

仅以OM池

i

为生存基础的种群动态（材料和方法）：

\frac{\partial B_{j} (t)}{\partial t} = (P_{j} y_{i j} ρ_{i j}^{max} \frac{C_{i} (t)}{C_{i} (t) + k_{i j}} - L_{j} (t)) B_{j} (t),

[1]

where

B_{j}

is the biomass,

P_{j}

is the probability of the presence of population

j

,

y_{i j}

is the biomass yield,

ρ_{i j}^{max}

is the maximum uptake rate,

k_{i j}

is the half-saturation concentration for uptake,

C_{i}

is the concentration of the OM pool, and

L_{j}

is the population-loss rate, which varies as a function of the biomass (Eq. 6 and Table 1). When the system is at or close to steady state (

\frac{\partial B_{j} (t)}{\partial t} \approx 0

), the concentration of pool

i

can be estimated as:
其中

B_{j}

是生物量，

P_{j}

是种群

j

存在的概率，

y_{i j}

是生物量产量，

ρ_{i j}^{max}

是最大摄取速率，

k_{i j}

是摄取的半饱和浓度，

C_{i}

是有机物池的浓度，

L_{j}

是种群损失率，其随生物量的变化而变化（方程6和表1）。当系统处于稳定状态（

\frac{\partial B_{j} (t)}{\partial t} \approx 0

）或接近稳定状态时，可以估计出池

i

的浓度。

C_{i j}^{*} = \frac{k_{i j}}{\frac{P_{j} y_{i j} ρ_{i j}^{max}}{L_{j}} - 1},

[2]

which is the subsistence concentration of OM pool

i

for specialist population

j

(30). For a pool with multiple competing consumers, the concentration of that pool will be set by the population with the lowest subsistence concentration for that pool (30). The population can then continue to consume the pool in proportion to its supply while maintaining the subsistence concentration (17, 30).
OM池的维持浓度是专业种群的浓度（30）。对于具有多个竞争消费者的池，该池的浓度将由具有该池最低维持浓度的种群确定（30）。种群可以继续按比例消耗该池的资源，同时保持维持浓度（17，30）。

For the OM pool to equilibrate (

C_{i j}^{*} > 0

in Eq. 2), the maximum rate of local biomass synthesis (

P_{j} y_{i j} ρ_{i j}^{max}

) must exceed the biomass loss rate at steady state (

L_{j}

). Using

C_{i j}^{*}

as a diagnostic, and extending the expression to generalists that can consume more than one OM pool (SI Appendix, Eqs. S17 and S18), we find that many concentrations of the modeled pools precisely match the minimum subsistence concentration among their consumers, and thus have equilibrated (Fig. 2A; SI Appendix, Figs. S8 and S9). Because these pools sustain microbial growth in this particular model environment, we consider these functionally labile. These low concentrations are consistent with the measured nanomolar or lower concentrations of known labile constituents of marine DOM, such as free amino acids and glucose (4, 39).
对于OM池达到平衡（在方程2中的

C_{i j}^{*} > 0

），局部生物量合成的最大速率（

P_{j} y_{i j} ρ_{i j}^{max}

）必须超过稳态下的生物量损失速率（

L_{j}

）。使用

C_{i j}^{*}

作为诊断工具，并将表达式扩展到能够消耗多个OM池的广义消费者（SI附录，方程S17和S18），我们发现模拟池的许多浓度与其消费者的最低维持浓度完全匹配，因此达到了平衡（图2A；SI附录，图S8和S9）。由于这些池在这个特定的模型环境中维持微生物生长，我们认为它们在功能上是不稳定的。这些低浓度与已知易变的海洋DOM成分（如游离氨基酸和葡萄糖）的纳摩尔级或更低浓度一致（4, 39）。

Most of the pools that accumulate to higher concentrations never equilibrate in the simple model. For these pools, the loss rates of all consuming populations match or exceed their maximum biomass synthesis rates. We consider these pools to be functionally recalcitrant. We can robustly define the threshold where pools transition from being functionally labile (depleted to

C_{i j}^{*}

) to functionally recalcitrant (accumulating). We define a recalcitrance indicator

Q_{i}

for pool

i

as:
大多数积累浓度较高的池塘在简单模型中不会达到平衡。对于这些池塘，所有消耗种群的损失速率与其最大生物量合成速率相匹配或超过。我们认为这些池塘在功能上是难降解的。我们可以确定一个阈值，使得池塘从功能上易降解（耗尽至

C_{i j}^{*}

）转变为功能上难降解（积累）。我们定义池塘

i

的难降解指标

Q_{i}

为：

Q_{i} = max_{j} [\frac{P_{j} ρ_{i j}^{max}}{L_{j}} (y_{i j} + \underset{impact of other pools}{\underset{︸}{\sum_{k} y_{k j} \frac{ρ_{k j}}{ρ_{i j}}}})],

[3]

where index

k

denotes a pool other than pool

i

consumed by generalist population

j

, and

ρ_{k j} / ρ_{i j}

is the relative uptake of pool

k

to pool

i

by population

j

(see SI Appendix, SI Text 4 for derivation). For specialists, the term representing the impact of other pools drops out of the equation. If

Q_{i} > 1

, pool

i

is functionally labile: At least one population can deplete it to its subsistence concentration given sufficient time, with the equilibration timescale dictated by the associated growth and loss parameters. If

Q_{i} \leq 1

, pool

i

is functionally recalcitrant, and it accumulates over time in our model. Thus,

Q_{i} = 1

serves as an emergent threshold between functional lability and functional recalcitrance (Fig. 2).
其中索引

k

表示除了一般人群

j

消耗的池塘

i

之外的其他池塘，而

ρ_{k j} / ρ_{i j}

是人群

j

对池塘

k

相对摄取量与池塘

i

之间的比例（详见附录SI，SI文本4的推导）。对于专家而言，表示其他池塘影响的项在方程中消失。如果

Q_{i} > 1

，池塘

i

在功能上是不稳定的：至少有一种人群可以在足够的时间内将其耗尽到其生存浓度，其平衡时间尺度由相关的生长和损失参数决定。如果

Q_{i} \leq 1

，池塘

i

在功能上是难降解的，并且在我们的模型中随时间累积。因此，

Q_{i} = 1

在功能不稳定性和功能难降解性之间起到了一个新兴的阈值（图2）。

The recalcitrance indicator

Q_{i}

demonstrates how recalcitrance is simultaneously governed by chemical, biological, ecological, and environmental characteristics. In Eq. 3, an enzyme-dependent substrate–microbe interaction

i

–

j

is captured by both

y_{i j}

and

ρ_{i j}^{max}

, which also reflect the energetic content and the accessibility of the OM (40–42). The encounter probability of the population with the OM pool (

