Review Special Issues

Potential applications of plant probiotic microorganisms in agriculture and forestry

  • Agriculture producers, pushed by the need for high productivity, have stimulated the intensive use of pesticides and fertilizers. Unfortunately, negative effects on water, soil, and human and animal health have appeared as a consequence of this indiscriminate practice. Plant probiotic microorganisms (PPM), also known as bioprotectants, biocontrollers, biofertilizers, or biostimulants, are beneficial microorganisms that offer a promising alternative and reduce health and environmental problems. These microorganisms are involved in either a symbiotic or free-living association with plants and act in different ways, sometimes with specific functions, to achieve satisfactory plant development. This review deals with PPM presentation and their description and function in different applications. PPM includes the plant growth promoters (PGP) group, which contain bacteria and fungi that stimulate plant growth through different mechanisms. Soil microflora mediate many biogeochemical processes. The use of plant probiotics as an alternative soil fertilization source has been the focus of several studies; their use in agriculture improves nutrient supply and conserves field management and causes no adverse effects. The species related to organic matter and pollutant biodegradation in soil and abiotic stress tolerance are then presented. As an important way to understand not only the ecological role of PPM and their interaction with plants but also the biotechnological application of these cultures to crop management, two main approaches are elucidated: the culture-dependent approach where the microorganisms contained in the plant material are isolated by culturing and are identified by a combination of phenotypic and molecular methods; and the culture-independent approach where microorganisms are detected without cultivating them, based on extraction and analyses of DNA. These methods combine to give a thorough knowledge of the microbiology of the studied environment.

    Citation: Luciana Porto de Souza Vandenberghe, Lina Marcela Blandon Garcia, Cristine Rodrigues, Marcela Cândido Camara, Gilberto Vinícius de Melo Pereira, Juliana de Oliveira, Carlos Ricardo Soccol. Potential applications of plant probiotic microorganisms in agriculture and forestry[J]. AIMS Microbiology, 2017, 3(3): 629-648. doi: 10.3934/microbiol.2017.3.629

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  • Agriculture producers, pushed by the need for high productivity, have stimulated the intensive use of pesticides and fertilizers. Unfortunately, negative effects on water, soil, and human and animal health have appeared as a consequence of this indiscriminate practice. Plant probiotic microorganisms (PPM), also known as bioprotectants, biocontrollers, biofertilizers, or biostimulants, are beneficial microorganisms that offer a promising alternative and reduce health and environmental problems. These microorganisms are involved in either a symbiotic or free-living association with plants and act in different ways, sometimes with specific functions, to achieve satisfactory plant development. This review deals with PPM presentation and their description and function in different applications. PPM includes the plant growth promoters (PGP) group, which contain bacteria and fungi that stimulate plant growth through different mechanisms. Soil microflora mediate many biogeochemical processes. The use of plant probiotics as an alternative soil fertilization source has been the focus of several studies; their use in agriculture improves nutrient supply and conserves field management and causes no adverse effects. The species related to organic matter and pollutant biodegradation in soil and abiotic stress tolerance are then presented. As an important way to understand not only the ecological role of PPM and their interaction with plants but also the biotechnological application of these cultures to crop management, two main approaches are elucidated: the culture-dependent approach where the microorganisms contained in the plant material are isolated by culturing and are identified by a combination of phenotypic and molecular methods; and the culture-independent approach where microorganisms are detected without cultivating them, based on extraction and analyses of DNA. These methods combine to give a thorough knowledge of the microbiology of the studied environment.


    Described for the first time by Monod [1], the diauxic growth consists in a biphasic growth in a bacterial population consuming two different sugars in a closed medium. The corresponding curve of biomass density at the macroscopic scale shows two distinct exponential phases separated by a "plateau" called lag-phase (Figure 1). The explanation proposed by Monod is that the preferred sugar (which is in some sense "easier" to metabolize) is consumed first while the metabolic pathway allowing the consumption of the second one is suppressed. When the concentration of the first sugar becomes low enough, this repression is lifted. Then, the microorganism may produce the enzymes necessary to metabolize the second sugar: This is the lag-phase. The second exponential growth is observed until the second sugar is eventually consumed.

    Figure 1.  Growth of Escherichia coli in the presence of different carbohydrate pairs serving as the only source of carbon in a synthetic medium [1].

    Until recently, it was admitted that the explanation given above was homogeneous within the cell population in the sense that each individual adopted exactly the same behavior at the same time: Each cell first consumed the sugar that was "easiest to metabolize" first, then the other one after a duration corresponding to the lag-phase. Such an assertion implies that the latency time would simply be a constant depending only on the sugars involved. In order to better understand this phenomenon and test hypotheses, many models of diauxic growth have been proposed in the literature [2,3,4]. All such models have in common to make the hypothesis that each cell of the microorganism under consideration exhibits the same behavior with respect to both substrates at a given time. In addition, most approaches make use of deterministic models that are not suited for low biomass densities.

    However, recent investigations suggest that lag phases are controlled by the inoculum history and organized with heterogeneity among individual cells [5]. This fact was called "metabolic heterogeneity". Takhaveev and Heinemann [6] suggested that this heterogeneity could be induced by mechanisms linked to ecological factors, gene expression, and other inherent dynamics, or by interaction between individuals, which all also depend on environment changes.

    In this paper, following the idea that there is an intrinsic heterogeneity of cells within the ecosystem—which yields a metabolic heterogeneity—we develop a stochastic model of diauxic growth. More precisely, we propose a model of a batch culture of a pure strain growing on two different sugars. In this model, the metabolic heterogeneity is modeled via the possible emergence of a subpopulation that consumes the second sugar while the first one is not yet totally consumed. In other words, all cells do not exhibit the same behavior with respect to each substrate at a given time. To be as close as possible to the observations, the model accounts for the fact that in such situations the acetate produced—which is a growth-inhibiting metabolite—is co-consumed by each cell, as shown by Enjalbert et al. [7]. One goal of this work is to link both stochastic and deterministic approaches in order to explain the observations available at different scales, and to study the main parameters that control the length of the lag-phase.

    The paper is organized as follows. First, the stochastic model is presented. Secondly, its behavior for large populations is approximated, allowing us to write a model consisting in a set of deterministic differential equations. Then, the model is used to investigate the role of a number of model parameters and of initial conditions on the substrate consumption dynamics and on the length of the lag-phases. Eventually the main conclusions and perspectives are drawn. An appendix provides some additional information on proofs and simulations.

    First and foremost, let us introduce the parameter K>0 that scales the initial number of individuals. Indeed, the population size varies widely between different kinds of bacterial cultures, and may range from a few individuals in microfluidics (then K is very small) to billions or more in fermenters (then K is very large). Letting K increase to infinity allows to make the link between the stochastic model and the deterministic limit model for large populations

    Let us consider two different substrates, Sugar 1 which is preferential and Sugar 2, and a stochastically described population of bacteria split into two compartments constituted respectively of Sugar 1 consumers and of Sugar 2 consumers. Let NK1(t) and NK2(t) denote respectively the numbers of individuals in each compartment and

    NK(t)=(NK1(t),NK2(t)),t0.

    Here we are introducing the specific scaling in which K can be seen as proportional to the carrying capacity of the medium and 1/K as proportional to the individual biomass, and in order to capture the two subpopulation densities per unit of volume we introduce the rescaling

    nK(t)=(nK1(t),nK2(t))=(NK1(t)VK,NK2(t)VK),t0.

