Ecology

Restoration opportunity area and costsMangrove restoration programmes have a greater chance of being successful when implemented in areas where mangroves have previously grown15. These areas have either been subject to deforestation or degradation and may be under government management or private ownership. They are locations that have undergone forest conversion into other land uses, including aquaculture, crops or plantations and urban settlements. Land ownership status is an important factor to consider for determining the availability of land for mangrove restoration7. For example, a higher opportunity and priority would be given to unproductive aquaculture ponds located in the protected and production forest areas which are under government management or leasehold, rather than in areas with other land uses that may be under private ownership (Methods gives detailed forest land tenure classifications in Indonesia). Therefore, managing mangrove rehabilitation should consider factors that include land tenure status and land-cover type as well as biogeomorphology (for example, ensuring that the correct mangrove species are used in hydrologically suitable locations) across landscape scales.We calculated that ~193,367 ha of land may be feasible for implementation of mangrove rehabilitation programmes (Fig. 4). This conservative assessment suggests that the potential for restoration may be only 30% of the current mangrove rehabilitation area target (600,000 ha). Depending on the challenges and opportunities for each of the biogeomorphological categories of land use and the forest land status we considered (see Methods for detailed mapping methodology), we identified that 9% of the potential restorable area was categorized as being within the high opportunity scenario, 33% as medium and 58% as areas falling within the low opportunity scenario. Among these scenarios, ~75% of identified areas have non-protected forest status, implying a greater tenurial challenge to establishing a rehabilitation programme. We identified the five provinces that are among the top ranked of high potential for mangrove restoration in Indonesia, namely East Kalimantan (20% of national restoration potential area), North Kalimantan (20%), South Sumatra (12%), West Kalimantan (5%) and Riau provinces (5%) (Fig. 1c). All of these provinces, except South Sumatra, are among the areas already identified in the current mangrove rehabilitation programme by the BRGM as having high opportunity for rehabilitation4. At the subprovincial scale, we identified the top six regencies with restoration area opportunity >10,000 ha, namely Banyuasin, Bulungan, Tana Tidung, Paser, Berau and Nunukan (Supplementary Table 1). Mangroves across these regions were commonly deforested after 2010 and converted into aquaculture ponds despite being designated as protected forest areas (Supplementary Table 1).Fig. 4: The distribution of mangrove loss area (in hectares) between 2001 and 2020 in Indonesia.Also shown are mangrove loss proportions within different biogeomorphological typology, loss drivers (land-use types), forest land status and identified scenarios of restoration opportunity (low, medium and high).Full size imageConsidering that previous successful (85% survival rates) mangrove rehabilitation around the world has been achieved only at small landscape scales (10–400 ha) with costs varying between US$1,500 ha−1 and US$9,000 ha−1 (refs. 8,16), the large-scale mangrove rehabilitation ambition of Indonesia must be carefully planned. Rehabilitating ~200,000 ha of degraded mangroves will require between US$0.29 billion and US$1.74 billion. The 2021 annual government budget allocation for mangrove rehabilitation under BRGM alone is ~US$0.10 billion17, which is 66–94% lower than the estimated total required budget but with additional international investment18 there is potential for scalable mangrove rehabilitation success.Lessons learned from the past failuresIn Indonesia, unproductive aquaculture ponds have become targets for mangrove rehabilitation programmes (Supplementary Fig. 1). However, metrics of rehabilitation success in these settings reveal low survival rates of planted seedlings, highlighting an urgency to develop new strategies for mangrove rehabilitation and strategies to assess the effectiveness of ecosystem rehabilitation6. For example, a silviculture approach—nursery-based mangrove planting using Rhizophora species—has been adopted for mangrove restoration and management for a long time in Indonesia19. When seedlings are directly planted in unused ponds (Supplementary Fig. 1), dense monoculture plantations often form, which despite providing some ecosystem services (for example, carbon sequestration20) have limited biodiversity value21 and may be less resilient to stressors compared to a diverse assemblages of tree species22.Mangrove restoration projects have often suffered low success rates due to inadequate hydrological site assessments before revegetation23. For example, mangrove planting programmes initiated after the 2004 tsunami were focused on mono-species planting and on reporting the number of seedlings being planted in a given area24. These planting projects most often occurred on undisputed land, such as mudflats, which are inappropriate locations for long-term mangrove growth because of high inundation frequency, high water flow rates and hypersaline conditions that limit seedling establishment and survival24. Planting has also focused in mangrove areas where low canopy cover is observed. While some mangrove areas with low canopy cover may respond to plantings because they are degraded, many sites naturally support low canopy cover, reflecting suboptimal environmental conditions for growth of Rhizophora species, instead favouring growth of highly salt tolerant species such as Avicennia spp.24. Such failures in mangrove rehabilitation efforts, however, have been under-reported with more than 50% of rehabilitation studies not monitored over time (Supplementary Fig. 1).Alternative restoration approaches through repairing hydrology, including excavation and removal of pond walls and tidal gates, have also been introduced15, although this approach has been only practiced in Indonesia at limited scales, mostly in unused aquaculture ponds25. A comprehensive understanding of the opportunity for mangrove rehabilitation in Indonesia is largely unquantified. Additionally, with limited monitoring of mangrove rehabilitation projects, the effectiveness and functionality of mangrove rehabilitation in Indonesia remains largely unknown and therefore it remains challenging to assess rehabilitation effectiveness between approaches and locations in Indonesia. Yet such assessments provide important data to achieve the ambitious mangrove rehabilitation goals of Indonesia.Mangrove governance in IndonesiaMangrove conservation in Indonesia was formally adopted in 1990 (Extended Data Fig. 1 and Supplementary Table 2), when mangroves were designated as protected forests under Law 5/1990 and the Presidential Decree 32/1990. When the Asian tsunami hit Aceh province in 2004, the role of mangroves in wave attenuation and therefore minimizing disaster risks for coastal communities was recognized26. As a result, nearly 30,000 ha of damaged mangroves were rehabilitated to recover coastal resiliency through planting of nearly 24 million seedlings over 60 projects24. However, the success of these programmes was low due to a lack of planning, monitoring and critical supplemental actions24,27. Despite the failure of many mangrove rehabilitation projects post-tsunami, the implementation of the subsequent programmes have not fully adopted best-practice mangrove rehabilitation principles6,7,15,23. In 2007, similar approaches to mangrove