P_{j}

) and the biomass loss rate (

L_{j}

) capture the ecological context—the diversity and abundances of the local microbial populations, predators, and viruses. Many factors control these processes, including selection and environmental connectivity (35), which is shaped in part by physical conditions such as circulation and sinking particles in the ocean and porosity and diffusion in soils. Diversity and connectivity also modulate the availability of other pools for uptake by generalists. In Eq. 3, the uptake of an additional OM pool

k

by population

j

can increase the population’s potential to deplete pool

i

(i.e.,

Q_{i}

increases). In other words, the ability of consumers of OM pool

i

to consume other pools increases the functional lability of pool

i

. This provides a mechanistic explanation for the observed “priming effect,” in which the addition of other substrates allows for the metabolization of a given pool (34, 43, 44).

Q_{i}

这个顽固性指标展示了顽固性同时受化学、生物、生态和环境特征的调控。在方程式3中，酶依赖的底物-微生物相互作用

i

-

j

被

y_{i j}

和

ρ_{i j}^{max}

所捕捉，这也反映了有机质的能量含量和可获取性（40-42）。种群与有机质库的相遇概率（

P_{j}

）和生物量损失率（

L_{j}

）捕捉了生态背景-当地微生物种群、捕食者和病毒的多样性和丰度。许多因素控制着这些过程，包括选择和环境连通性（35），这部分受到物理条件（如海洋中的环流和沉降颗粒以及土壤中的孔隙度和扩散）的影响。多样性和连通性还调节了其他池塘对广义专性生物的可利用性。在方程式3中，种群

j

对额外的有机质库

k

的摄取可以增加种群耗尽池塘

i

的潜力（即

Q_{i}

增加）。换句话说，OM池的消费者能够消费其他池的能力增加了池

i

的功能稳定性。这为观察到的“启动效应”提供了机制解释，即添加其他底物可以使给定池的代谢发生（34, 43, 44）。

In the environment, a functionally recalcitrant OM pool may accumulate or diminish at a rate dependent on production, consumption, and physical transport over time, or it can equilibrate due to an abiotic, concentration-dependent sink such as photolysis (8, 34). In the model version with many generalists,

Q_{i}

reaches a minimum of one (to within 1%) (Fig. 2A). When

Q_{i} \approx 1

, pools are unequilibrated and functionally recalcitrant, but consumption can continue by consumers whose loss rates have dynamically adjusted to approach their maximum biosynthesis rates.
在环境中，功能上难以降解的有机物（OM）池可能会以生产、消耗和物理运输的速率累积或减少，或者由于非生物的浓度依赖性汇（如光解）而达到平衡（8, 34）。在具有许多广义物种的模型版本中，

Q_{i}

最小为一（误差在1%以内）（图2A）。当

Q_{i} \approx 1

时，池不平衡且功能上难以降解，但消耗可以继续进行，消费者的损失速率已动态调整以接近其最大生物合成速率。

Recalcitrance emerges as a community- and context-specific phenomenon that can change in time and space (SI Appendix, Fig. S10). Critically, the recalcitrance indicator for each OM pool (

Q_{i}

) is defined as the maximum of multiple population-specific values (Eq. 3)—one for each population

j

that consumes pool

i

. Consequently, whether each pool is functionally labile or recalcitrant depends on the local microbial community. For a diverse community of consumers, we can analyze the fraction of the community that experiences each pool as recalcitrant (SI Appendix, Fig. S11). This community dependency implies that, statistically, functional recalcitrance may be more prominent when OM is exposed to a lower diversity of heterotrophic microorganisms. This also implies that functional recalcitrance may arise from the requirement for specialized enzymes or expensive consumption pathways for some types of OM (45): If specialization is required, there may be fewer possible consumers overall, and so it becomes less likely that any one consumer is present in the given environment. This is consistent with evidence that specific heterotrophic clades consume carboxyl-rich alicyclic molecules, which comprise a significant fraction (up to 8%) of marine DOC (6, 46).
顽固性是一个与社区和环境相关的现象，可以随时间和空间的变化而改变（附录SI，图S10）。关键是，每个有机质池的顽固性指标（

Q_{i}

）被定义为多个群体特定值（方程3）的最大值-每个消耗池

i

的群体

j

一个。因此，每个池是否在功能上易变或顽固取决于当地的微生物群落。对于一个多样化的消费者群体，我们可以分析每个池被视为顽固的群体的比例（附录SI，图S11）。这种社区依赖性意味着，在有机质暴露于较低多样性的异养微生物群体时，功能性顽固性可能更为突出。这也意味着功能性顽固性可能源于某些类型的有机质需要专门的酶或昂贵的消耗途径（45）：如果需要专门化，总体可能存在较少的可能消费者，因此在给定环境中出现任何一个消费者的可能性较小。这与特定异养类群消耗富含羧基的脂环分子的证据一致，这些分子占海洋DOC的重要部分（高达8%）（6, 46）。

Unification of Hypotheses.

The three current hypotheses for DOM accumulation in the ocean—recalcitrance, dilution, and dependency on ecosystem properties—each explain aspects of the total amount of carbon in the model. Additional processes, such as mineral protection and diverse redox conditions of soils and sediments, can also be incorporated into the framework to modify it for these other systems. We may consider each hypothesis individually as a limit case for the formation of large organic carbon reservoirs in natural environments. Total organic carbon content is the sum of all OM pools. A traditional view of recalcitrance, focused on intrinsic qualities of the substrate or of the microbe–substrate-specific reaction, is represented in the model by the biomass yield

y_{i j}

and maximum uptake rate

ρ_{i j}^{m a x}

. The quality of electron acceptor or mineral protection can also be represented by these parameters. As

y_{i j} ρ_{i j}^{m a x}

becomes small, while other parameters remain constant, OM becomes recalcitrant (Eq. 3), and the total organic carbon pool becomes large. The number of OM pools

n

that are present can impact total carbon in two opposing ways. As

n

increases, total carbon increases, even for low, equilibrated subsistence concentrations (the dilution hypothesis). However, the impact of other OM pools (priming) means that as

n

increases, the likelihood of

Q_{i} > 1

increases, decreasing the likelihood of functional recalcitrance and, thus, potentially decreasing total carbon. Dependency on ecosystem properties is encapsulated in the population’s steady-state loss rate