    The mass concentration of each sugar is described by a continuous process

    RK(t)=(RK1(t),RK2(t)),t0,

    which corresponds in the same order to Sugar 1 and Sugar 2. We also take into account the mass concentration AK(t) of a metabolite produced during the consumption of sugars by each individual and co-consumed with them. As an illustration, we may consider a mixed medium with glucose and xylose as Sugar 1 and Sugar 2, and acetate as the metabolite: Sugars are consumed sequentially, and when the preferential sugar glucose is abundant the xylose consumers switch to consume it; the reverse transition is more complex and requires that an activated xylR protein binds to the DNA of each switching individual. The activation of this protein is caused by the presence of xylose but inhibited by glucose due to the catabolic repression.

    We describe the complete culture medium by the Markov process

    (nK(t),RK(t),AK(t))t0=(nK1(t),nK2(t),RK1(t),RK2(t),AK(t))t0 (2.1)

    evolving as follows.

    Demography. An individual growing on Sugar 1 divides at rate b1(RK1(t),AK(t)) due to Sugar 1 and metabolite co-consumption. Likewise, an individual growing on Sugar 2 divides at rate b2(RK2(t),AK(t)) due to Sugar 2 and metabolite co-consumption. This results in the jumps transitions

    n1n1+1VKat rateb1(RK1(t),AK(t))VKn1,n2n2+1VKat rateb2(RK2(t),AK(t))VKn2. (2.2)

    State transitions. An individual growing on Sugar 1 switches its state in order to consume Sugar 2 at rate η1(RK(t)), which depends on both resources since this is inhibited by the catabolic repression due to Sugar 1, the preferential sugar. Likewise, an individual growing on Sugar 2 switches its metabolic state to consume Sugar 1 at rate η2(RK1(t)) which depends only on the abundance of Sugar 1. This results in the jumps transitions

    (n1,n2)(n11VK,n2+1VK)at rateη1(RK(t))VKn1,(n1,n2)(n1+1VK,n21VK)at rateη2(RK1(t))VKn2. (2.3)

    Resource dynamics. These are linked to the biomass and metabolite synthesis by the biochemical reactions that happen continuously inside the batch. An individual growing on Sugar 1 consumes a small amount μ1(RK1(t),AK(t))/q1K of Sugar 1 and produces a small amount θ1μ1(RK1(t),AK(t))/K of metabolite per unit of time, before dividing as a result of this consumption. Similarly, an individual growing on Sugar 2 consumes a small amount μ2(RK2(t),AK(t))/q2K of Sugar 2 and produces a small amount θ2μ2(RK2(t),AK(t))/K of metabolite per unit of time, before dividing as a result of this consumption. Note that it could happen that the metabolite inhibits the consumption of sugars as is the case for acetate in glucose-xylose consumption, see Enjalbert et al. [7]. Finally, each individual consumes a small amount μ3(AK(t))/q3K of metabolite per unit of time by a separate independent pathway before dividing as a result of this consumption. This leads us to describe the resource dynamics by the dynamical system

    {dRK1dt(t)=μ1(RK1(t),AK(t))q1nK1(t),dRK2dt(t)=μ2(RK2(t),AK(t))q2nK2(t),dAKdt(t)=μ3(AK(t))q3(nK1(t)+nK2(t))+θ1μ1(RK1(t),AK(t))nK1(t)+θ2μ2(RK2(t),AK(t))nK2(t). (2.4)

    The typical situation we will consider is the following. The initial conditions satisfy

    nK(0)=(n01VKVK,n02VKVK),RK(0)=r0,AK(0)=0,

    in which (n0,r0)=(n01,n02,r01,r02) is fixed. The above rate functions involve Monod-type and classic inhibition functions and are of the forms

    μj(rj,a)=ˉμjrjκj+rjλλ+a,j=1,2,μ3(a)=ˉμ3aκ3+aλλ+a,η1(r)=ˉη1r2k1+r2kiki+r1,η2(r1)=ˉη2r1k2+r1.

    Note that the terms of inhibition (due to the metabolite on each growth rate, and due to Sugar 1 on the switching rate) and their incidence are antagonistic. Indeed, decreasing any of the coefficients λ and ki increase the repression on the corresponding mechanisms. In addition, since the sugars and the metabolite are co-consumed by independent pathways, the birth rates defined in the transitions (2.2) chosen as

    bj(rj,a)=μj(rj,a)+μ3(a),j=1,2, (2.5)

    ensure a conservation law on average:

    E{nK1(t)+nK2(t)+q1(1+θ1q3)RK1(t)+q2(1+θ2q3)RK2(t)+q3AK(t)}=Cst. (2.6)

    To illustrate this model, we use the parameters described in Table 1 taken from recent batch experiments [8] for the sugars glucose and xylose.

    Table 1.  Parameters for the rate functions in the example.
    Parameter Biological signification Default value for simulations Units
    ˉμ1 Maximal growth rate on Sugar 1 6.50e-01 h1
    κ1 Monod constant on Sugar 1 3.26e-01 g/L
    λ Inhibition coefficient due to the metabolite 4.70e-01 g/L
    ˉμ2 Maximal growth rate on Sugar 2 5.70e-01 h1
    κ2 Monod constant on Sugar 2 4.68e-01 g/L
    ˉμ3 Maximal growth rate on the metabolite 1.47e-01 h1
    κ3 Monod constant on the metabolite 6.45e-01 g/L
    ˉη1 Maximal switching rate from Sugar 1 to Sugar 2 2.04e-03 h1
    k1 Regulation coefficient of the Sugar 1 to Sugar 2 transition 1.20e-02 g/L
    ki Inhibition coefficient of the Sugar 1 to Sugar 2 transition 1.03e-03 g/L
    ˉη2 Maximal switching rate from Sugar 2 to Sugar 1 6.60e-01 h1
    k2 Regulation coefficient of the Sugar 2 to Sugar 1 transition 4.50e-02 g/L
    q1 Individual yield on Sugar1 5.50e-01 gbiomass/gsubstrate
    θ1 Metabolite yield on Sugar1 6.00e-01 gsubstrate/gbiomass
    q2 Individual yield on Sugar2 4.50e-01 gbiomass/gsubstrate
    θ2 Metabolite yield on Sugar2 5.60e-01 gsubstrate/gbiomass
    q3 Individual yield on the metabolite 2.50e-01 gbiomass/gsubstrate

     | Show Table
    DownLoad: CSV

    The subpopulation densities per unit of volume (or biomass concentrations) and the resources mass concentrations are expressed in g/L. For the typical case that will be illustrated in simulations, the volume is one liter and the default initial conditions are given by

    n0=(0.28,0.0),r0=(8.15,9.05).

    Figure 2 shows that this model is able to predict the diauxic growth observed by Monod (Figure 1). This can be observed even for a small number of individuals. We additionally observe that the trajectories oscillate randomly for small K and become smoother as K becomes larger. This observation will be developed in the next section, in which the stochastic model will be shown to be approximated by a deterministic model when K increases to infinity.

    Figure 2.  Total population and resource concentrations for a small (K=10) and a moderately large (K=1000) population.

    The amplitude of any jump occurring in the population is bounded by a factor of the weight 1/K attributed to a single individual and hence has a variance of order 1/K2. Moreover, the mean number of jumps per unit of time is of order K, the order of magnitude of the number of individuals. Heuristically, for a large population the process should approach a limit deterministic continuous process dictated by the mean values, with random oscillations around this limit corresponding to variances of order 1/K and hence to standard deviations of order 1/K. We can build on these heuristics and prove that the stochastic model is indeed approximated by a deterministic model in the limit of large K. This yields the following deterministic limit.