rehabilitation and conservation were adopted at a larger, national scale under the Spatial Planning Law (Law 26/2007) and the Coastal Area and Small Islands Management Law (Law 27/2007).In 2012, the National Mangrove Management Strategy (STRANAS Mangrove) was first established and followed by the formalization of the National and Regional Mangrove Working Group whose task was to guide mangrove conservation and rehabilitation. Its main goal was to involve more stakeholders, including civil society organizations and subnational government bodies, in mangrove conservation and rehabilitation28. Until 2017, the technical regulation of strategy and performance indicators for mangrove management was implemented with targets set to rehabilitate 3.49 Mha of mangroves by 204529. In 2020, however, the Mangrove Working Group and its supporting regulations were abolished and the mangrove rehabilitation strategy was subsequently managed by BRGM4. This effectively removed the regional governments (subnational working groups) from decisions related to mangrove management and concentrated development of policy at the level of the national government. The new strategy includes a tenfold increase in the annual rehabilitation target (from 11,250 to ~120,000 ha yr−1) with an overall target of 600,000 ha to be achieved within a shorter timeline (2020–2024). Without clear planning and appropriate strategies, these ambitious targets may not be feasible. For example, the annual mangrove rehabilitation area reached between 2017 and 2020 was only 5,318 ha (50% of the target) despite 2.6 million seedlings being planted (Supplementary Table 3). Given the lessons from the previous mangrove rehabilitation and the emerging processes of mangrove governance, it is timely to set an achievable restoration framework with improved planning, evaluation and monitoring.Implication for international environmental agendasA successful mangrove rehabilitation programme can directly contribute to reducing poverty (SDG 1) and maintaining food security and livelihoods (SDG 2), thereby increasing the health and well-being of 74 million coastal people in Indonesia (see Supplementary Table 1 for total population of regions with restoration potential area >5 ha). Additionally, mangrove rehabilitation will directly contribute to other relevant SDGs, such as improving water quality (SDG 6), providing healthy coastal habitats for fish and other marine biodiversity (SDG 14), contributing to emissions reductions and improving coastal resilience from sea level rise (SDG 13) and sustainably managing and protecting terrestrial ecosystems (SDG 15). Mangrove rehabilitation contributions to SDG 1 and 2 are particularly relevant as the current rehabilitation programme is delivered as cash-for-works activities under the National Economic Recovery strategy (PEN) as part of the social welfare payments to alleviate economic impacts of the COVID-19 pandemic17. With the current annual mangrove rehabilitation budget of US$0.10 billion17, further implementation of scalable community-based mangrove restoration with technical support from subnational and non-government stakeholders could increase the benefits to local communities, if administered properly. Therefore, the large investments planned for coastal communities via a national mangrove restoration programme will not only contribute to the economy of coastal communities, potentially reducing poverty across 199 regencies but will also help in securing nearly 4% of the national greenhouse gas emissions reduction target from the land sector.Restoring 193,367 ha of mangroves in the next 5 years (2021–2025) may contribute to carbon sequestration of 22 ± 10 MtCO2e by 2030 (see Methods for detailed estimate calculation and assumptions). Moreover, stopping the current annual rates of mangrove loss of 7,436 ha yr−1 between 2021 and 2030 will reduce up to 58 ± 37 MtCO2e or 12% of the national land sector emissions reduction targets. Clearly, climate benefits from mangrove rehabilitation and conservation in Indonesia are substantial if rehabilitation and conservation can be implemented appropriately and large annual rehabilitation targets are achieved. Indonesia has submitted its updated Nationally Determined Contributions (NDCs) to the United Nations Framework Convention on Climate Change, within which integrated management and rehabilitation of mangroves is a component of the actions to enhance the resilience of coastal ecosystems30. Further ecological aquaculture practices such as silvofisheries which are commonly applied in Indonesia31,32 may provide promising potential for climate change mitigation through mangrove biomass enhancement. With the increased potential for international investment to support mangrove rehabilitation in Indonesia, there is an opportunity for Indonesia to take the lead and show the world how mangrove conservation and rehabilitation can contribute to multiple international environmental agendas.In the past three decades, the governance of mangrove conservation and rehabilitation in Indonesia has been highly variable in approach (Extended Data Fig. 1). The current approach is top-down4 which has risks and may be ineffective at achieving landscape-scale increases in mangrove extent, as was demonstrated post-tsunami24,29. This top-down approach set by national-level agencies, which are responsible for achieving rehabilitation targets, has limited involvement (or investment) by subnational governments. While we have identified key factors that determine land available for mangrove rehabilitation, the success of mangrove rehabilitation is not necessarily assured because of the limited involvement of subnational mangrove working groups. A current ‘one size fits all’ strategy of the national government may not be appropriate to achieve successful mangrove rehabilitation and thus more flexible, localized approaches may increase the likelihood of success. More

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Plant species and pollinatorsMedicago sativa L. (Fabaceae), also called alfalfa or lucerne, is a perennial legume with flowers arranged in a cluster or raceme. It is a self-compatible plant with fairly high outcrossing rate (5.3–30%)46, and it requires insect visits for seed production47. No plant material was collected for this study. Honey bees, Apis mellifera, and alfalfa leafcutting bees, Megachile rotundata, are used as managed pollinators in alfalfa seed-production fields in the USA while bumble bees are commonly used in alfalfa breeding47.Experimental design and pollinator observationsFive 11 m × 11 m patches of M. sativa plants were set up in an east–west linear arrangement at the West Madison Agricultural Research Station in Madison, Wisconsin, USA. Within each patch, we transplanted 169 young plants grown from seeds in the greenhouse, each placed 90 cm apart. These plants grew and, at flowering, a plant had an average of 30.65 ± 16.4 stems per plant, with 4.93 ± 3.41 racemes per stem, and 7.53 ± 2.44 open flowers per raceme.A honey bee hive was placed approximately 100 m from the patches and a bumble bee hive was set up at the center of the southern edge of the patches. For leafcutting bees, a 60 × 30 × 7.6 cm bee board was set up in each of two boxes placed 1/3 and 2/3 along the southern edge of the patches and a half gallon of bees was released at periodic intervals throughout the alfalfa flowering season.Over two consecutive summers, observers followed bees foraging in the alfalfa patches, marked each raceme visited in succession within a foraging bout with a numbered clip, and recorded the number of flowers visited per raceme. After a bee had left a patch, observers went back to the marked racemes and measured the distance and direction traveled between