L_{j}

and probability of presence

P_{j}

. As

L_{j}

increases, OM becomes recalcitrant, and total carbon increases. As the frequency of nearby consumers decreases,

P_{j}

decreases, increasing total carbon.
DOM在海洋中积累的三个当前假设——难降解性、稀释和对生态系统属性的依赖——每个都解释了模型中碳的总量的一些方面。还可以将其他过程，如矿物保护和土壤和沉积物的多样化氧化还原条件，纳入框架中以修改其适用于这些其他系统。我们可以将每个假设单独考虑为自然环境中形成大型有机碳储库的极限情况。总有机碳含量是所有有机物池的总和。对难降解性的传统观点，侧重于底物或微生物-底物特异反应的内在特性，在模型中通过生物量产率

y_{i j}

和最大摄取速率

ρ_{i j}^{m a x}

来表示。电子受体或矿物保护的质量也可以用这些参数表示。当

y_{i j} ρ_{i j}^{m a x}

变小，而其他参数保持不变时，有机物变得难降解（方程3），总有机碳池变大。存在的有机物池的数量

n

可以以两种相反的方式影响总碳含量。随着

n

的增加，总碳含量也增加，即使对于低浓度的平衡维持（稀释假说）。然而，其他有机物质库（启动作用）的影响意味着随着

n

的增加，

Q_{i} > 1

的可能性增加，降低了功能性难降解性的可能性，从而潜在地降低了总碳含量。对生态系统属性的依赖体现在种群的稳态损失率

L_{j}

和存在概率

P_{j}

中。随着

L_{j}

的增加，有机物质变得难降解，总碳含量增加。随着附近消费者的频率减少，

P_{j}

减少，总碳含量增加。

The degree to which each mechanism controls OM accumulation in different environments therefore depends on the parameter space that sets the population and OM characteristics. Here, we assume uniform distributions for these parameters using plausible ranges for the ocean (Table 1; SI Appendix, SI Text 1). These ranges will vary with the environment. For example, if stochasticity in population presence does not apply to a given sediment ecosystem, then probability of presence

P

may be set to one for analysis of that environment. The model is consistent with that of ref. 17 in that intrinsic recalcitrance is not necessary for OM accumulation in the ocean, as well as with experimental evidence for dilution-limited consumption (SI Appendix, SI Text 5 and Fig. S12) (29). Here, we provide a generalized framework that encapsulates a more complete set of dynamics than in ref. 17—one that is also consistent with evidence of recalcitrance (8, 18, 19) and the impact of the microbial community (31, 33, 34, 45, 46). The emergent distributions of OM degradation rates are consistent with theory and observations that remineralization rates are lognormally distributed over a wide range due to multiplicative stochasticity in the underlying processes (27) (SI Appendix, Fig. S13). They are also consistent with continuum intrinsic reactivity models, which assume a wide distribution of rates (10, 11) which tend toward lognormal distributions (47).
每个机制在不同环境中控制有机质积累的程度取决于设置人口和有机质特征的参数空间。在这里，我们假设这些参数的分布是均匀的，并使用海洋的合理范围（表1；SI附录，SI文本1）。这些范围会随环境而变化。例如，如果种群存在的随机性不适用于给定的沉积生态系统，则分析该环境时存在概率

P

可以设为1。该模型与参考文献17的模型一致，即在海洋中，有机质积累并不需要固有的难降解性，同时也与稀释限制消耗的实验证据一致（SI附录，SI文本5和图S12）（29）。在这里，我们提供了一个更完整的动力学集合的广义框架，比参考文献17中的框架更加一致，也与难降解性的证据（8, 18, 19）以及微生物群落的影响（31, 33, 34, 45, 46）一致。 OM降解速率的新兴分布与理论和观测结果一致，即由于基础过程中的乘法随机性，重矿化速率在广泛范围内呈对数正态分布（27）（附录SI，图S13）。它们还与连续内在反应模型一致，该模型假设速率分布广泛（10, 11），并趋向于对数正态分布（47）。

Predicting OM Accumulation Patterns.

Our framework can help explain large-scale patterns in OM accumulation. Here, we use our model to understand the vertical structure of dissolved organic carbon (DOC) in the ocean. Globally, DOC concentrations peak at the sea surface and approach a minimum at depth (Fig. 3A) (8). Since the stochastic model is not practical for multidimensional biogeochemical models, we utilize a reduced-complexity model analog that captures the essence of the stochastic model, resolving 25 aggregate pools. We incorporate this model analog into a fully dynamic ecosystem model of a stratified marine water column, where production and consumption of all organic and inorganic pools are resolved mechanistically as the growth, respiration, and mortality of photoautotrophic and heterotrophic microbial populations (SI Appendix, SI Text 6 and Fig. S14). The model is integrated for 6,000 y to quasi-equilibrium (SI Appendix, SI Text 6).
我们的框架可以帮助解释有机物积累的大规模模式。在这里，我们使用我们的模型来理解海洋中溶解有机碳（DOC）的垂直结构。全球范围内，DOC浓度在海洋表面达到峰值，并在深度处接近最小值（图3A）（8）。由于随机模型对于多维生物地球化学模型来说不实用，我们利用一个捕捉随机模型本质的简化复杂模型模拟，解决了25个聚合池。我们将这个模型模拟引入到一个完全动态的分层海洋水柱生态系统模型中，其中所有有机和无机池的生产和消耗都以机械方式解决，作为光合和异养微生物群落的生长、呼吸和死亡（SI附录，SI文本6和图S14）。该模型在6000年内达到准平衡（SI附录，SI文本6）。

Fig. 3.