    Theorem 3.1. Let us assume that

    ε>0,P((nK(0),RK(0),AK(0))(n0,r0,a0)>ε)K0,

    and that supKE((nK(0),RK(0),AK(0)))<+. Let (n(t),r(t),a(t))t0 be the unique solution with initial condition (n0,r0,a0) of the differential system\\

    {n1(t)={b1(r1(t),a(t))η1(r(t))}n1(t)+η2(r1(t))n2(t),n2(t)={b2(r2(t),a(t))η2(r1(t))}n2(t)+η1(r(t))n1(t),r1(t)=μ1(r1(t),a(t))q1n1(t),r2(t)=μ2(r2(t),a(t))q2n2(t),a(t)=μ3(a(t))q3(n1(t)+n2(t))+θ1μ1(r1(t),a(t))n1(t)+θ2μ2(r2(t),a(t))n2(t). (3.1)

    Then the stochastic process (nK(t),RK(t),AK(t))t0 is approximated for large K by (n(t),r(t),a(t))t0 in the sense that

    T>0,ε>0,P(sup0tT(nK(t),RK(t),AK(t))(n(t),r(t),a(t))>ε)K0.

    This theorem allows to explain on a rigorous basis the observations we have made on the simulations in the previous section. Before discussing the proof methods, let us address the important question of the range of validity of the approximation.

    For small K and most notably for populations consisting of a few individuals, the deterministic system is not a good approximation of the stochastic model and does not provide a pertinent model for the population. On the contrary, when K is large enough for the approximation to be accurate, the deterministic system provides a pertinent model on which theoretical studies and numerical computations can be performed for qualitative and quantitative investigations on the population.

    Therefore, it is fundamental to obtain a precise evaluation of the size of K required for the approximation to be tight and to assess the error made in terms of K. The heuristics given before the theorem indicate that that the error terms should be of order 1/K. Under adequate assumptions on the initial conditions, this can be made rigorous through a functional central limit theorem: The process

    K((nK(t),RK(t),AK(t))(n(t),r(t),a(t))),t0,

    converges as K goes to infinity to a Gaussian process of Ornstein-Uhlenbeck type, with mean and covariance structure expressed solely in terms of the limit process (n(t),r(t),a(t))t0 and of the variance of the jumps in a sufficiently explicit fashion to be well evaluated. This allows to evaluate the minimal size of K required for a tight approximation and to provide confidence intervals on this, as well as the possibility for intermediate sizes of K to simulate the deterministic limit process and add to it fluctuations simulated according to this Gaussian process in order to obtain a tighter approximation.

    The proofs of Theorem 3.1 and of the functional central limit theorem build on the heuristic explanation given before the theorem using probabilistic compactness-uniqueness methods. Ethier and Kurtz [9] is a classic book on the subject, and Anderson and Kurtz [10] and Bansaye and Méléard [11] provide pedagogical expositions well suited to the present field of application.

    We illustrate these convergence results in Figure 3, by the simulations of a hundred trajectories of the total biomass for the stochastic and the limiting model, for three increasing values of the scale parameter K.

    Figure 3.  Ten independent stochastic trajectories, the empirical mean over a hundred independent trajectories, and the deterministic limit simulated for each of the total populations in the cases K=10, K=100, and K=1000.

    As shown in Figure 4, the model is able to capture the heterogeneity of the population observed by biologists as well as the diauxic growth at the level of the total population size highlighted by Monod.

    Figure 4.  Metabolic Heterogeneity. Diauxic growth of the total population and growths of the subpopulations for a simulation of the stochastic model with K=100 (left) and of the deterministic limit (right). The evolutions of the two resources are plotted for each.

    Furthermore, we are interested in how the metabolic parameters and initial conditions can influence the length of the lag-phase in the deterministic model. We perform a sensitivity analysis by considering an approximation of the lag duration defined as the time elapsed between the instant when the intake of preferential sugar and metabolite reaches a minimum threshold ϵ1>0, and the instant when a new phase of population growth is detected beyond another thresold ϵ2>0. Note that as in Eq (2.6) for the birth rate (2.5) in the stochastic model, we have the following conservation law for the deterministic limit

    n1(t)+n2(t)+q1(1+θ1q3)r1(t)+q2(1+θ2q3)r2(t)+q3r3(t)=Cst. (4.1)

    Then, since Sugar 2 is almost constant during the lag-phase, the intake of the preferred sugar and metabolite is proportional to the quantity

    q1(1+θ1q3)r1(t)+q3r3(t).

    We then set

    τϵ=tϵ1,ϵ2tϵ1 (4.2)

    where

    tϵ1=inf{t0:q1(1+θ1q3)r1(t)+q3r3(t)ϵ1},tϵ1,ϵ2=inf{ttϵ1:n1(t)+n2(t)n1(tϵ1)+n2(tϵ1)+ϵ2}.

    For all simulations of the deterministic model, we use the classical Runge-Kutta numerical scheme of order 4. Figure 5 illustrates this construction of the interval [tϵ1,tϵ1,ϵ2] approximating the lag phase.

    Figure 5.  Approximation of the lag-phase during the diauxic growth by the interval [tϵ1,tϵ1,ϵ2] delimited by the blue dashed lines, for ϵ1=0.07 and ϵ2=0.10.

    We present several simulations in which we vary the values of the maximal switching rate ˉη1, the inhibition coefficient ki and the initial conditions in different intervals and plot the corresponding lag duration approximation. Figure 6 reveals that as the switching rate ˉη1 increases, the lag phase become considerably shorter. This is particularly noticeable for small values of this parameter. This is also the case for the inhibition coefficient ki that affects the lag phase considerably for small values. Hence, the lag phase sensitivity is significant for strong inhibition. Finally, we consider varied initial conditions for the subpopulations which all have the same total population size, and observe that the lag phase duration seems to be well correlated to the initial proportion of sugar1 consumers. This situation is interesting in order to understand how the transplantation from a first culture medium to another could affect the lag.

    Figure 6.  Effects of changes in the switch parameter ˉη1 (left), in the inhibition coefficient ki (center) and in the initial population (right) on the lag phase duration. In this last figure, the initial population is assumed to be (n1(0),n2(0))=(δw,(1δ)w) with w=0.28.

    In this paper, we proposed a stochastic model of diauxic growth of a microorganism on two different sugars. The model assumes that the individuals preferentially consume one of the sugars while the metabolic pathway allowing the consumption of the second one is repressed until the first sugar is exhausted. To account for the fact that all individual do not behave homogeneously with respect to the consumption of sugars—which is called metabolic heterogeneity—it is supposed that some individuals can switch their metabolism in such a way they can consume the second sugar while the first one is not totally exhausted. Thus the model involves two different subpopulations: the first one which grows on the first sugar, and the second one, which emerges from the first subpopulation and consumes the second sugar. In addition, three resource variables with continuous dynamics are added: The two sugars, and the intermediate metabolite which is produced when the sugars are consumed and then re-consumed by both subpopulations. Then, the deterministic model that approximates the stochastic model dynamics is derived using a large population approximation. Using parameter values that are supposed to be close to those we can find in real experiments, for instance when Escherichia coli grows on both glucose (the preferential sugar) and xylose, we performed a number of simulations in order to investigate the influence of the most important parameters on the model dynamics. Further, we show the importance of the weighting factor K, which allows us to understand what is the population size starting from which the deterministic model can be used to approximate the stochastic model dynamics. Finally, it is shown that several parameters, such as the maximal switching rate ˉη1 from Sugar 1 to Sugar 2 consumption and the inhibition coefficient ki of the Sugar 1 to Sugar 2 transition, as well as the initial conditions of the system significantly influence the lag-phase, allowing us to pave the way and to suggest strategies to minimize the lag-phase in practical experiments.