consecutive racemes. Directions were recorded as one of the cardinal directions: North (N), South (S), East (E) or West (W), or inter-cardinal directions: Northeast (NE), Southeast (SE), Northwest (NW) and Southwest (SW). The frequency distributions of distances and directions traveled between two successive racemes are presented for each bee species each year in Figs. 1 (distances) and 2 (directions). The low pollinator abundance permitted observers to follow individual bees foraging in a patch. Little interference among bee species was observed in the patches.Figure 1Frequency distributions for distances traveled between consecutive racemes (cm) for each bee species each year.Full size imageFigure 2Frequency distributions of directions traveled between consecutive racemes for each bee species each year.Full size imageModel for the distance traveled between consecutive racemesWe first determined whether a statistical model best described the distance traveled between consecutive racemes (Modeled Distance), and examined whether the model differed among bee species. We used mixed effect linear models (proc Mixed in SAS 9.3)48 to identify the model that best described the distance traveled by pollinators between consecutive racemes. The model included loge distance as a linear function of loge flower number and bee species as fixed effects. The distance traveled between consecutive racemes and the number of flowers visited per raceme were log transformed prior to analyses in order to improve the models’ residuals. In addition, we included patch and foraging bout as random effects in the model. A foraging bout includes the racemes visited in succession from the time a bee is spotted in a patch to the time it leaves that patch. We used foraging bout instead of individual bee as the random effect because bees were not individually marked in this study. Moreover, to take into consideration the potential correlation between successive observations within a foraging bout, we added clip to the model. Clip 1 represents the first and second racemes visited in the foraging bout; clip 2, the second and third, and so on. Clip was added to the model either as a random effect or as a repeated measure with an AR(1) structure. The combination of random clip and random foraging bout creates a model that is sometimes called the “compound symmetry” model. The AR(1) structure represents correlations that decline exponentially as the gap between measurements increases such that measurements closer together in time are more strongly correlated than measurements further apart. Because we expected bees to visit flowers at close proximity when resources are abundant, we chose this correlation structure as a good potential descriptor of the way distances might be correlated within foraging bouts. We started with a full model which included loge flower number, bee species, patch, foraging bout, and clip either as a random effect or as a repeated measure with an AR(1) structure. We then removed variables and compared models by inspecting AIC values and the p values for each term in the model. We considered both low AIC and statistically significant (p  More

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In this section, we introduce flapping flight dynamics and describe the bird model used in our computational framework. Furthermore, we describe how such a dynamical model is used in order to identify steady and level flapping flight regimes, study their stability, and assess their energetic performance.Equations of motion modelling flapping flightFlight dynamics is restricted to the longitudinal plane and thus the bird main body is captured as a rigid-body with three degrees of freedom, i.e. two in translation and one in rotation. This model preserves symmetry with respect to this plane, without any lateral force and moment. The aerodynamic model of the wing relies on the theory of quasi-steady lifting line23. Additionally, the present work does not account for the inertial forces due to the acceleration of the wing, and thus also neglecting the so-called inertial power. This inertial power was shown to be negligible in fast forward flight conditions, in comparison to the other contributions to actuation power24, and is thus systematically neglected in similar work10,11,25 since wing inertia is neglected.The body is thus modelled with a mass (m_b) and a rotational inertia (I_{yy}) about its center of mass. The equations of motion are expressed in the body frame (G(x’, y’, z’)) with unit vectors ((hat{textbf{e}}_{x’}, hat{textbf{e}}_{y’}, hat{textbf{e}}_{z’})), and an origin located at the center of mass, as pictured in Fig. 1a. The state space vector is thus$$begin{aligned} textbf{x} = {u, w, q, theta } end{aligned}$$where u and w are the body velocities along the (x’-) and (z’-)axis and (theta) and q are the pitch angle and its time derivative about the (y’-)axis, respectively. Consequently, the equations of motion read11,13,26$$begin{aligned} begin{aligned} dot{u}&= -qw – gsin theta + frac{1}{m_b}big ( {F_{x’}(textbf{x}(t), t)} \&quad + {F_{x’, t}(textbf{x}(t), t)} + D (textbf{x}(t), t) big )\ dot{w}&= qu + gcos theta +frac{1}{m_b} big ( F_{z’}(textbf{x}(t), t) + F_{z’, t}(textbf{x}(t), t) big ) \ dot{q}&=frac{1}{I_{yy}} big ( M_{y’}(textbf{x}(t), t) + M_{y’, t}(textbf{x}(t), t) big )\ dot{theta }&= q end{aligned} end{aligned}$$
(1)
Figure 1(a) Bird model for describing the flight dynamics in the longitudinal plane. The state variables are expressed with respect to the moving body-frame located at the flier’s center of mass (G(x’,z’)). These state variables are the component of forward flight velocity, u, the velocity component of local vertical velocity, w, the orientation of this body-centered moving frame with respect to the fixed frame, (theta) and its angular velocity, q. A second frame (O(x’_{w}, z’_{w})) is used to compute the position of the wing, relative to the body. The wings (dark gray) and the tail (red) are the surfaces of application of aerodynamic forces. (b) Top view of the bird model. The left wing emphasizes a cartoon model of the skeleton. The shoulder joint s connects the wing to the body via three rotational degrees of freedom (RDoF), the elbow joint e connects the arm with the forearm via one RDoF and the wrist joint w connects the forearm to the hand via two RDoF. Each feather is attached to a bone via two additional RDoF, except the most distal one ”1” which is rigidly aligned with the hand. The right wing further emphasizes the lifting line (red) which is computed as a function of the wing morphing. The aerodynamic forces generated on the wing are computed on the discretized elements (P_{i}). The tail is modelled as a triangular shape with fixed chord (c_{t}) and maximum width (b_{t}) that can be morphed as a function of its opening angle (beta). (c) Wing element i between two wing profiles, identifying a plane (Sigma) containing the lifting line (red). (d) Cross section of the wing element, containing the chord point (mathbf {P_i}) where the velocities are computed (Color figure online).Full size imageThe forcing terms in Eq. (1) are the aerodynamic forces and moments applied to the wing (namely (F_{x’}), (F_{z’}), and (M_{y’}) ) and to the tail ((F_{x’, t}), (F_{z’, t}), and (M_{y’, t})). The whole drag is captured by an extra force D that sums contributions due to the body (D_{b}), the skin friction of the wing (wing profile) (D_{p,w}), and the skin friction of the tail (tail profile) (D_{p,t}). These terms are described in detail in the next sections. Importantly, we accounted for the drag acting purely along (x’) direction, after proving that the projection of the drag forces along (z’)-axis is between two and three orders of magnitude smaller with respect to the aerodynamic forces produced by two other main lifting surfaces. This assumptions holds for the fast forward flight regime that are subject of our study, but such components of drag along (z’) axis should be accounted for other flight situations.Wing modelThe bird has two wings. Each wing is a rigid poly-articulated body, comprising the bird arm, forearm and hand, as pictured in Fig. 1b. Each segment is actuated by a joint to induce wing morphing. We refer to13,15 for a complete description of this wing kinematic model.Each joint is kinematically driven to follow a sinusoidal trajectory specified as:$$begin{aligned} q_{i}(t) = q_{0,i}(t) + A_{i} sin (omega t + phi _{0,i}) end{aligned}$$