Marine ecosystem water-column model results showing the accumulation of DOC. (A) Phytoplankton biomass, total DOC-consuming biomass $B$ , and total DOC. Annual average profiles of total DOC from two open ocean time series stations are illustrated: HOT (the Hawaii Ocean Time-series in the Pacific Ocean) and BATS (the Bermuda Atlantic Time-series Station in the Atlantic Ocean) (50). (B) The concentration of each of the 25 resolved DOC pools, which are differentiated in the water-column model by maximum uptake rate $ρ^{max}$ (color scale). Each pool is categorized as functionally labile (solid line) or functionally recalcitrant (dashed line) as a function of depth using recalcitrance indicator $Q$ (Eq. 3). (C) The maximum (max) (surface) concentration $C$ of each DOC pool and the associated diagnostic $C^{*}$ , the subsistence concentration of the microbial consumer population (Eq. 2), plotted against the maximum uptake rate for that pool. (D) The turnover time of each DOC pool calculated diagnostically from the integrated concentration and the integrated consumption rate, plotted against the maximum uptake rate.
海洋生态系统水柱模型结果显示DOC的积累。(A) 海洋浮游植物生物量、总DOC消耗生物量和总DOC。图中展示了两个开放海洋时间序列站点的年均总DOC剖面：HOT（太平洋夏威夷海洋时间序列）和BATS（大西洋百慕大时间序列站）(50)。(B) 25个已解析的DOC池的浓度，根据最大摄取速率在水柱模型中区分（颜色标度）。每个池根据深度使用难降解指标（方程3）被分类为功能易降解（实线）或功能难降解（虚线）。(C) 每个DOC池的最大（表面）浓度和相关的诊断，微生物消费者种群的维持浓度（方程2），根据该池的最大摄取速率绘制。(D) 从综合浓度和综合消耗速率诊断计算的每个DOC池的周转时间，根据最大摄取速率绘制。

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Ecological interactions in the model result in characteristics typical of a marine water column (Fig. 3; SI Appendix, Fig. S15). Modeled DOC accumulates throughout the water column. Total DOC decreases smoothly with depth, with higher surface DOC transported to depth by vertical mixing (Fig. 3A). Most pools are depleted to subsistence concentrations throughout the water column (Fig. 3 B and C). One pool remains functionally recalcitrant throughout the entire water column due to its slow consumption rate (lightest yellow line in Fig. 3B), which is consistent with the observed homogenous composition of aged marine DOC (7, 48).
模型中的生态相互作用导致了典型的海洋水柱特征（图3；附录图S15）。模拟的溶解有机碳（DOC）在整个水柱中积累。总DOC随深度平滑减少，较高表层DOC通过垂直混合被输送到深处（图3A）。大部分池塘在整个水柱中都被消耗至维持生存的浓度（图3B和C）。由于其缓慢的消耗速率（图3B中最浅黄色线），一个池塘在整个水柱中保持功能上难降解，这与观察到的老化海洋DOC的均质组成一致（7, 48）。

Many DOC pools in the model accumulate at the surface and become depleted at depths of 500 to 1,000 m. This transition is due to the increase in

Q

for these pools from the surface to depth (Fig. 3B). Specifically, the loss rates of the populations are highest at the surface and attenuate with depth. This is because productivity peaks in the surface, and so total biomasses, activity rates, and, therefore, predation rates (represented implicitly in the model; Eq. 6) also peak at the surface. The subsistence concentrations for the functionally labile pools also decrease with depth as loss rates decrease, and so the total concentration of functionally labile OM also decreases with depth, contributing slightly to the vertical DOC gradient. Thus, an ecologically determined transition from functional recalcitrance to functional lability for some pools explains much of the decrease in DOC with depth. This transition is consistent with observations that a subset of DOC is resistant to consumption by surface communities, but able to be remineralized by deep communities (31).
模型中的许多DOC池在表面积累，并在500到1,000米的深度变得耗尽。这种转变是由于从表面到深度这些池的

Q

增加（图3B）。具体而言，种群的损失速率在表面最高，并随深度减弱。这是因为生产力在表面达到峰值，因此总生物量、活性率和因此捕食率（在模型中隐含表示；方程6）也在表面达到峰值。对于功能易变池的维持浓度也随深度减少，因为损失速率减少，因此功能易变OM的总浓度也随深度减少，略微贡献于垂直DOC梯度。因此，生态学确定的从功能难降解到功能易变的转变解释了DOC随深度减少的大部分原因。这种转变与观察结果一致，即DOC的一个子集对表面群落的消耗具有抵抗力，但能够被深层群落再矿化（31）。

Our framework may also be employed to investigate microbial control on OM in soils and sediments. The model can be adapted to incorporate the different characteristics of these environments. For example, here, we employ a simple parameterization for the supply of each OM class, but a sediment or soil model version could include more sophisticated descriptions of how the physics and chemistry of solid particles and mineral matrices impact the supply rate. Though Michaelis–Menten uptake kinetics do not apply to the enzymatically catalyzed degradation of polymeric organic compounds to monomeric compounds, the ecological principles of our framework should still hold (SI Appendix, SI Text 7). Indeed, we find that, even in its current form, the simple model captures a key observation of sediment OM: the proportional increase in OM decomposition rate with increased OM concentration (49) (SI Appendix, Fig. S16). This further demonstrates consistency with the predictions of established first-order kinetic decomposition models (12, 49). Our framework can also be used to explore the impact of more enzymatically diverse sedimentary communities relative to pelagic communities on OM accumulation (33) by altering the community consumption matrix to include a greater degree of generalist ability. Also, varying the yields or uptake rates with electron acceptors could incorporate diverse redox conditions into the model. A decrease in yield with a lower-quality electron acceptor may suggest that some types of OM are functionally labile when oxygen is available, but functionally recalcitrant in anoxic environments.
我们的框架也可以用于研究微生物对土壤和沉积物中有机质的控制。该模型可以根据这些环境的不同特点进行调整。例如，在这里，我们采用了每种有机质类别供应的简单参数化，但沉积物或土壤模型版本可以包括更复杂的描述，以说明固体颗粒和矿物基质的物理和化学特性如何影响供应速率。尽管Michaelis-Menten摄取动力学不适用于酶催化的聚合有机化合物降解为单体化合物，但我们框架的生态原理仍然适用（附录SI，附录SI文本7）。事实上，我们发现，即使在当前形式下，简单模型也能捕捉到沉积物有机质的一个关键观察结果：随着有机质浓度的增加，有机质分解速率成比例增加（49）（附录SI，图S16）。这进一步证明了与已建立的一级动力学分解模型（12, 49）的预测一致性。我们的框架还可以用来探索酶多样性沉积群落相对于浮游群落对有机物积累的影响（33），通过改变群落消耗矩阵以包括更高程度的广义能力。此外，通过改变产量或电子受体的摄取速率，可以将多样的氧化还原条件纳入模型中。当使用质量较低的电子受体时，产量的降低可能表明某些类型的有机物在氧气可用时具有功能上的易变性，但在缺氧环境中具有功能上的难降解性。

Implications.