    We warmly thank our biologist colleagues Manon Barthe, Muriel Cocaign and Brice Enjalbert who have brought this problem to our attention and shared fruitful discussions with us. This work has been supported by the Chair "Modélisation Mathématique et Biodiversité" of Veolia Environnement-École Polytechnique-Muséum national d'Histoire naturelle-Fondation X and by the ANR project JANUS (ANR-19-CE43-0004-01).

    The authors declare no conflict of interest.

    A.1. Proof of main results

    Let us comment the proof of Theorem 3.1 which can easily adapted from the results in [9,10,11]. Let us firstly note that we can express the stochastic process (nK(t),RK(t))t0 as

    nK1(t)=nK1(0)+MK1(t)+t0({b1(RK1(s),AK(s))η1(RK(s))}nK1(s)+η2(RK1(s))nK2(s))ds,nK2(t)=nK2(0)+MK2(t)+t0({b2(RK2(s),AK(s))η2(RK1(s))}nK2(s)+η1(RK(s))nK1(s))ds,

    where the processes MK1 and MK2 are square integrable martingales such that

    E((MK1(t))2)=1VKt0({b1(RK1(s),AK(s))+η1(RK(s))}nK1(s)+η2(RK1(s))nK2(s))ds,E((MK2(t))2)=1VKt0({b2(RK2(s),AK(s))+η2(RK1(s))}nK2(s)+η1(RK(s))nK1(s))ds,E(MK1(t)MK2(t))=1VKt0(η1(RK(s))nK1(s)+η2(RK1(s))nK2(s))ds. (A.1)

    The proof firstly consists in showing that the sequence of laws of the stochastic processes (nK(t),RK(t),AK(t),t0)K is relatively compact. It is based on 2-moments estimates, uniform on finite time intervals and on K and on a well known criterion of uniform tightness (cf. for example [11]). Then there exists at least one limiting probability measure (on the path space). Using the fact that the jump amplitudes are going to 0 when K tends to infinity, uniformly on finite time intervals, we deduce that these probability measures only charge continuous trajectories. Moreover, the moment estimates and Eq (A.1) allow to prove that the martingale part converges in probability to 0 when K tends to infinity. Therefore, it is easy to deduce that the limiting probability measures only charge the solutions of the dynamical system (3.1). The last step consists in proving the uniqueness of such a solution, which is due to a Cauchy-Lipschitz Theorem.

    A.2. Numerical simulations

    In order to simulate the Markov process (XK(t))t0=(nK(t),RK(t),AK(t))t0 defined in Eq (2.1) for various sets of parameters, we propose an algorithm simulating numerically the differential system satisfied by the resources in between the jump instants, while the jump instants and the jump amplitudes are simulated directly in terms of the past. The ideas are based on first principles according to the Markov property.

    The jump structure of (XK(t))t0 can be described locally at each state x by the value α(x)0 of a jump rate function α and if α(x)>0 by a probability measure π(x,dh) for drawing the amplitudes of the jumps. More precisely, there are overall p1 possible non-null jump amplitudes h1,,hp, taken at each state x=(n,r,a) at respective rates α1(x)0,,αp(x)0, and

    α(x)=pi=1αi(x),π(x,hi)=αi(x)α(x),i=1,,p.

    The strong Markov property yields interesting consequences for the construction of the process. The future of the process after each jump is independent from its past given the new state. Thus, in order to construct the process it is sufficient to be able to do so from time 0 until the first jump instant, and then iterate the procedure by considering each jump instant as a new time origin. Moreover, starting at time 0 the probability that the process (XK(t))t0 has not jumped yet at time t>0 is given in terms of the rate function α by

    exp(t0α(XK(s))ds).

    This allows to construct the first jump instant as follows. If the non-decreasing continuous process (Λ(t))t0 and its left-continuous inverse (Λ1(t))t0 are defined by

    Λ(t)=t0α(XK(s))ds,Λ1(t)=inf{u0:Λ(u)t}, (A.2)

    and D is an exponential random variable of parameter 1, then

    P(Λ1(D)>t)=P(D>t0α(XK(s))ds)=exp(t0α(XK(s))ds).

    Hence, we can simulate the first jump instant T1 of the process by taking T1=Λ1(D) while simultaneously constructing the process on [0,T1). If XK(T1)=x then XK(T1)=x+h for a jump amplitude h drawn according to π(x,dh).

    Using this construction directly for an actual simulation raises several issues.

    The first problem is that we must be able to simulate the process (XK(t))t0 up to the first jump instant. In the present situation this consists in simulating the components (RK(t),AK(t))t0 of the Markov process (2.1) by solving the differential system (2.4) in which the other components of (2.1) remain constant between jumps. This cannot be done exactly but can be approximated numerically quickly and with precision.

    The second problem is that simultaneously to (RK(t),AK(t))t0 we must be able to compute the integral Λ(t) and its inverse Λ1(t) defined in Eq (A.2). This can be done numerically but is often costly in computer time and inefficient. This has a practical solution which we proceed to describe. We introduce a function ˜α such that α˜α and that the corresponding ˜Λ and that ˜Λ1 defined similarly to Eq (A.2) are simpler to compute than Λ and Λ1. We simulate the process (XK(t))t0 by an acceptance-rejection method which proposes a jump from state x at rate ˜α(x) and accepts it with probability α(x)/˜α(x) and else rejects it. There are various ways to justify that this construction is correct. One of these is to consider the rejection as the introduction of a jump of amplitude 0 taken at the excessive rate ˜α(x)α(x) (the process does not actually jump, and this is called a "fictitious jump") and reason as above. The simplest situation is when the dominating function ˜α is a constant. Then the true jump instants of (XK(t))t0 constitute a thinning of a Poisson process of constant intensity ˜α, which can be easily simulated, in which a jump instant of this Poisson process taken when XK(T1)=x is accepted with probability α(x)/˜α(x).

    Let us come back to our model and denote by L(XK(0)) the distribution of the initial random vector XK(0), by E(λ) the exponential law with parameter λ>0 and by U([0,1]) the uniform law on~[0,1]. If we moreover denote by (ϕ(x,tt0))tt0 the flow of the process (XK(t))t0 from an initial condition XK(t0)=x until the next jump time, the above description can be summarized in the following algorithm.

    Algorithm:

    Simulate x0L(XK(0))

    T00;

    k0;

    Repeat

      Simulate ϵk+1E(˜α(xk));

      Tk+1Tk+ϵk+1;

      Follow the flow (ϕ(xk,tTk))tTk for resources, until the moment Tk+1T;

      xk+1ϕ(xk,Tk+1TTk);

      If Tk+1<T, then

       Simulate U2kU([0,1]);

       If U2k˜α(xk+1)α(xk+1), then

        i1;

        Simulate U2k+1U([0,1]);

        sα1(xk+1);

        While i<p and U2k+1α(xk+1)>s, do

          ii+1;

          ss+αi(xk+1);

        End_While.

        xk+1xk+1+hi;

       End_If.