(2)
with (omega = 2 pi f) and f being the flapping frequency which is identical for each joint, (q_{0,i}) being the mean angle over a period (or offset), (A_i) the amplitude, and (phi _{0,i}) the relative phase of joint i. A complete wingbeat cycle is therefore described through a set of 19 kinematic parameters, including the frequency f.We assume that the wing trajectory is rigidly constrained, and therefore we do not need to explicitly solve the wing dynamics. Under this assumption, the motion generation does not require the computation of joint torques. The model further embeds seven feathers of length (l_{ki}) in each wing. The feathers in the model have to be considered a representative sample of the real wing feathers. They thus have a limited biological relevance; their number is chosen so as to interpolate the planform satisfactorily and to smoothly capture the morphing generated by the bone movements. These feathers are attached to their respective wing bones via two rotational degrees of freedom allowing them to pitch and spread in the spanwise direction. These two degrees of freedom are again kinematically driven by relationships that depend on the angle between the wing segments13. This makes the feathers spreading and folding smoothly through the wingbeat cycle. In sum, the kinematic model of the wing yields the position of its bones and feathers at every time step. This provides a certain wing morphing from which the wing envelope (leading edge and trailing edge) can be computed (see Fig. 1b). From the wing envelope, the aerodynamic chord and the lifting line are computed. The lifting line is the line passing through the quarter of chord, which is itself defined as the segment connecting the leading edge to the trailing edge and orthogonal to the lifting line (Fig. 1b). This extraction algorithm is explained in detail in15.In order to calculate the aerodynamic forces, the angle of attack of the wing profile has to be evaluated. Each wing element defines a plane containing the lifting line and the aerodynamic chord as pictured in Fig. 1c. The orientation of the plane is identified by the orthogonal unit vectors ((hat{textbf{e}}_n, hat{textbf{e}}_t, hat{textbf{e}}_b)), where (hat{textbf{e}}_n) is the vector perpendicular to the plane and (hat{textbf{e}}_t) is the tangent to the lifting line. To compute the effective angle of attack, the velocity perceived by the wing profile is computed as the sum of the velocities due to the body and wing motion, and the velocity induced by the wake. The first contribution, (textbf{U}), accounts for$$begin{aligned} textbf{U} = textbf{U}_{infty } – textbf{v}_{kin} – textbf{v}_{q}end{aligned}$$where (textbf{U}_{infty } = u hat{textbf{e}}_{x’} + w hat{textbf{e}}_{z’}) is the actual flight velocity, (textbf{v}_{kin}) is the relative velocity of the wing due to its motion, and (textbf{v}_{q}) is the component induced by the angular velocity of the body q and calculated as$$begin{aligned} textbf{v}_{q} = qhat{textbf{e}}_{y’} wedge (textbf{P}_{i} – textbf{G})end{aligned}$$This velocity vector (textbf{U}) defines the angle (alpha), as pictured in Fig. 1d.The second contribution is due to the induced velocity field by the wake, i.e. the downwash velocity (w_{d}), and acting along the normal unit vector (-w_{d}hat{textbf{e}}_n). The resulting effective angle of attack, (alpha _{r}), is thus$$begin{aligned} alpha _{r} = alpha – frac{w_{d}}{|textbf{U}|}end{aligned}$$The downwash velocity (w_d) is computed according to the Biot-Savart law23, assuming the wake being shed backwards in the form of straight and infinitely long vortex filaments at each time step of the simulation13,15. This quasi-steady approximation is justified a posteriori by ensuring that our reduced frequency, inversely proportional to the unknown airspeed, never exceeds the value of 0.2, below which the effects of time-dependent wake shapes on wing circulation are negligible (e.g. see discussion in27). Once the downwash is evaluated, it is possible to evaluate the circulation, and consequently the aerodynamic force and moment acting at the element (P_i), i.e. (F_{x’, i}(textbf{x}(t), t), F_{z’, i}(textbf{x}(t), t), M_{y’, i}(textbf{x}(t), t)), as explained in detail in13. We use the thin airfoil theory for the estimation of the lift coefficient, with a slope of (2pi) that saturates at an effective angle of attack (alpha _{r}) of (pm 15^{circ }).Drag production by body and wingThe main body and the wings induce drag that should be accounted for in a model aiming at characterizing energetic performance. Body-induced drag is named parasitic because the body itself does not contribute to lift generation, and only induces skin friction and pressure drag around its envelope28. The total body drag is$$begin{aligned} D_{b} = frac{1}{2}rho C_{d, b} S_{b}|textbf{U}_{infty }|^{2} end{aligned}$$
(3)
where (rho) is the air density. We implemented the model described by Maybury28 to compute the body drag coefficient (C_{d, b}). This depends on the morphology of the bird and the Reynolds number Re according to$$begin{aligned} C_{d,b} = 66.6m_{b}^{-0.511}FR_{t}^{0.9015}S_{b}^{1.063}Re^{-0.197} end{aligned}$$
(4)
with (S_{b}) and (FR_{t}) are respectively the frontal area of the body and the fitness ratio of the bird, and both of them can be estimated from other allometric formulas i.e.28,29.$$begin{aligned} S_{b}= & {} 0.00813m_{b}^{2/3} end{aligned}$$
(5)
$$begin{aligned} FR_{t}= & {} 6.0799m_{b}^{0.1523} end{aligned}$$
(6)
The Reynolds number (Re = rho |textbf{U}_{infty }| overline{c} / mu) is calculated with the reference length of the mean aerodynamic chord (overline{c}), with (mu) being the dynamic viscosity. This model is found to be suitable for Reynolds number in the range (10^{4}-10^{5})28. Another source of drag is the profile drag due to friction between the air and the feathers on the wings. It is the sum of the profile drag at each section along the wingspan, i.e.$$begin{aligned} D_{p,w} = frac{1}{2} rho C_{d, pro} sum _{i=1}^{n} c_{i}|textbf{U}_{r,i}|^{2} ds_{i} end{aligned}$$
(7)
with (c_{i}) the chord length, (ds_{i}) the length of the lifting line element along the wingspan, and (textbf{U}_{r,i}) the velocity at the wing section i accounting for the body velocity, the kinematics velocity of the wing and the downwash velocity (Fig. 1c,d). We used a value of profile drag of (C_{d, pro} = 0.02) and this is assumed to be constant over the wingspan and throughout the flapping cycle30. In reality, due to the wing motion, this value should be gait dependent. However, the aforementioned assumption has been largely used in previous works31,32.Tail modelSince the span of the tail is of the same magnitude as its aerodynamic chord, here the lifting line approach cannot be used23. Therefore, the tail is modelled according to the slender delta wing theory, as a triangular planform33. Its morphology is illustrated in Fig. 1b and characterized by the opening angle (beta) and the chord (c_t). This latter parameter is kept constant, thus the tail span is controlled via (beta) from the trigonometrical relationship$$begin{aligned} b_{t} = 2c_{t}tan frac{beta }{2}end{aligned}$$The main limitation of this framework is the low range of angles of attack ((alpha _{tail} More