Our model is consistent with the observations and previous sediment modeling results that the majority of the diverse types of OM are present at relatively low (

< 1

μ

M C) concentrations, while the majority of the total standing stock is functionally recalcitrant (8, 10, 51) (Figs. 2B and 3B). The recalcitrant portion may equilibrate if subjected to abiotic concentration-dependent sinks (8) or may change slowly with time (7, 8). Our framework further emphasizes that apparently slow consumption rates of recalcitrant DOC in the ocean may be controlled by the frequency of encounter of “the right” populations and substrates, in addition to biochemical and energetic limitations. This is consistent with the understanding that localized sinks cause the 10 to 20% decrease in deep ocean DOC along the deep ocean circulation pathway (32).
我们的模型与观察结果和先前的沉积物模拟结果一致，即大多数不同类型的有机物以相对较低的浓度存在（

< 1

μ

M C），而大部分总存量是功能性难降解的（8、10、51）（图2B和3B）。如果受到非生物浓度依赖的汇聚物的影响，难降解部分可能会达到平衡（8），或者可能随时间变化缓慢（7、8）。我们的框架进一步强调，海洋中难降解的溶解有机碳（DOC）的消耗速率明显较慢，可能受到“正确”的种群和底物相遇频率的控制，除了生化和能量限制。这与局部汇聚物导致沿深海环流路径深海DOC减少10%至20%的理解是一致的（32）。

The water column model links the millennial timescales of OM turnover (24) to microbial consumption occurring on subannual timescales (Fig. 3D). Although OM transformation through a complex interaction network can also explain old carbon ages (17), slow turnover as an additional mechanism is consistent with inferences that the size of organic carbon reservoirs does not reach a steady state over geologic timescales (2). While our model is compatible with the dilution hypothesis, it also incorporates the other explanations for accumulation, and so it is consistent with a broader set of observations, including the compositional uniformity of ubiquitous recalcitrant classes (7, 48).
水柱模型将千年尺度的有机物转化（24）与亚年尺度的微生物消耗联系起来（图3D）。虽然通过复杂的相互作用网络解释老化碳年龄（17）也可以解释有机物的转化，但缓慢的转化作为一种额外机制与有机碳储量在地质时间尺度上不达到稳定状态的推断是一致的（2）。虽然我们的模型与稀释假设相容，但它也包含了其他积累解释，因此与更广泛的观测结果一致，包括普遍存在的难降解类群的组成均一性（7, 48）。

A key aspect of our framework is the threshold behavior of the accumulation. The threshold,

Q = 1

, is set by the dynamics of the microbial populations that consume the OM pools.

Q = 1

represents an ecological threshold along a continuum of OM and microbial characteristics, including factors known to influence recalcitrance, such as thermodynamic limitations (40), enzymatic control (33), mineral protection (41, 44, 52), and molecular properties (19). The nonlinear behavior of the threshold suggests that small changes in the environment can drive large depletions or accumulations of OM.
我们框架的一个关键方面是积累的阈值行为。阈值

Q = 1

由消耗有机物池的微生物群落动力学设定。

Q = 1

代表了有机物和微生物特征的连续生态阈值，包括已知影响难降解性的因素，如热力学限制（40）、酶控制（33）、矿物保护（41、44、52）和分子特性（19）。阈值的非线性行为表明环境的微小变化可以引起有机物的大量消耗或积累。

Consumption of recalcitrant OM depends on the rate of microbial processing, which increases with temperature. If other factors remain constant, the model predicts that less OM accumulates at higher temperatures (SI Appendix, SI Text 3 and Fig. S10C). Indeed, the loss of soil OM is a likely positive feedback to current warming (53). The framework here additionally suggests that a decrease in OM with warming may be nonlinear due to some OM pools crossing the threshold from functionally recalcitrant to functionally labile (SI Appendix, Fig. S10c). This may help to understand the correlations between temperature and organic carbon reservoirs in past earth climates, such as increased ocean carbon burial, “inert” soil carbon reservoirs, and perhaps marine DOC during glacial periods (54, 55). Temperature-driven nonlinearity may also constitute an explanation for the 10-fold higher microbial utilization rates of DOC in the warmer deep Mediterranean compared to the colder deep open ocean (56). Using this framework to quantitatively predict changes in organic carbon reservoirs with current increases in global temperature will require accurate estimates of microbial community loss rates, as well as an understanding of how temperature will impact both microbial rates and the diversity of the community.
难降解有机物的消耗取决于微生物处理的速率，这个速率随着温度的升高而增加。如果其他因素保持不变，模型预测在较高温度下会积累较少的有机物（SI附录，SI文本3和图S10C）。事实上，土壤有机质的流失可能是当前变暖的一个积极反馈（53）。此外，这个框架还表明，由于一些有机质库从功能上难降解到功能上易降解，随着变暖有机质的减少可能是非线性的（SI附录，图S10c）。这可能有助于理解过去地球气候中温度和有机碳储量之间的相关性，例如增加的海洋碳埋藏、“惰性”土壤碳储量，以及冰期期间的海洋溶解有机碳（54, 55）。温度驱动的非线性也可能解释了地中海深层与开放海洋深层相比，DOC的微生物利用率高出10倍的原因（56）。使用这个框架来定量预测有机碳储量随着全球温度的升高而发生的变化，需要准确估计微生物群落损失率，以及了解温度如何影响微生物速率和群落的多样性。

We identify a set of controls on OM accumulation and turnover rooted in the complexity of microbial ecosystems. Previously disconnected hypotheses for OM accumulation, including the many mechanisms giving rise to functional recalcitrance, are subsumed within one framework. OM concentrations are mediated by the characteristics of substrate–microbe interactions, the heterogeneity of organic substrates, microbial community dynamics, and the ecological and biogeochemical diversity set by the connectivity of the environment (Fig. 4). The model is consistent with a comprehensive set of observations and theory of OM concentrations, turnover rates, and ages. The framework can be used to quantify the degree to which each of the subsumed hypotheses explains OM accumulation in different environments and to develop testable hypotheses for how organic reservoirs change with the biogeochemical environment.
我们确定了一组控制有机物积累和周转的因素，这些因素根植于微生物生态系统的复杂性。以往关于有机物积累的孤立假设，包括导致功能难降解的多种机制，都被纳入了一个框架之中。有机物浓度受底物-微生物相互作用特征、有机底物的异质性、微生物群落动态以及环境连接性所决定的生态和生物地球化学多样性的调节（图4）。该模型与一系列有关有机物浓度、周转速率和年龄的观测和理论一致。该框架可用于量化每个纳入的假设在不同环境中解释有机物积累的程度，并提出可验证的假设，以了解有机储层如何随着生物地球化学环境的变化而改变。

Fig. 4.