      End_If.

      kk+1;

    Until TkT.

    [1] Picard C, Baruffa E, Bosco M (2008) Enrichment and diversity of plant-probiotic microorganisms in the rhizosphere of hybrid maize during four growth cycles. Soil Biol Biochem 40: 106–115. doi: 10.1016/j.soilbio.2007.07.011
    [2] Benrebah F, Prevost D, Yezza A, et al. (2007) Agro-industrial waste materials and wastewater sludge for rhizobial inoculant production: A review. Bioresour Technol 98: 3535–3546. doi: 10.1016/j.biortech.2006.11.066
    [3] Mayak S, Tirosh T, Glick BR (2004) Plant growth-promoting bacteria confer resistance in tomato plants to salt stress. Plant Physiol Biochem 42: 565–572. doi: 10.1016/j.plaphy.2004.05.009
    [4] Singh JS, Pandey VC, Singh DP (2011) Efficient soil microorganisms: A new dimension for sustainable agriculture and environmental development. Agric Ecosyst Environ 140: 339–353. doi: 10.1016/j.agee.2011.01.017
    [5] Gomez CG, Valero NV, Brigard RC (2012) Halotolerant/alkalophilic bacteria associated with the cyanobacterium Arthrospira platensis (Nordstedt) Gomont that promote early growth in Sorghum bicolor (L.). Moench Agron Colomb 30: 111–115.
    [6] Yang J, Kloepper JW, Ryu CM (2009) Rhizosphere bacteria help plants tolerate abiotic stress. Trends Plant Sci 14: 1–4. doi: 10.1016/j.tplants.2008.10.004
    [7] Bhattacharyya D, Yu SM, Lee YH (2015) Volatile compounds from Alcaligenes faecalis JBCS1294 confer salt tolerance in Arabidopsis thaliana through the auxin and gibberellin pathways and differential modulation of gene expression in root and shoot tissues. Plant Growth Regul 75: 297–306. doi: 10.1007/s10725-014-9953-5
    [8] Zhang Z, Lin W, Yang Y, et al. (2011) Effects of consecutively monocultured Rehmannia glutinosa L. on diversity of fungal community in rhizospheric soil. Agric Sci China 10: 1374–1384.
    [9] Zhang H, Kim MS, Sun Y, et al. (2008) Soil bacteria confer plant salt tolerance by tissue-specific regulation of the sodium transporter HKT1. Mol Plant Microbe In 21: 737–744.
    [10] Porcel R, Zamarreño Á, García-Mina J, et al. (2014) Involvement of plant endogenous ABA in Bacillus megaterium PGPR activity in tomato plants. BMC Plant Biol 14: 36. doi: 10.1186/1471-2229-14-36
    [11] Tsuda K, Tsuji G, Higashiyama M, et al. (2016) Biological control of bacterial soft rot in Chinese cabbage by Lactobacillus plantarum strain BY under field conditions. Biol Control 100: 63–69. doi: 10.1016/j.biocontrol.2016.05.010
    [12] Waqas M, Khan AL, Kamran M, et al. (2012) Endophytic fungi produce gibberellins and indoleacetic acid and promotes host-plant growth during stress. Molecules 17: 10754–10773. doi: 10.3390/molecules170910754
    [13] Khan AL, Hamayun M, Ahmad N, et al. (2011) Exophiala sp. LHL08 reprograms Cucumis sativus to higher growth under abiotic stresses. Physiol Plant 143: 329–343.
    [14] Khan AL, Hamayun M, Ahmad N, et al. (2011) Salinity stress resistance offered by endophytic fungal interaction between Penicillium minioluteum LHL09 and glycine max. L. J Microbiol Biotechnol 21: 893–902. doi: 10.4014/jmb.1103.03012
    [15] De Palma M, D'Agostino N, Proietti S, et al. (2016) Suppression Subtractive Hybridization analysis provides new insights into the tomato (Solanum lycopersicum L.) response to the plant probiotic microorganism Trichoderma longibrachiatum MK1. J Plant Physiol 190: 79–94.
    [16] Qin Y, Druzhinina IS, Pan X, et al. (2016) Microbially mediated plant salt tolerance and microbiome-based solutions for saline agriculture. Biotechnol Adv 34: 1245–1259. doi: 10.1016/j.biotechadv.2016.08.005
    [17] Upadhyay SK, Singh JS, Saxena AK, et al. (2012) Impact of PGPR inoculation on growth and antioxidant status of wheat under saline conditions. Plant Biol 14: 605–611. doi: 10.1111/j.1438-8677.2011.00533.x
    [18] Redman RS, Kim YO, Woodward CJDA, et al. (2011) Increased fitness of rice plants to abiotic stress via habitat adapted symbiosis: A strategy for mitigating impacts of climate change. PLoS One 6: e14823. doi: 10.1371/journal.pone.0014823
    [19] Belimov AA, Dodd IC, Safronova VI, et al. (2014) Abscisic acid metabolizing rhizobacteria decrease ABA concentrations in planta and alter plant growth. Plant Physiol Biochem 74: 84–91. doi: 10.1016/j.plaphy.2013.10.032
    [20] Banaei-Asl F, Bandehagh A, Uliaei ED, et al. (2015) Proteomic analysis of canola root inoculated with bacteria under salt stress. J Proteomics 124: 88–111. doi: 10.1016/j.jprot.2015.04.009
    [21] Melnick RL, Zidack NK, Bailey BA, et al. (2008) Bacterial endophytes: Bacillus spp. from annual crops as potential biological control agents of black pod rot of cacao. Biological Control 46: 46–56.
    [22] Strobel GA (2002) Rainforest endophytes and bioactive products. Crit Rev Biotechnol 22: 315–333. doi: 10.1080/07388550290789531
    [23] Shoresh M, Yedidia I, Chet I (2005) Involvement of jasmonic acid/ethylenesignaling pathway in the systemic resistance induced in cucumber by Trichoderma asperellum T203. Phytopathology 95: 76–84. doi: 10.1094/PHYTO-95-0076
    [24] Glick BR (2015) Beneficial Plant-Bacterial Interactions, Heidelberg: Springer, 243.
    [25] Santoyo G, Moreno-Hagelsieb G, Del COM, et al. (2016) Plant growth-promoting bacterial endophytes. Microbiol Res 183: 92–99. doi: 10.1016/j.micres.2015.11.008
    [26] Cerozi BDS, Fitzsimmons K (2016) Use of Bacillus spp. to enhance phosphorus vailability and serve as a plant growth promoter in aquaponics systems. Sci Hortic -Amsterdam 211: 277–282.
    [27] Vinale F, Sivasithamparam K, Ghisalberti EL, et al. (2008) A novel role for Trichoderma secondary metabolites in the interactions with plants. Physiol Mol Plant P 72: 80–86. doi: 10.1016/j.pmpp.2008.05.005
    [28] Larsen J, Pineda-Sánchez H, Delgado-Arellano I, et al. (2017) Interactions between microbial plant growth promoters and their effects on maize growth performance in different mineral and organic fertilization scenarios. Rhizosphere 3: 75–81. doi: 10.1016/j.rhisph.2017.01.003
    [29] Kuklinsky-Sobral J, Araújo WL, Mendes R, et al. (2004) Isolation and characterization of soybean-associated bacteria and their potential for plant growth promotion. Environ Microbiol 6: 1244–1251. doi: 10.1111/j.1462-2920.2004.00658.x