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Sets of interaction-associated mutants change across interactive conditionsTo investigate how microbial interactions are reorganized in a microbial community with increasing complexity, we reconstructed in vitro a modified bloomy rind cheese-associated microbiome on Cheese Curd Agar plates (CCA plates) as described in our previous work14 Growth as a biofilm on agar plates models the surface-associated growth of these communities, and allows inclusion of the filamentous fungus, P. camemberti, which grows poorly in shaken liquid culture. The original community is composed of the gamma-proteobacterium H. alvei, the yeast G. candidum and the mold P. camemberti. Using a barcoded transposon library of the model bacterium E. coli as a probe to identify interactions, we investigated microbial interactions in 2-species cultures (E. coli + 1 community member), in 3-species cultures (E. coli + 2 community members) and in 4-species cultures (or whole community: E. coli + 3 community members) (Fig. 1a).Figure 1Changes of E. coli’s genes associated with interaction-associated mutants in 2-species, 3-species and 4-species cultures. (a) Experimental design for the identification of interaction-associated mutants in 7 interactive conditions from the Brie community. The E. coli RB-TnSeq Keio_ML9 (Wetmore et al. 2015) is either grown alone or in 2, 3 or 4 species cultures to calculate E. coli gene fitness in each condition (in triplicate). Interaction fitness effect (IFE) is calculated for each gene in each interactive culture as the difference of the gene fitness in the interactive condition and in growth alone. IFE that are significantly different from 0 (two-sided t-test, Benjamini–Hochberg correction for multiple comparisons) highlight interaction-associated mutants in an interactive condition. (b) Volcanoplots of IFEs calculated for each interactive condition. Adjusted p-values lower than 0.1 highlight significant IFEs. Negative IFEs (blue) identify negative interactions and positive IFE (red) identify positive interactions. Numbers on each plot indicate the number of negative (blue) or positive (red) IFEs. (c) Functional analysis of the interaction-associated genes (significant IFEs). Genes of interaction-associated mutants have been separated into two groups: negative IFE and positive IFE. For each group, we represent the STRING network of the genes associated with interaction-associated mutants (Nodes). Edges connecting the genes represent both functional and physical protein association and the thickness of the edges indicates the strength of data support (minimum required interaction score: 0.4—medium confidence). Nodes are colored based on their COG annotation and the size of each node is proportional to the number of interactive conditions in which that given gene has been found associated with a significant IFE. Higher resolution of the networks with apparent gene names are found in Supplementary Figs. 2, 3.Full size imageQuantification of species’ final CFUs after 3 days of growth highlighted consistent growth for H. alvei and G. candidum independent of the culture condition and slightly reduced growth for E. coli in interactive conditions compared to growth alone (Dunnett’s test against growth alone; adjusted-p value ≤ 5%) except for the 2-species growth with P. camemberti (Supplementary Fig. 1). Although we were unable to quantify spores of P. camemberti after three days, growth of P. camemberti was visually evident in all of the expected samples. Quantitative analysis of E. coli’s library final growth using an epistatic model highlighted that the growth of E. coli in the 3-species and 4-species condition can be predicted from the corresponding 2-species growths (Supplementary Fig. 1).Previously, we developed an assay and a pipeline to identify microbial genes associated with interactions by adapting the original RB-TnSeq approach19 to allow for consistent implementation of biological replicates as well as for direct quantitative comparison of fitness values between different culture conditions15. More specifically, the original RB-TnSeq assay relies on the use of a dense pooled library of randomly barcoded transposon mutants of a given microorganism (RB-TnSeq library)19 containing multiple insertion mutants for each gene as well as intergenic insertion mutants. Measuring the variation of the abundance of each transposon mutant before and after growth, the pipeline allows the calculation of a fitness value for each insertion-mutant as well as a fitness value for each gene corresponding to the average of the insertion-mutants’ fitness of the associated genes across biological replicates. A negative fitness indicates that disruption of this gene decreases growth of the mutant relative to a wild type strain, whereas a positive fitness value indicates increased growth in the studied condition. Then, we infer the interactions based on the effects of insertion-mutants between interactive growth and growth alone. In other words, we measure and compare gene fitness across the different studied conditions. Any significant change in fitness values identifies an interaction-associated mutant. The subsequent analysis of interactions, including the inference of the interaction mechanisms and the comparison of interactions across the different interactive conditions, is mainly based on the nature of the disrupted genes by the transposon and their characterized function. Also, by measuring interactions as the difference of fitness value of a given gene between growth with other species and growth alone, we consider that interactions between insertion-mutants of the RB-TnSeq library are controlled and included in our calculation. Then, any interaction-associated mutant predominantly identifies inter-species interactions.In this work, we used the E. coli RB-TnSeq Keio_ML9 library19 and grew it for 3 days alone or in the seven different interactive conditions studied here (Fig. 1a). This library contains 152,018 pooled insertion mutants with an average of 16 individual insertion mutants per gene and many intergenic insertion mutants. For each interactive condition, we calculated the Interaction Fitness Effect (IFE) associated with 3699 E. coli genes as the difference between the gene fitness in the studied interactive condition and the gene fitness in growth alone (Supplementary Data 1). Negative IFE occurs when gene fitness decreases in the interactive condition, and positive IFE occurs when gene fitness improves in the interactive condition. We then tested for all the IFEs that are significantly different from 0 (adjusted p-value ≤ 0.1; two-sided t-test and Benjamini–Hochberg correction for multiple comparison20) to screen for interactions and to identify, in each condition, the insertion-mutants that are associated with inter-species interactions. Here, we identified between 6 (with P. camemberti) and 71 (with H. alvei + P. camemberti) significant IFEs per condition (Fig. 1b). Both negative IFEs and positive IFEs were found in each interactive condition except for the 2-species culture with P. camemberti, where only negative interactions were identified. A total of 330 significant IFEs associated with 218 unique genes were identified (as the same gene can be associated with a significant IFE in multiple conditions) including 125 genes associated with negative IFE and 120 genes associated with positive IFE (Supplementary Figs. 2, 3). Altogether, we didn’t notice any strong correlation between the number and type of IFE identified by condition and the overall growth impact measured on E. coli.