Controls on OM accumulation by microbial consumption. Starting from a representative, arbitrary concentration in the center, the change in total OM carbon is calculated for a 10-fold change in each of four parameters (i.e., two parameters vary in each quadrant): slower microbial processing via a reduced maximum uptake rate, faster turnover via an increased population-loss rate, less connectivity via a reduced likelihood of population presence, and more substrates (chemical diversity) via a greater number of OM pools.
通过微生物消耗对有机物积累的控制。从中心的代表性任意浓度开始，计算在四个参数中每个参数的10倍变化下总有机物碳的变化（即，每个象限中有两个参数变化）：通过减少最大摄取速率来减慢微生物处理速度，通过增加种群损失速率来加快周转速度，通过减少种群存在的可能性来减少连接性，通过增加有机物池的数量来增加底物（化学多样性）。

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Materials and Methods

Model Equations.

We describe microbial consumption and growth on pools of organic carbon. The model framework is sufficiently general to also account for inorganic nutrients and may be extended to account for the cycling of other elements. We model the uptake

ρ_{i j}

of each OM pool

i

, according to its concentration

C_{i}

, by microbial population

j

as a function of time

t

using a saturating (Michaelis–Menten) form as
我们描述了微生物对有机碳库的消耗和生长。该模型框架足够通用，也可以考虑无机营养物，并可以扩展到考虑其他元素的循环。我们根据每个有机碳库的浓度，通过微生物群落对其的摄取进行建模，作为时间的函数，使用饱和（Michaelis-Menten）形式。

ρ_{i j} (t) = ρ_{i j}^{max} \frac{C_{i} (t)}{C_{i} (t) + k_{i j}},

[4]

where

ρ_{i j}^{max}

is the maximum uptake rate and

k_{i j}

is the half-saturation constant (Table 1).
其中

ρ_{i j}^{max}

是最大摄取速率，

k_{i j}

是半饱和常数（表1）。

Each population synthesizes biomass according to a growth efficiency for each pool (yield

y_{i j}

) and loses biomass at a rate proportional to its biomass according to a quadratic mortality parameter

m_{j}^{q}

(implicitly representing predators and viruses) and linear mortality parameter

m_{j}^{l}

(representing cell maintenance and senescence). The rates of change of the concentration

C_{i}

of pool

i

and the biomass

B_{j}

of population

j

are
每个种群根据每个池的生长效率（产量

y_{i j}

）合成生物量，并根据二次死亡参数

m_{j}^{q}

（隐含表示捕食者和病毒）和线性死亡参数

m_{j}^{l}

（表示细胞维护和衰老）以与其生物量成比例的速率失去生物量。池

i

的浓度

C_{i}

变化率和种群

j

的生物量

B_{j}

变化率。

\frac{\partial C_{i} (t)}{\partial t} = s_{i} (t) - \sum_{j} I_{j} (t) ρ_{i j} (t) B_{j} (t),

[5]

\frac{\partial B_{j} (t)}{\partial t} = \sum_{i} I_{j} (t) y_{i j} ρ_{i j} (t) B_{j} (t) - m_{j}^{q} B_{j} {(t)}^{2} - m_{j}^{l} B_{j} (t),

[6]

where

s_{i} (t)

is the supply rate of pool

i

, which is governed by the probability of the supply of each pool

q_{i}

as
其中

s_{i} (t)

是池

i

的供应率，由每个池

q_{i}

的供应概率决定

s_{i} (t) = \{\begin{matrix} σ_{i} & with probability q_{i} \\ 0 & with probability 1 - q_{i}, \end{matrix}

[7]

where

σ_{i}

is the potential supply rate, which here is a fraction of total OM supply to the domain (Table 1). The term

I_{j} (t)

indicates the presence of population

j

at time

t

according to the probability of presence

P_{j}

(see detail below) as
其中

σ_{i}

是潜在供应率，这里是总OM供应量在该领域的一部分（表1）。术语

I_{j} (t)

表示根据存在概率

P_{j}

（详见下文）在时间

t

存在

j

人口。

I_{j} (t) = \{\begin{matrix} 1 & with probability P_{j} \\ 0 & with probability 1 - P_{j} . \end{matrix}

[8]

Because the presence of population

j

averages to

P_{j}

over time, we include

P_{j}

in Eqs. 1–3 for conciseness. All parameter values (

ρ^{max}, k

[via the affinity

ρ^{max} k^{- 1}

],

y, m^{q}, m^{l}, q

, and

P

) are set by randomly sampling from uniform distributions (Table 1; SI Appendix, SI Text 1).
由于人口

j

随时间的平均存在，我们在方程1-3中包括

P_{j}

以简洁表达。所有参数值（通过亲和力

ρ^{max} k^{- 1}

确定的

ρ^{max}, k

，

y, m^{q}, m^{l}, q

和

P

）都是通过从均匀分布中随机抽样设置的（表1；附录SI，附录SI文本1）。

Yield

y_{i j}

reflects the cost of enzymes and the free energy released by OM oxidation.

ρ_{i j}^{max}

and

y_{i j}

may be interdependent due to cellular optimization strategies, reflecting inherent tradeoffs between protein allocation and efficiency (57, 58). The varying combinations of

ρ_{i j}^{max}

and

y_{i j}

can also represent the different modes of uptake of high-molecular-weight DOM (59). Analogously, the different parameter combinations can account for the additional feedback between the external concentration and the rate of cellular processing

ρ_{i j}^{max}

(60). Real populations may change their cellular machinery due to plasticity, where, in the model, the many sets of parameters represent static phenotypes among these different modes.
产量

y_{i j}

反映了酶的成本和有机物氧化释放的自由能。由于细胞优化策略，

ρ_{i j}^{max}

和

y_{i j}

可能相互依赖，反映了蛋白质分配和效率之间固有的权衡（57, 58）。

ρ_{i j}^{max}

和

y_{i j}

的不同组合也可以代表高分子DOM的不同摄取方式（59）。类似地，不同的参数组合可以解释外部浓度和细胞处理速率之间的额外反馈关系

ρ_{i j}^{max}

（60）。真实的群体可能会因为可塑性而改变其细胞机制，在模型中，许多参数集代表了这些不同模式中的静态表型。

Probability of Presence.