    [30] Meng Q, Jiang H, Hao JJ (2016) Effects of Bacillus velezensis strain BAC03 in promoting plant growth. Biol Control 98: 18–26. doi: 10.1016/j.biocontrol.2016.03.010
    [31] Cohen AC, Travaglia CN, Bottini R, et al. (2009) Participation of abscisic acid and gibberellins produced by endophytic Azospirillum in the alleviation of drought effects in maize. Botany 87: 455–462. doi: 10.1139/B09-023
    [32] Silva HSA, Tozzi JPL, Terrasan CRF, et al. (2012) Endophytic microorganisms from coffee tissues as plant growth promoters and biocontrol agents of coffee leaf rust. Biol Control 63: 62–67. doi: 10.1016/j.biocontrol.2012.06.005
    [33] Miransari M (2010) Current research, technology and education topics in applied microbiology and microbial biotechnology, In: Microbiology Book Series-2010 Edition, Spain.
    [34] Vessey JK (2003) Plant growth promoting rhizobacteria as biofertilizers. Plant Soil 255: 571–586. doi: 10.1023/A:1026037216893
    [35] Richardson AE, Barea JM, Mcneill AM, et al. (2009) Acquisition of phosphorus and nitrogen in the rhizosphere and plant growth promotion by microorganisms. Plant Soil 321: 305–339. doi: 10.1007/s11104-009-9895-2
    [36] Rodriguez H, Fraga R (1999) Phosphate solubilizing bacteria and their role in plant growth promotion. Biotechnol Adv 17: 319–339. doi: 10.1016/S0734-9750(99)00014-2
    [37] Sturz AV, Nowak J (2000) Endophytic communities of rhizobacteria and the strategies required to create yield enhancing associations with crops. Appl Soil Ecol 15: 183–190. doi: 10.1016/S0929-1393(00)00094-9
    [38] Sudhakar P, Chattopadhyay GN, Gangwar SK, et al. (2000) Effect of foliar application of Azotobacter, Azospirillum and Beijerinckia on leaf yield and quality of mulberry (Morus alba). J Agric Sci 134: 227–234. doi: 10.1017/S0021859699007376
    [39] Karlidag H, Esitken A, Turan M, et al. (2007) Effects of root inoculation of plant growth promoting rhizobacteria (PGPR) on yield, growth and nutrient element contents of leaves of apple. Sci Hortic-Amsterdam 114: 16–20. doi: 10.1016/j.scienta.2007.04.013
    [40] Ilyas N, Bano A (2012) Potencial use of soil microbial community in agriculture, In: Bacteria in Agrobiology: Plant Probiotics, 1 Eds., Berlin: Springer Berlin Heidelberg, 45–64.
    [41] Glick BR (2012) Plant growth-promoting bacteria: mechanisms and applications. Scientifica.
    [42] Glick BR (2014) Bacteria with ACC deaminase can promote plant growth and help to feed the world. Microbiol Res 169: 30–39. doi: 10.1016/j.micres.2013.09.009
    [43] Brígido C, Glick BB, Oliveira S (2017) Survey of plant growth-promoting mechanisms in native Portuguese Chickpea Mesorhizobium isolates. Microbial Ecol 73: 900–915. doi: 10.1007/s00248-016-0891-9
    [44] Bhattacharyya PN, Jha DK (2012) Plant growth-promoting rhizobacteria (PGPR): emergence in agriculture. World J Microb Biotechnol 28: 1327–1350. doi: 10.1007/s11274-011-0979-9
    [45] Gray EJ, Smith DL (2005) Intracellular and extracellular PGPR: commonalities and distinctions in the plant-bacterium signaling processes. Soil Biol Biochem 37: 395–412. doi: 10.1016/j.soilbio.2004.08.030
    [46] Figueiredo MVB, Martinez CR, Burity HA, et al. (2008) Plant growth-promoting rhizobacteria for improving nodulation and nitrogen fixation in the common bean (Phaseolus vulgaris L.). World J Microb Biotechnol 24: 1187e93.
    [47] Ahemad M, Kibret M (2014) Mechanisms and applications of plant growth promoting rhizobacteria: Current perspective. J King Saud Univ-Sci 26: 1–20.
    [48] Antoun H, Prévost D (2006) Ecology of Plant Growth Promoting Rhizobacteria, In: Siddiqui ZA, Editor, PGPR: Biocontrol and Biofertilization, Dordrecht: Springer Netherlands, 1–38.
    [49] Brunner SM, Goos RJ, Swenson SJ, et al. (2015) Impact of nitrogen fixing and plant growth-promoting bacteria on a phloem-feeding soybean herbivore. Appl Soil Ecol 86: 71–81. doi: 10.1016/j.apsoil.2014.10.007
    [50] Smith SE, Manjarrez M, Stonor R, et al. (2015) Indigenous arbuscular mycorrhizal (AM) fungi contribute to wheat phosphate uptake in a semi-arid field environment, shown by tracking with radioactive phosphorus. Appl Soil Ecol 96: 68–74. doi: 10.1016/j.apsoil.2015.07.002
    [51] Mensah JA, Koch AM, Antunes PM, et al. (2015) High functional diversity within species of arbuscular mycorrhizal fungi is associated with differences in phosphate and nitrogen uptake and fungal phosphate metabolism. Mycorrhiza 25: 533–546. doi: 10.1007/s00572-015-0631-x
    [52] Augé RM, Toler HD, Saxton AM (2015) Arbuscular mycorrhizal symbiosis alters stomatal conductance of host plants more under drought than under amply watered conditions: a meta-analysis. Mycorrhiza 25: 13–24. doi: 10.1007/s00572-014-0585-4
    [53] Schübler A, Schwarzott D, Walker C (2001) A new fungal phylum, the Glomeromycota: phylogeny and evolution. Mycol Res 105: 1413–1421. doi: 10.1017/S0953756201005196
    [54] Dodd JC, Boddington CL, Rodriguez A, et al. (2000) Mycelium of Arbuscular Mycorrhizal fungi (AMF) from different genera: form, function and detection. Plant Soil 226: 131–151. doi: 10.1023/A:1026574828169
    [55] Artursson V, Finlay RD, Jansson JK (2006) Interactions between arbuscular mycorrhizal fungi and bacteria and their potential for stimulating plant growth. Environ Microbiol 8: 1–10. doi: 10.1111/j.1462-2920.2005.00942.x
    [56] Miransari M (2011) Interactions between arbuscular mycorrhizal fungi and soil bacteria. Appl Microbiol Biotechnol 89: 917–930. doi: 10.1007/s00253-010-3004-6
    [57] Zhang L, Xu M, Liu Y, et al. (2016) Carbon and phosphorus exchange may enable cooperation between an arbuscular mycorrhizal fungus and a phosphate-solubilizing bacterium. New Phytologist 210: 1022–1032. doi: 10.1111/nph.13838
    [58] Chaiyasen A, Young JPW, Teaumroong N, et al. (2014) Characterization of arbuscular mycorrhizal fungus communities of Aquilaria crassna and Tectona grandis roots and soils in Thailand plantations. Plos One 9: e112591. doi: 10.1371/journal.pone.0112591
    [59] Chaiyasen A, Douds DD, Gavinlertvatan P, et al. (2017) Diversity of arbuscular mycorrhizal fungi in Tectona grandis Linn.f. plantations and their effects on growth of micropropagated plantlets. New Forest 48: 547–562.
    [60] Brundrett MC, Bougher N, Dell B, et al. (1996) Working with mycorrhizas in forestry and agriculture.