To gain insight into the interaction mechanisms among microbes, we next analyzed the functions of the genes of the interaction-associated mutants (i.e., genes associated with a significant IFE). Here, the vast majority of the genes associated with interaction-associated mutants are part of an interaction network (Fig. 1c). These STRING networks connect genes that code for proteins that have been shown or are predicted to contribute to a shared function, with or without having to form a complex21. A significant fraction of the interaction-associated mutants associated with a negative IFE are part of amino acid biosynthesis and transport (17%—Fig. 1c and Supplementary Figs. 2, 4), and more specifically with histidine, tryptophan and arginine biosynthesis. This points to competition for these nutrients between E. coli and the other species. Another large set of interaction-associated mutants is related to nucleotide metabolism and transport (14%—Fig. 1c and Supplementary Figs. 2, 5), highlighting competitive interactions for nucleotides and/or their precursors. The majority of the associated genes relate to purine nucleotides and more specifically to the initial steps of their de novo biosynthesis associated with the biosynthesis of 5-aminoimidazole monophosphate (IMP) ribonucleotide. Of the genes associated with interaction-mutants with a positive IFE, 15% are related to amino acid biosynthesis and transport (Fig. 1c and Supplementary Figs. 3, 4), suggesting cross feeding of amino acids between E. coli and the other species. More specifically, this includes phosphoserine, serine, homoserine, threonine, proline and arginine. The presence of amino acid biosynthetic genes among both negative and positive IFEs indicate that trophic interactions (competition versus cross-feeding) depend on the type of amino-acid and/or the species interacting with E. coli. For both negative and positive IFEs, numerous genes of the associated interaction-mutants were annotated as transcriptional regulators (Fig. 1c and Supplementary Figs. 2, 3) emphasizing the importance of transcriptional reprogramming in response to interactions. These transcriptional regulators include metabolism regulators as well as regulators of growth, cell cycle and response to stress. Finally, these interaction-associated mutants and the infered interaction mechanisms are consistent with previous findings in this microbiome14 as well as in a study of bacterial-fungal interactions involving E. coli and cheese rind isolated fungal species15. While this approach allows us to infer the interaction mechanisms that are happening between the transposon library and the other species, further experimental validation would be needed to confirm that these interactions more generally happen between a WT strain and the other species.Introduction of a third interacting species deeply reshapes microbial interactionsThe differences in the number and sign of significant IFEs observed among the different interactive conditions, with different numbers of interaction species, suggest that the number and type of interacting partners influence interaction mechanisms. To characterize how the interactions are reorganized with community complexity, we then investigated if and how the genetic basis of interactions changes when the number of interacting partners increases by comparing the genes associated with interaction-associated mutants with significant IFE in 2-species cultures, in 3-species cultures and then in 4-species cultures.First, we have identified 104 IFEs associated with 98 genes in 2-species cultures as well as 168 IFEs associated with 136 unique genes in 3-species conditions (Supplementary Fig. 6 and Supplementary Data 2). Comparing these gene sets, we can identify how the interaction-associated mutants change when a third-species is added to a 2-species culture. We identified 45 genes associated with 2-species interaction-associated mutants maintained in at least one 3-species condition (maintained interaction-mutants), 55 genes associated with 2-species interaction-associated mutants no longer associated with interaction in any 3-species condition (dropped interaction-mutants) and 100 genes associated with 3-species interaction-associated mutants that aren’t related to any 2-species interaction-associated mutants (emergent interaction-mutants) (Fig. 2a, Supplementary Fig. 6 and Supplementary Data 3). Both dropped and emerging interaction-associated mutants represent 3-species HOIs; the third species either removes an existing interaction or brings about a new one.Figure 2Comparison of the genetic basis of interaction for 2-species and 3-species conditions. (a) Venn Diagram of 2-species and 3-species sets of genes related to interaction-associated mutants. This Venn Diagram identifies 2-species interaction-mutants that are dropped when a third species is introduced (Left side; Dropped interaction-mutants = any 2-species gene that is not found in any 3-species condition), 2-species interaction-mutants that are maintained in at least one associated 3-species condition (Intersection; Maintained interaction-mutants) and interaction-mutants that are specific to 3-species condition (Right side; Emerging interaction-mutants). (b) Functional analysis of the genes associated with dropped, maintained and emerging interaction-mutants from 2-species to 3-species. Each dot represents the fraction of genes of the studied gene set associated with a given COG category (Number of genes found in the category / Total number of genes in the gene set). The color of the dots indicates the general COG group of the COG category: Teal: Metabolism; Blue: Information storage and processing; Orange: Cellular Processes and Signaling; Grey: Unknown or no COG category. (c) Species-level analysis of 3-species HOIs: for each 2-species condition, we measure the fraction of interaction-mutants that are dropped in associated 3-species cultures (Dropped in 3-species) or maintained in at least one of the 3-species cultures (Maintained in 3-species); for each 3-species condition, we measure the fraction of interaction-mutants that have been conserved from at least one associated 2-species condition (Maintained from 2-species) or that are emerging with 3-species (Emerging in 3-species).Full size imageWe further carried out functional analysis of the genes related to maintained, dropped and emerging interaction-mutants to elucidate whether maintained and HOIs interaction-mutants would be associated with specific functions and thus interaction mechanisms (Fig. 2b). For each set of genes, we calculated the fraction of genes of that set associated with a given COG ontology category. Metabolism and transport is the most observed COG group (Fig. 2b—teal dots). For genes related to maintained interaction-mutants, this indicates that some trophic interactions can be maintained from 2-species to 3-species conditions. For instance, serine biosynthetic genes serA, serB and serC as well as threonine biosynthetic genes thrA, thrB and thrC are associated with positive IFEs in the 2-species condition with G. candidum as well as in the 3-species conditions involving G. candidum (Supplementary Fig. 4). This suggests that, (i) G. candidum facilitates serine and threonine cross feeding and (ii) this cross-feeding is still observed when another species is introduced. However, metabolism-related genes identified among the dropped and emerging interaction-mutants indicate that many trophic interactions are also rearranged through HOIs. Genes associated with lactate catabolism (lldP and lldD) and lactate metabolism regulation (lldR) have a negative IFE in the 2-species culture with H. alvei, suggesting competition for lactate between E. coli and H. alvei. Yet, mutants of these genes are no longer associated with a significant IFE when at least another partner is introduced (Supplementary Fig. 7). Histidine biosynthesis genes hisA, hisB, hisD, hisH and hisI are associated with interaction-mutants with negative IFE in the 2-species culture with H. alvei and sometimes in the 3 species culture with H. alvei + P. camemberti. However, the negative IFE is alleviated whenever G. candidum is present, suggesting that potential competition for histidine between E. coli and H. alvei is alleviated by this fungal species (Supplementary Fig. 4). Also, genes related to the COG section “Information storage and processing” are mostly found among genes of HOIs-mutants suggesting a fine-tuning of specific cellular activity depending on the interacting condition. For instance, we identified many transcriptional regulators of central metabolism among the dropped interaction-mutants genes (rbsR and lldR) and the emerging interaction-mutants genes (purR, puuR, gcvR and mngR), highlighting again the reorganization of trophic interactions associated with HOIs. Also, many transcriptional regulators broadly associated with growth control, cell cycle and response to stress were found among the emerging interaction-mutants genes with 3-species (hyfR, chpS, sdiA, slyA and rssB), underlining a noticeable modification of E. coli’s growth environment with 3-species compare to with 2-species.Finally, we further aimed to understand whether HOIs are associated with the introduction of any specific species (Fig. 2c and Supplementary Fig. 8). We observe that interaction-associated mutants with H. alvei are more likely to be dropped, as 65% of them are alleviated by the introduction of a fungal