Observations show that community composition dictates the character of DOM remineralization in seemingly unpredictable ways (61, 62), and evidence supports localized sinks of deep DOM (32). To simulate this impact, we include a population presence–absence dynamic in the model. Each population is assigned an overall probability of presence

P_{j}

, simulating the sporadic presence of rare functional types and the nearly guaranteed presence of ubiquitous types. When

I_{j} (t) = 0

(Eq. 8), the population does not consume OM or synthesize biomass at that timestep, but its biomass is still subject to loss. In effect, this dynamic extends the range of maximum processing (synthesis) rates to lower values, demonstrating how the absences of particular functional types contribute to longer effective remineralization timescales. This dynamic results in the majority of interactions at intermediate (though still widely ranging) rates, with very slow and very fast interactions being fairly rare (SI Appendix, Fig. S13). Over time, the average presence approaches

P_{j}

, and the steady-state balances calculated with the overall probability

P_{j}

closely match the model solutions.
观察表明，社区组成以看似不可预测的方式决定DOM再矿化的特性（61, 62），证据支持深层DOM的局部汇（32）。为了模拟这种影响，我们在模型中包括了人口存在-缺失的动态。每个人口被分配一个存在的总概率

P_{j}

，模拟罕见功能类型的零星存在和普遍类型的几乎确定存在。当

I_{j} (t) = 0

（方程8）时，该人口在该时间步不消耗OM或合成生物量，但其生物量仍然会损失。实际上，这种动态将最大处理（合成）速率的范围扩展到较低的值，展示了特定功能类型的缺失如何导致更长的有效矿化时间尺度。这种动态导致大多数相互作用在中等（尽管仍然广泛变化）速率下进行，非常慢和非常快的相互作用相对较少（SI附录，图S13）。随着时间的推移，平均存在趋近于

P_{j}

，并且使用总体概率

P_{j}

计算的稳态平衡与模型解非常接近。

Consumption Matrix.

A consumption matrix dictates which populations consume which OM pools (SI Appendix, Fig. S1). We vary the specialist vs. generalist capabilities of the populations with respect to the number of OM pools taken up by each population (

n_{u p}

, which can vary from one to

n

, the number of OM pools), as well as with the widespread popularity of each pool with respect to the number of consumers of each (

n_{c o n s}

, which can vary from one to

m

, the number of populations) (Fig. 1). In the model version with solely specialists (Fig. 2; SI Appendix, Fig. S2), each population consumes only one unique pool. For the generalist populations (Fig. 2; SI Appendix, Fig. S2), we first randomly assign

n_{u p}

to each population drawing from the linear range from one to

n

. Second, we assign a weight to each OM pool of its probability of being consumed

n_{c o n s}

, varying the weights linearly. Finally, we assign the specific pools taken up by each population (i.e., we fill each column of the consumption matrix) by sampling from the

n

possibilities with the weights. For the weighted sampling, we use the algorithms “ProbabilityWeights” and “sample” in the StatsBase package in Julia.
消费矩阵决定了哪些群体消费哪些OM池（附录SI，图S1）。我们根据每个群体对OM池的吸收数量（

n_{u p}

，可以从1到

n

，即OM池的数量）以及每个池子受欢迎程度（

n_{c o n s}

，可以从1到

m

，即群体的数量）的不同来变化群体的专业与广泛能力（图1）。在仅有专家的模型版本中（图2；附录SI，图S2），每个群体只消费一个独特的池子。对于广泛能力的群体（图2；附录SI，图S2），我们首先随机分配

n_{u p}

给每个群体，范围从1到

n

。其次，我们为每个OM池分配一个权重，表示其被消费的概率

n_{c o n s}

，权重线性变化。最后，我们通过从具有权重的

n

可能性中进行抽样，为每个群体分配特定的池子（即填充消费矩阵的每一列）。对于加权抽样，我们在Julia的StatsBase包中使用算法“ProbabilityWeights”和“sample”。

Simulations.

In the simulations illustrated in Fig. 2, we resolve 1,000 OM classes and 1,000 or 2,000 pools of biomass: a model version with 1,000 specialists, and a model version with the 1,000 specialists and an additional 1,000 with a range of generalist ability. Results with the latter 2,000 pools are similar to a model with only the 1,000 generalists. For each experiment, we integrate the model forward in time for 10 y, until the pools that have the potential to equilibrate have equilibrated. The concentrations of many of the recalcitrant pools continue to increase over time (unless a concentration-dependent sink is added to the model). SI Appendix, Fig. S13 illustrates the resulting distributions of biomass concentrations, OM concentrations, and remineralization rates of the ensembles, which are consistent with observed and inferred distributions of OM characteristics, remineralization rates, and ages in the ocean, sediments, soils, and lakes (10, 21–27, 63–65).
在图2所示的模拟中，我们解决了1,000个OM类别和1,000或2,000个生物量池：一个具有1,000个专家的模型版本，以及一个具有1,000个专家和1,000个具有一定广义能力的额外专家的模型版本。后面2,000个池的结果与仅有1,000个广义专家的模型相似。对于每个实验，我们将模型向前推进10年的时间，直到具有平衡潜力的池达到平衡。许多难降解池的浓度随时间继续增加（除非在模型中添加浓度依赖的汇）。SI附录，图S13说明了生物量浓度、OM浓度和集合物的再矿化速率的分布，这与海洋、沉积物、土壤和湖泊中观察到和推断出的OM特征、再矿化速率和年龄的分布一致（10, 21-27, 63-65）。

In SI Appendix, SI Text 2 and Figs. S2–S7, we demonstrate the qualitative consistency of the solutions across variations of the model. All simulations support the conclusions presented. Solutions vary quantitatively, but not qualitatively, with variations in the generalist capabilities of the microbial populations, the number of OM pools resolved, the ratios of OM pools to populations resolved, the length of numerical integration, and the mode of uptake by the populations (additive consumption vs. switching over time to optimize growth). In the model version, where generalists switch their consumption over time (SI Appendix, Fig. S7), values of

Q < 1

result for some pools as generalists cease to consume functionally recalcitrant pools, despite their capability to do so.
在SI附录中，SI文本2和图S2-S7中，我们展示了模型变化下解的定性一致性。所有的模拟都支持所提出的结论。解在定性上没有变化，但在定量上有所变化，这取决于微生物群落的广义能力、解决的OM池的数量、OM池与解决的群体的比例、数值积分的长度以及群体的摄取方式（加法消耗与随时间切换以优化生长）。在模型版本中，广义消费者随时间切换其消费行为（SI附录，图S7），尽管它们有能力这样做，但对于一些池来说，广义消费者停止消费功能上难降解的池，导致

Q < 1

的值。

Reduced-Complexity Model Version.