    [61] Smith S, Read D (2008) Mycorrhizal Symbiosis, New York: Academic Press.
    [62] Porcel R, Ruiz-Lozano JM (2004) Arbuscular mycorrhizal influence on leaf water potential, solute accumulation, and oxidative stress in soybean plants subjected to drought stress. J Exp Bot 55: 1743–1750. doi: 10.1093/jxb/erh188
    [63] Doubková P, Vlasáková E, Sudová R (2013) Arbuscular mycorrhizal symbiosis alleviates drought stress imposed on Knautia arvensis plants in serpentine soil. Plant Soil 370: 149–161. doi: 10.1007/s11104-013-1610-7
    [64] Azcón-Aguilar C, Barea JM (1996) Arbuscular mycorrhizas and biological control of soil-borne plant pathogens-an overview of the mechanisms involved. Mycorrhiza 6: 457–464.
    [65] Wright SF, Upadhyaya A (1998) A survey of soils for aggregate stability and glomalin, a glycoprotein produced by hyphae of arbuscular mycorrhizal fungi. Plant Soil 198: 97–107. doi: 10.1023/A:1004347701584
    [66] Rillig MC (2004) Arbuscular mycorrhizae, glomalin, and soil aggregation. Can J Soil Sci 84: 355–363. doi: 10.4141/S04-003
    [67] Rillig MC, Ramsey PW, Morris S, et al. (2003) Glomalin, an arbuscularmycorrhizal fungal soil protein, responds to land-use change. Plant Soil 253: 293–299. doi: 10.1023/A:1024807820579
    [68] Bhardwaj D, Ansari MW, Sahoo K, et al. (2014) Biofertilizers function as key player in sustainable agriculture by improving soil fertility, plant tolerance and crop productivity. Microb Cell Fact 13: 1–10. doi: 10.1186/1475-2859-13-1
    [69] Goswami D, Thakker JN, Dhandhukia PC (2016) Portraying mechanics of plant growth promoting rhizobacteria (PGPR): A review. Cogent Food Agr 2: 1–19.
    [70] Kang SM, Khan AL, Waqas M, et al. (2014) Plant growth-promoting rhizobacteria reduce adverse effects of salinity and osmotic stress by regulating phytohormones and antioxidants in Cucumis sativus. J Plant Interact 9: 673–682. doi: 10.1080/17429145.2014.894587
    [71] Bartels D, Sunkar R (2005) Drought and salt tolerance in plants. Crit Rev Plant Sci 24: 23–58. doi: 10.1080/07352680590910410
    [72] Hussain TM, Chandrasekhar T, Hazara M, et al. (2008) Recent advances in salt stress biology-A review. Biotechnol Mol Biol Rev 3: 8–13.
    [73] Saleem M, Arshad M, Hussain S, et al. (2007) Perspective of plant growth promoting rhizobacteria (PGPR) containing ACC deaminase in stress agriculture. J Ind Microbiol Biotechnol 34: 635–648. doi: 10.1007/s10295-007-0240-6
    [74] Shaharoona B, Arshad M, Zahir ZA (2006) Performance of Pseudomonas spp. containing ACC-deaminase for improving growth and yield of maize (Zea mays L.) in the presence of nitrogenous fertilizer. Soil Biol Biochem 38: 2971–2975.
    [75] Egamberdiyeva D (2007) The effect of plant growth promoting bacteria on growth and nutrient uptake of maize in two different soils. Appl Soil Ecol 36: 184–189. doi: 10.1016/j.apsoil.2007.02.005
    [76] Barriuso J, Solano BR, Gutiérrez MFJ (2008) Protection against pathogen and salt stress by four plant growth-promoting Rhizobacteria isolated from Pinus sp. on Arabidopsis thaliana. Biol Control 98: 666–672.
    [77] Kohler J, Hernández JA, Caravaca F, et al. (2009) Induction of antioxidant enzymes is involved in the greater effectiveness of a PGPR versus AM fungi with respect to increasing the tolerance of lettuce to severe salt stress. Environ Exp Botany 65: 245–252. doi: 10.1016/j.envexpbot.2008.09.008
    [78] Sandhya V, Ali SZ, Grover M, et al. (2010) Effect of plant growth promoting Pseudomonas spp. on compatible solutes, antioxidant status and plant growth of maize under drought stress. Plant Growth Regul 62: 21–30.
    [79] Seneviratne G, Jayasekara APDA, De Silva MSDL, et al. (2011) Developed microbial biofilms can restore deteriorated convencional agricultural soils. Soil Biol Biochem 43: 1059–1062. doi: 10.1016/j.soilbio.2011.01.026
    [80] Shukla PS, Agarwal PK, Jha B (2012) Improved salinity tolerance of Arachis hypogaea (L.) by the interaction of halotolerant plant-growth-promoting-rhizobacteria. J Plant Growth Regul 31: 195–206.
    [81] Swarnalakshmi K, Prasanna R, Kumar A, et al. (2013) Evaluating the influence of novel cyanobacterial biofilmed biofertilizers on soil fertility and plant nutrition in wheat. Eur J Soil Biol 55: 107–116. doi: 10.1016/j.ejsobi.2012.12.008
    [82] Sarma RK, Saikia R (2014) Alleviation of drought stress in mug bean by strain Pseudomonas aeruginosa GGRJ21. Plant Soil 377: 111–126. doi: 10.1007/s11104-013-1981-9
    [83] Cardinale M, Ratering S, Suarez C, et al. (2015) Paradox of plant growth promotion potencial of rhizobacteria and their actual promotion effect on growth of barley (Hordeum vulgare L.) under salt stress. Microbiol Res 181: 22–32.
    [84] Islam F, Yasmeen T, Arif MS, et al. (2016) Plant growth promotion bacteria confer salt tolerance in Vigna radiata by up-regulating antioxidant defense and biological soil fertility. Plant Growth Regul 80: 23–36. doi: 10.1007/s10725-015-0142-y
    [85] Shahzad R, Khan AL, Bilal S, et al. (2017) Inoculation of abscisic acid-producing endophytic bacteria enhances salinity stress tolerance in Oryza sativa. Environ Exp Botany 136: 68–77. doi: 10.1016/j.envexpbot.2017.01.010
    [86] Rajkumar M, Sandhya S, Prasad MNV, et al. (2012) Perspectives of plant-associated microbes in heavy metal phytoremediation. Biotechnol Adv 30: 1562–1574. doi: 10.1016/j.biotechadv.2012.04.011
    [87] Saleh S, Huang XD, Greenberg BM, et al. (2004) Phytoremediation of persistent organic contaminants in the environment, In: Singh A, Ward O, Editors, Appl ied Bioremediation Phytoremediation, Berlin: Springer-Verlag, 115–134.
    [88] Zhuang X, Chen J, Shim H, et al. (2007) New advances in plant growth-promotion rhizobacteria for bioremediation. Environ Int 33: 406–413. doi: 10.1016/j.envint.2006.12.005
    [89] Ma Y, Prasad MNV, Rajkumar M, et al. (2010) Plant growth promoting rhizobacteria and endophytes accelerate phytoremediation of metalliferous soils. Biotechnol Adv 29: 248–258.
    [90] Pinter IF, Salomon MV, Berli F, et al. (2017) Characterization of the As(III) tolerance conferred by plant growth promoting rhizobacteria to in vitro-grown grapevine. Appl Soil Ecol 109: 60–68. doi: 10.1016/j.apsoil.2016.10.003