species (Fig. 2c). This can be seen, for instance, with the reorganization of E. coli and H. alvei trophic interactions following the introduction of G. candidum (alleviation of lactate and histidine competition for instance). Also, we observe that 76% of the interactions in the 3-species cultures with H. alvei + P. camemberti and 65% in the 3-species culture with H. alvei + G. candidum are emerging interaction-mutants (compared to 38% of emerging interaction-associated mutants in the 3-species condition with G. candidum + P. camemberti) (Fig. 2c). For the interaction-associated mutans found in the 3-species with H. alvei + P. camemberti, they include for instance the genes associated with purine de novo biosynthesis (purR, purF, purN, purE, purC) and the genes associated with pyrimidine de novo biosynthesis (pyrD, pyrF, pyrC, carA and ulaD), suggesting important trophic HOIs. For the 3-species condition with H. alvei + G. candidum, emerging interaction-mutants include for example the transcriptional regulator genes chpS, sdiA and slyA, indicating the presence of a stress inducing environment. Together, these observations suggest that the introduction of a fungal partner may introduce multiple 3-species HOIs by both canceling existing interactions and introducing new ones.HOIs are prevalent in a 4-species communityTo further decipher whether microbial interactions continue to change with increasing community complexity, we investigated the changes in the genetic basis of interactions going from 3-species to 4-species experiments. We identified 58 interaction-associated mutants in the 4-species condition (E. coli with H. alvei + G. candidum + P. camemberti), compared with 145 interaction-associated mutants in any 3-species condition. Comparing the two sets of interaction-associated mutants and corresponding genes we identify: 26 3-species interaction-mutants that are maintained in the 4-species condition (including 16 directly from 2-species interactions), 115 3-species interaction-mutans that are no longer associated with interactions in the 4-species condition (dropped interaction-mutants) and 32 interaction-mutants that are observed solely in the 4-species condition (emerging interaction-mutants) (Fig. 3a, Supplementary Fig. 6 and Supplementary Data 3). Both dropped and emerging interaction-mutants represent 4-species HOIs. Here, HOIs are remarkably abundant when introducing a single new species and moving up from 3-species interactions to 4-species interactions. Functional analysis of the genes of maintained-mutants and HOI-mutants reveals the presence of many metabolism related genes in every gene set (Fig. 3), suggesting that some trophic interactions can be maintained from 3-species to 4-species interactions while some other trophic interactions are rearranged with HOIs. For instance, most of the genes of the initial steps of de novo purine biosynthesis have been found to be associated with a negative IFE in the 3 species condition with H. alvei + P. camemberti (purC, purE, purF, purL and purN) as well as in the pairwise condition with H. alvei for purH and purK (Supplementary Fig. 5), suggesting competition for purine initial precursor IMP in these conditions. Yet, the introduction of the yeast G. candidum as a fourth species cancels the negative IFE value, suggesting that the competition is no longer happening in its presence. Altogether, the observation of noticeable trophic HOIs moving up from 2 to 3 species and then from 3 to 4-species interaction highlights a consistent reorganization of trophic interactions along with community complexity. Also, genes related to Cell wall/membrane/envelope biogenesis are found abundantly among the 4-species emerging-mutants (Fig. 3b) and they represent the largest functional fraction of this gene set. These genes are associated with a negative IFE and are related to Enterobacterial Common Antigen (ECA) biosynthetic processes (wecG, wecB and wecA) (Supplementary Fig. 9). While the roles of ECA can be multiple but are not well defined22, they have been shown to be important for response to different toxic stress, suggesting the development of a specific stress in the presence of the four species.Figure 3Organization of the interactions in the 4-species community. (a) Venn Diagram of 3-species and 4-species sets of genes related to interaction-associated mutants. This Venn Diagram identifies 3-species interaction-mutants that are dropped when a fourth species is introduced (Left side; Dropped interaction-mutants = any 3-species interaction-associated mutant that is not found in the 4-species condition), 3-species interaction-mutants that are maintained in the 4-species condition (Intersection; Maintained interaction-mutants) and interaction-mutants that are specific to 4-species condition (Right side; Emerging interaction-mutants). (b) Functional analysis of the genes associated with dropped, maintained and emerging interaction-mutants from 3-species to 4-species. Each dot represents the fraction of genes of the studied gene set associated with a given COG category (Number of genes found in the category/Total number of genes in the gene set). The color of the dots indicates the general COG group of the COG category: Teal: Metabolism; Blue: Information storage and processing; Orange: Cellular Processes and Signaling; Grey: Unknown or no COG category. (c) Species-level analysis of 4-species HOIs: for each 3-species cultures we measure the fraction of interaction-genes that is conserved in the 4-species culture (Maintained in 4-species) and the fraction of interaction-genes that has been dropped (Dropped in 4-species). (d) Alluvial plots of the interaction genes across community complexity levels. (e) STRING network of the 4-species interaction genes (Nodes). Edges connecting the genes represent both functional and physical protein association and the thickness of the edges indicates the strength of data support (minimum required interaction score: 0.4—medium confidence). Nodes are colored based on the level of community complexity the genes are conserved from.Full size imageAs for the 2 to 3 species comparison, we investigated whether the introduction of a specific fourth species would be most likely associated with HOIs. The 3-species culture that appears to be the least affected by the introduction of a fourth member is with G. candidum + P. camemberti where 34% of the observed interactions are still conserved in the 4-species condition after the introduction of H. alvei (versus 22% for with H. alvei + G. candidum when P. camemberti is added and 21% for with H. alvei + P. camemberti when G. candidum is added) (Fig. 3c and Supplementary Fig. 10). Together, these observations suggest that, again, the introduction of a fungal partner may introduce multiple 4-species HOIs.Finally, by increasing the number of interacting species in our system and investigating interaction-mutants maintenance and modification with every increment of community complexity, we are able to build our understanding of the architecture of interactions in a microbial community. Altogether, we have observed a total of 218 individual interaction-associated mutants in any experiment. Only 16 of them (7%) were conserved across all levels of community complexity (Fig. 3d). Starting from 2-species interaction-mutants, 48% of them were maintained with 3-species and only 15% (16 out of 104) were still maintained with 4-species. Thus, we demonstrate here a progressive loss and replacement of 2-species interactions as community complexity increases and the prevalent apparition of HOIs. Tracking back the origins of the genetic basis of interactions in the 4-species experiment that represents the full community of our model, we identify that 28% of the full community interactions can be traced back to 2-species interactions, 18% are from 3-species interaction and 54% are specific to the 4-species interaction (Fig. 3d,e). Most of the maintained interaction-mutants from 2-species as well as from 3-species are associated with metabolism (Fig. 3d and Supplementary Fig. 11) while Signal transduction and cell membrane biosynthesis genes are most abundant among the 4-species interaction-mutants as previously mentioned. To conclude, this shows that the genetic basis of interactions and thus the sets of microbial interaction are deeply reprogrammed at every level of community complexity and illustrates the prevalence of higher order interactions (HOIs) even in simple communities.The majority of maintained 2-species interaction-mutants in the 4-species culture follows an additive conservation behaviorWhile HOIs are abundant in the 4-species condition, our data yet suggest that up to 28% of the interactions are maintained from 2-species interactions. However, we don’t know whether and how 2-species interactions are quantitatively affected by the introduction of other species and whether they would follow specific quantitative models of conservation. For instance, we can wonder how the strength of a given 2-species interaction is modified by the introduction of one or two other species, or how two 2-species interactions associated with the same gene will combine when all the species are present. In other words, can we treat species interactions as additive when we add multiple species? Such information would generate a deeper mechanistic understanding of the architecture of microbial interactions while allowing us to potentially predict some