For the reduced-complexity model of OM consumption used in the marine ecosystem model, we collapse the complexity onto one master lability parameter—the maximum uptake rate—and we resolve fewer OM pools (

n = 25

) (SI Appendix, Fig. S15). The values of

y

,

m^{q}

,

m^{l}

, and uptake affinity are kept constant, since their variation affects the solutions quantitatively, but not qualitatively. A specialist population, which represents multiple clades in aggregate, consumes each pool. Since we don’t include stochastic processes, the probability of presence

P = 1

for all populations. In accordance with theory and our stochastic model results (27, 66), we assume a lognormal distribution for the partitioning of total OM production into the 25 pools (SI Appendix, Fig. S15D), which represents the average outcome of microbial transformation over time and space.
对于海洋生态系统模型中使用的OM消耗的简化模型，我们将复杂性折叠到一个主要的可变性参数——最大摄取速率上，并且解决较少的OM池（

n = 25

）（附录SI，图S15）。

y

，

m^{q}

，

m^{l}

和摄取亲和力的值保持不变，因为它们的变化对解决方案的数量影响较大，但对质量影响不大。一个代表多个聚类的专业种群消耗每个池。由于我们不包括随机过程，所有种群的存在概率

P = 1

。根据理论和我们的随机模型结果（27, 66），我们假设总OM产量分配到25个池中的对数正态分布（附录SI，图S15D），这代表了微生物转化随时间和空间的平均结果。

Marine Ecosystem Model.

The reduced-complexity model version is incorporated into a dynamic marine ecosystem model of a stratified vertical water column, where the production and consumption of all organic and inorganic pools are due to the growth, respiration, excretion, and mortality of microbial populations (SI Appendix, Fig. S14). Light and vertical mixing attenuate with depth. Two populations of phytoplankton convert dissolved inorganic carbon and nitrogen into biomass using light energy. Populations of microbial heterotrophs consume DOM (25 pools) and particulate OM (POM) (one pool), oxidize a portion of the carbon for energy, and excrete inorganic carbon and nitrogen as waste products. For simplicity, POM is resolved as one aggregate pool sinking at a constant rate. Total DOM is produced from POM degradation (due to the extracellular hydrolysis of POM) and the biomass loss of all populations. The model is a modified version of a published model in which carbon and nitrogen of the organic pools and the biomasses are each resolved independently (67). Parameter values are listed in SI Appendix, Table S1. See SI Appendix, SI Text 6 for model equations and further detail.
简化的模型版本被纳入了一个分层垂直水柱的动态海洋生态系统模型中，其中所有有机和无机池的生产和消耗都是由微生物群落的生长、呼吸、排泄和死亡引起的（SI附录，图S14）。光线和垂直混合随深度衰减。两个浮游植物群体利用光能将溶解无机碳和氮转化为生物量。微生物异养消费DOM（25个池）和颗粒OM（POM）（一个池），氧化一部分碳作为能量，并排泄无机碳和氮作为废物。为简化起见，POM被解析为以恒定速率下沉的一个聚合池。总DOM是由POM降解（由于POM的细胞外水解）和所有群体的生物量损失产生的。该模型是一种修改版本的已发表模型，其中有机池的碳和氮以及生物量分别独立解析（67）。参数值列于SI附录，表S1中。有关模型方程和更多细节，请参见SI附录，SI文本6。

Data Availability

Julia code for the stochastic OM consumption model and Fortran code for the marine ecosystem model are publicly accessible on GitHub (https://github.com/emilyzakem/OMconsumption) (68).
Julia代码用于随机OM消耗模型，Fortran代码用于海洋生态系统模型，可以在GitHub上公开访问（https://github.com/emilyzakem/OMconsumption）（68）。

Acknowledgments

We acknowledge funding from the Simons Foundation: The Simons Collaboration on Principles of Microbial Ecology Grant 542389 (to N.M.L.) and the Simons Postdoctoral Fellowship in Marine Microbial Ecology (to E.J.Z.); National Environmental Research Council Grant NE-R015953-1 (to B.B.C.); and European Union Horizon 2020 Research and Innovation Program Grant 820989 (to B.B.C.). We thank R. Letscher for providing the DOC data compilations; and N. Norris, J. McNichol, E. McParland, and the N.M.L. group for comments on the manuscript. The work reflects only the view of the authors; the European Commission and their executive agency are not responsible for any use that may be made of the information the work contains.
我们感谢Simons基金会的资助：Simons微生物生态学原则合作基金542389（给N.M.L.）和Simons海洋微生物生态学博士后奖学金（给E.J.Z.）；国家环境研究委员会资助NE-R015953-1（给B.B.C.）；以及欧盟Horizon 2020研究与创新计划资助820989（给B.B.C.）。我们感谢R. Letscher提供DOC数据编译；以及N. Norris，J. McNichol，E. McParland和N.M.L.小组对手稿的评论。本工作仅代表作者的观点；欧洲委员会及其执行机构对本工作所包含的信息的任何使用不承担责任。

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References

1

P. Ciais et al., “Carbon and other biogeochemical cycles” in Climate Change 2013: The Physical Science Basis. Contributions of Working Group I to the Fifth Assessment Report of the Intergovernmental Panel on Climate Change, T. Stocker, Eds. (Cambridge University Press, Cambridge, UK, 2013), pp. 465–570.
P. Ciais等人，“碳和其他生物地球化学循环”在《气候变化2013：物理科学基础》中。第五次评估报告工作组I对政府间气候变化专门委员会的贡献，T. Stocker主编。（剑桥大学出版社，英国剑桥，2013年），第465-570页。

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A Mechanistic Model of OM Consumption.

Diagnosing Functional Recalcitrance.

Unification of Hypotheses.

Predicting OM Accumulation Patterns.

Implications.

Materials and Methods

Model Equations.

Probability of Presence.

Consumption Matrix.

Simulations.

Reduced-Complexity Model Version.

Marine Ecosystem Model.

Data Availability

Acknowledgments

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Emily J. Zakem1 https://orcid.org/0000-0001-6799-5063 zakem@usc.edu

B. B. Cael https://orcid.org/0000-0003-1317-5718

Naomi M. Levine https://orcid.org/0000-0002-4963-0535

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Affiliations

Emily J. Zakem¹ https://orcid.org/0000-0001-6799-5063 zakem@usc.edu

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