    [91] Babu AG, Kim JD, Oh BT (2013) Enhancement of heavy metal phytoremediation by Alnus firma with endophytic Bacillus thuringiensis GDB-1. J Hazard Mat 250: 477–483.
    [92] Kuklinsky-Sobral J, Araújo WL, Mendes R, et al. (2004) Isolation and characterization of soybean-associated bacteria and their potential for plant growth promotion. Environ Microbiol 12: 1244–1251.
    [93] Chelius MK, Triplett EW (2001) The diversity of archaea and bacteria in association with the roots of Zea mays L. Microb Ecol 41: 252–263. doi: 10.1007/s002480000087
    [94] Garbeva P, van Overbeek LS, van Vuurde JEL, et al. (2001) Analysis of endophytic bacterial communities of potato by plating and denaturing gradient gel electrophoresis (DGGE) of 16S rDNA based PCR fragments. Microb Ecol 41: 369–383. doi: 10.1007/s002480000096
    [95] Araújo WL, Marcon J, Maccheroni WJ, et al. (2002) Diversity of endophytic bacterial populations and their interaction with Xylella fastidiosa in citrus plants. Appl Environ Microbiol 68: 4906–4914. doi: 10.1128/AEM.68.10.4906-4914.2002
    [96] Zinniel DK, Lambrecht P, Harris B, et al. (2002) Isolation and characterization of endophytic colonizing bacteria from agronomic crops and prairie plants. Appl Environ Microbiol 68: 2198–2208. doi: 10.1128/AEM.68.5.2198-2208.2002
    [97] Idris R, Trifonova R, Puschenreiter M, et al. (2004) Bacterial communities associated with flowering plants of the Ni Hyperaccumulator Thlaspi goesingense. Appl Environ Microbiol 70: 2667–2677. doi: 10.1128/AEM.70.5.2667-2677.2004
    [98] Andreote FD, Carneiro RT, Salles JF, et al. (2009) Culture-independent assessment of Alphaproteobacteria related to order Rhizobiales and the diversity of cultivated Methylobacterium in the rhizosphere and rhizoplane of transgenic eucalyptus. Microb Ecol 57: 82–93. doi: 10.1007/s00248-008-9405-8
    [99] Sagaram US, DeAngelis KM, Trivedi P, et al. (2009) Bacterial diversity analysis of Huanglongbing pathogen-infected citrus, using phylochip arrays and 16S rRNA gene clone library sequencing. Appl Environ Microbiol 75: 1566–1574. doi: 10.1128/AEM.02404-08
    [100] Gv DMP, Magalhães KT, Lorenzetii ER, et al. (2012) A multiphasic approach for the identification of endophytic bacterial in strawberry fruit and their potential for plant growth promotion. Microb Ecol 63: 405–417. doi: 10.1007/s00248-011-9919-3
    [101] Xia X, Lie TK, Qian X (2011) Species diversity, distribution, and genetic structure of endophytic and epiphytic Trichoderma associated with banana roots. Microb Ecol 61: 619–625. doi: 10.1007/s00248-010-9770-y
    [102] Ikeda AC, Bassani LL, Adamoski D, et al. (2013) Morphological and genetic characterization of endophytic bacteria isolated from roots of different maize genotypes. Microb Ecol 65: 154–160. doi: 10.1007/s00248-012-0104-0
    [103] Verma VC, Gond SK, Kumar A, et al. (2009) Endophytic actinomycetes from Azadirachta indica A. Juss.: isolation, diversity, and anti-microbial activity. Microb Ecol 57: 749–756.
    [104] Manter DK, Delgado JA, Holm DG, et al. (2010) Pyrosequencing reveals a highly diverse and cultivar-specific bacterial endophyte community in potato roots. Microb Ecol 60: 157–166. doi: 10.1007/s00248-010-9658-x
    [105] Cruz LM, Souza EM, Weber OB, et al. (2001) 16S Ribosomal DNA characterization of nitrogen-fixing bacteria isolated from banana (Musa spp.) and pineapple (Ananas comosus (L.) Merril). Appl Environ Microbiol 67: 2375–2379.
    [106] Marques ASA, Marchaison A, Gardan L, et al. (2008) BOXPCR-based identification of bacterial species belonging to Pseudomonas syringae: P. viridiflava group. Gen Mol Biol 31: 106–115. doi: 10.1590/S1415-47572008000100019
    [107] Menna P, Barcellos FG, Hungria M (2009) Phylogeny and taxonomy of a diverse collection of Bradyrhizobium strains based on multilocus sequence analysis of 16S rRNA, ITS, glnII, recA, atpD and dnaK genes. Int J Syst Evol Microbiol 59: 2934–2950. doi: 10.1099/ijs.0.009779-0
    [108] Zhang XX, Gao JS, Cao YH (2013) Long-term rice and green manure rotation alters the endophytic bacterial communities of the rice root. Microb Ecol 66: 917–926. doi: 10.1007/s00248-013-0293-1
    [109] Onstott TC, Phelps TJ, Colwell FS, et al. (1998) Observations pertaining to the origin and ecology of microorganisms recovered from the deep subsurface of Taylorsville Basin, Virginia. Geomicrobiol J 15: 353–385. doi: 10.1080/01490459809378088
    [110] Nadkarni MA, Martin FE, Hunter N, et al. (2009) Methods for optimizing DNA extraction before quantifying oral bacterial numbers by real-time PCR. FEMS Microbiol Lett 296: 45–51. doi: 10.1111/j.1574-6968.2009.01629.x
    [111] Muyzer G, De WEC, Uitterlinden AG (1993) Profiling of complex microbial populations by denaturing gradient gel electroforesis analysis of polymerase chain reaction-amplified genes coding for 16S rRNA. Appl Environ Microbiol 59: 695–700.
    [112] Orphan VJ, Taylor LT, Hafenbradl D, et al. (2000) Culture-dependent and culture-independent characterization of microbial assemblages associated with high-temperature petroleum reservoirs. Appl Environ Microbiol 66: 700–711. doi: 10.1128/AEM.66.2.700-711.2000
    [113] Monteiro JM, Vollú RE, Coelho MRR, et al. (2009) Comparison of the bacterial community and characterization of plant growth-promoting rhizobacteria from different genotypes of Chrysopogon zizanioides (L.) Roberty (Vetiver) rhizospheres. J Microbiol 4: 363–370.
    [114] Sun L, Qiu F, Zhang X, et al. (2008) Endophytic bacterial diversity in rice (Oryza sativa L.) roots estimated by 16S rDNA sequence analysis. Microb Ecol 55: 415–424.
    [115] Snyder LAS, Loman N, Pallen MJ, et al. (2009) Next-generation sequencing-the promise and perils of charting the great microbial unknown. Microb Ecol 57: 1–3.
    [116] Studholme DJ, Glover RH, Boonham N (2011) Application of high-throughput DNA sequencing in phytopathology. Annu Rev Phytopathol 49: 87–105. doi: 10.1146/annurev-phyto-072910-095408
    [117] Lundberg DS, Lebeis SL, Paredes SH (2012) Defining the core Arabidopsis thaliana root microbiome. Nature 488: 86–90. doi: 10.1038/nature11237
    [118] Akinsanya MA, Goh JK, Lim SP, et al. (2015) Metagenomics study of endophytic bacteria in Aloe vera using next-generation technology: Genom Data 6: 159–163.
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