whole community interactions from 2-species interactions. Here, two main hypothetical scenarios can be anticipated. First, the conservation of 2-species interactions follows a linear or additive behavior, where the introduction of other species either doesn’t affect the strength of the conserved 2-species interaction or two similar 2-species interactions combine additively. The second scenario identifies non-linear or non-additive conservation of 2-species interactions, where the strength of the conserved 2-species interaction is modified by the introduction of other species or two similar 2-species interactions are not additive. The second scenario would encompass for instance synergistic effects or inhibitory effects following the introduction of more species. We next use an epistasis and quantitative genomics approach to understand whether interactions that are conserved follow a linear, or additive, pattern. For the 16 interaction-associated mutants that are associated with interaction in 2-species cultures, in associated 3-species cultures and in the 4-species condition, we use epistasis analysis to test the linear behavior of their IFE when the number of interacting species increases, as IFEs are quantitative traits related to the interaction strength. In multi-dimensional systems, an epistasis analysis quantifies the additive (or linear) behavior of conserved quantitative traits. In quantitative genetics, for instance, epistasis measures the quantitative difference in the effects of mutations introduced individually versus together18,23,24. Using a similar rationale, we can use IFEs as a quantitative proxy for interaction strength and test whether the IFEs of the maintained interaction genes in 3-species and in 4-species conditions result from the linear combination of associated 2-species IFEs (Fig. 4a). Nonlinear combination, or non-additivity of 2-species IFEs in higher community level also highlights higher-order interactions.Figure 4Quantitative analysis of IFE conservation for the interaction-associated mutants conserved from 2-species to 4-species conditions. (a) Schematized quantitative epistasis/non-linearity measured in 3-species conditions (with partner i and j). Epistasis (εij) is the difference between the individual IFE of partner i and partner j (red and orange bars) versus placing them together (green). Mathematically, we need three terms (IFEi, IFEj, and εij) to reproduce the observed IFE for the 3-species condition. (b) This analysis can be extended to higher levels of community complexity: 4-species (E. coli with 3-partners i, j, and k). The model first accounts for epistasis between i/j, i/k, and j/k. In this example, i and j exhibit epistasis; i/k and j/k are additive (dark blue and purple). The predicted IFE for the 4-species community is the sum of the individual 2-species effects (red, orange, light blue) and the 3-species epistatic terms (green). The 4-species epistatic coefficient is the difference between this low-order prediction and the observed IFE for the i,j,k community (pink). (c) Conservation profiles of the 16 2-species interaction-associated mutants conserved up to 4-species. 2-species conditions: a colored square indicates the 2-species condition(s) in which the interaction-associated mutant was identified; a grey square indicates non-significant 2-species IFEs. 3-species conditions: a teal square indicates that the associated IFE is associated with additive behavior from associated 2-species IFE (no εij epistatic coefficient), a red square indicates that the associated IFE displays non-additivity from 2-species IFE and thus epistasis, a grey square corresponds to a 3-species condition that is not associated with significant 2-species IFE (no epistasis analysis performed); 4-species condition: a teal square indicates that the associated IFE is associated with additive behavior (no εijk epistatic coefficient) , a red square indicates that the associated IFE is associated with non-additivity from lower-order IFE. (d) Comparison of the observed and predicted IFE for the genes and condition associated with 3-species and 4-species non-additive IFE.Full size imageWe adapted the pipeline Epistasis17, originally designed for quantitative genetics investigation. We implemented the linear model with the gene fitness values of the interaction-associated mutants for growth alone, for each of the 2-species conditions, for each of the 3-species cultures and for the 4-species condition. For each gene, the software finds the simplest mathematical model that reproduces the observed IFEs across all levels of community complexity. In the simplest case, the model will have a term describing the effects for adding each species individually to the E. coli alone culture; that term corresponds to the 2-species IFE. Then, if the IFE for two E. coli’s partners combined (3-species IFE) differs from the sum of their individual effects (corresponding 2-species IFE), the software adds a term capturing this epistasis (Fig. 4a). Here, we call that term 3-species epistatic coefficient or εi,j. Finally, if the IFE for the combined community (E. coli plus all three species; 4-species condition) differs from the prediction based on the 2-species and 3-species terms, the software will add a high-order interaction term to the model (Fig. 4b). Here, we name that term 4-species epistatic coefficient or εijk.We performed this analysis on the 16 interaction-associated mutants that are associated with interactions at every level of community complexity. To identify real additive behavior of IFE from non-additivity, we screen for 3-species epistatic coefficients and 4-species epistatic coefficients that are significantly different from 0 (adjusted p-value ≤ 0.01, Benjamini–Hochberg correction for multiple testing). We found that 13 interaction-associated mutants behaved additively from 2-species to 4-species culture, with no epistatic contributions in the 3-species conditions nor in the 4-species condition (Fig. 4c, (i)). One interaction-associated mutant (gene (gadW)) exhibited nonlinear conservation of IFE only in the 4-species condition, but additive IFE conservation from 2-species to 3-species (Fig. 4c, (ii)). Another interaction-associated mutant (gene (lsrG)) showed epistasis in one 3-species condition but no epistasis in the 4-species condition (Fig. 4c, (iii)) Finally, one interaction-associated mutant (gene (gltB)) displayed both non-additivity in 3-species and 4-species conditions (Fig. 4c, (iv)). If we look more closely at the genes related to interaction-associated mutant with an additive behavior, we find genes (betA, betT, purD and purH) that are associated with the conservation of negative IFEs (Supplementary Fig. 12). While betA and betT are associated with choline transport (betT) and glycine betaine biosynthesis from choline (betA)25, purD and purH are associated with de novo purine biosynthesis26. This suggests that requirements for glycine betaine biosynthesis from choline and for purine biosynthesis caused by microbial interactions, possibly due to competition for the nutrients used as precursors, are additively conserved from individual 2-species interactions requirements. Also, 5 genes associated with amino acid biosynthesis (serA, thrC, cysG, argG and proA) are associated with the additive conservation of positive IFE (Supplementary Fig. 12), suggesting that cross feeding can be additive when the community complexity increases. Altogether, this highlights the existence of 2-species interactions, including trophic ones, conserved in an additive fashion in the highest-level of complexity.This leaves 3 interaction-associated mutants (18%) of the maintained 2-species interaction-mutants, that are associated with non-additive behavior, and thus HOIs, at at least one higher level of community complexity (Fig. 4c—(ii), (iii) and (iv)). The interaction-associated mutant for the gene gadW is associated with non-additivity at the 4-species level, suggesting that while IFEs are additive in 3-species cultures, the introduction of a fourth species introduces HOI. Moreover, the observed 4-species IFE is greater than the IFE predicted by a linear model (Fig. 4d), highlighting a potential synergistic effect when the 4 species are together. The interaction-assoacited mutant for the gene lsrg is associated with non-additivity only at the 3-species culture w G.c + P.c. More specifically, this indicates that HOI arise when these 2 fungal species are interacting together with E. coli, but that no more HOI emerge when H. alvei is introduced (i.e., the 4-species IFE can be predicted by the linear combination of the lower levels IFEs). As the observed IFE for the 3-species condition w G.c + P.c is greater than the predicted IFE (Fig. 4c), this suggests a synergistic effect between the 2 fungal species. Finally, the interaction-associated mutants for the gene gltB is associated with non-additivity at both the 3-species and 4-species levels. For this interaction-associated mutant, the conservation of IFE is never associated with an additive model. Here, the observed 4-species IFE is not as negative as it would be as the result of the linear combination of the associated lower IFE (Fig. 4d), suggesting the existence of a possible IFE threshold, or plateau effect. Altogether, this indicates that maintained 2-species-interactions can follow nonlinear behaviors that could involve synergistic effects, inhibitory effects or constraints. More