microPop: Modelling microbial populations and communities in R

Abstract

1. Microbial communities perform highly dynamic and complex ecosystem functions that impact plants, animals and humans. Here we present an R‐package, microPop, which is a dynamic model based on a functional representation of different microbiota.
2. microPop simulates the dynamics and interactions of microbial populations by solving a system of ordinary differential equations that are constructed automatically based on a description of the system.
3. Data frames for a number of microbial functional groups (MFG) and default functions for rates of microbial growth, resource uptake, metabolite production are provided but can be modified or replaced by the user.
4. microPop can simulate growth in a single compartment (e.g. bio‐reactor) or “compartments” in series (e.g. human colon) or in a simple 1D application (e.g. phytoplankton in a water column). Furthermore, an MFG may contain multiple strains in order to study adaptation and diversity or parameter uncertainty. Also simple interactions between viruses (bacteriophages) and bacteria can be included in microPop.
5. microPop is hosted on CRAN and can be installed directly from within R. This paper describes version 1.3 of microPop. The code is also hosted on GitHub for future development (https://github.com/HelenKettle/microPop).

1 INTRODUCTION

Microbial communities play a crucial role in bio‐geochemical cycling and perform ecosystem functions important to plants, animals and humans. Building predictive models that link microbial community composition to function is a key emerging challenge in microbial ecology (Widder et al., 2016). Here, we present microPop, an R package which is a mechanistic model using ordinary differential equations (ODEs) to predict the dynamics and interactions of microbial functional groups (MFG). The general equations for rates of change of a MFG, with quantity X, growing on a resource, with quantity R, at time, t, can be expressed as,

(1)

(2)

where and are the inflow and outflow to the system (units of inverse time) for microbes (i = X) and resources (i = R), and Xⁱⁿ(t) and Rⁱⁿ(t) are the incoming quantities of microbes and resources respectively. G(t) is the specific growth rate of microbes on the resource (units of inverse time) and can be expressed in a variety of ways (see Appendix B in Supporting Information). The second term on the right‐hand side of Equation 2 is the uptake rate of the resource due to microbial growth where Y is the yield i.e. the quantity of microbial growth per unit of resource taken up.

When there are multiple resources and several microbial groups with multiple strains then Equations 1 and 2 expand into a large system with multiple metabolic pathways. This is where microPop is a useful tool. Rather than coding these equations, the user simply gives a description of the system (using 2 data frames, “resourceSysInfo” and “microbeSysInfo”) and a data frame for each MFG and these equations are constructed and solved by microPopModel (ODE solvers are provided by the deSolve package (Soetaert, Petzoldt, & Setzer, 2010)).

Data frames for a number of MFGs found in the human large intestine (e.g. Bacteroides, Acetogens, Methanogens, Butyrate Producers, Lactate Producers and so on) as described by Kettle, Louis, Holtrop, Duncan, and Flint (2015) and the rumen (by Munoz‐Tamayo, Giger‐Reverdin, & Sauvant, 2016) are included in the package (Table 1). If the user simply wishes to use these MFGs, then microPop can be used “off the shelf,” however, any number of other MFGs may also be added by the user by defining a data frame in the correct format.

Table 1. Microbial functional groups (MFGs) included in microPop. The first 10 groups are described by Kettle et al. (2015), the last three are described by Munoz‐Tamayo et al. (2016). It should be noted that these two sets of microbial groups are not fundamentally different but rather a different approach has been used to subdivide the microbiota. To see these data frames simply type in the group name at the R prompt. Users should be aware that the parameter values given in these data frames will almost certainly change with increasing knowledge of gut microbiota and in some cases are simply a “best guess.” The csv files for these groups can be found using “system.file(‘extdata/groupname.csv’,package=‘microPop’)” where “groupname” is any one of the entries in the first column below

MFG (Kettle et al., 2015)	Description	Examples
Bacteroides	Acetate‐propionate‐succinate group	Bacteroides spp.
NoButyStarchDeg	Non‐butyrate‐forming starch degraders	Ruminococcaceae related to Ruminococcus bromii. Might also include certain Lachnospiraceae
NoButyFibreDeg	Non‐butyrate‐forming fibre degraders	Ruminococcaceae related to Ruminococcus albus, Ruminococcus flavefaciens. Might also include certain Lachnospiraceae
LactateProducers	Lactate producers	Actinobacteria, especially Bifidobacterium spp., Collinsella aerofaciens
ButyrateProducers1	Butyrate Producers	Lachnospiraceae related to Eubacterium rectale, Roseburia spp.
ButyrateProducers2	Butyrate Producers	Certain Ruminococcaceae, in particular Faecalibacterium prausnitzii
PropionateProducers	Propionate producers	Veillonellaceae e.g. Veillonella spp., Megasphaera elsdenii
ButyrateProducers3	Butyrate Producers	Lachnospiraceae related to Eubacterium hallii, Anaerostipes spp.
Acetogens	Acetate Producers	Certain Lachnospiraceae, e.g. Blautia hydrogenotrophica
Methanogens	Methanogenic archaea	Methanobrevibacter smithii
MFG (Munoz‐Tamayo et al., 2016)	Description	Examples
Xsu	Sugar utilizers
Xaa	Amino acid utilizers
Xh2	Hydrogen utilizers	Methanobrevibacter smithii

Since many of the required parameter values for the MFGs are not well known, it should be noted that the parameter values stated in the included MFG data frames will almost certainly change with increasing knowledge and in some cases can be interpreted as simply a “best guess.” One way of coping with this parameter uncertainty is addressed in our previous work (Kettle et al., 2015) (and included in microPop) where we assigned multiple strains to each MFG with stochastically generated parameter values. The strains will compete with each other; some will flourish, some will die out, and by the time a steady state is reached a viable microbial community for the given environment will have been created. By changing the seed for the random number generator in microPopModel, multiple viable communities can be created and ensemble statistics can be used to define the solution.

Since microbial growth, resource uptake and metabolite production may be modelled in a number of ways, the choices behind microPop's default growth and uptake rate functions are explained fully in the Appendix. All of these functions are contained in a list called “rateFuncs” (Table 2) and may be redefined by the user (see Appendix A in Supporting Information), allowing microPop to be applied to a large number of different microbial ecosystems. Section 2 gives some examples of what microPop can do and Section 3 gives a brief description of how to use microPop; these sections can be read in either order.

Table 2. MicroPop functions. The top section of the table contains functions contained in the list rateFuncsDefault (further details in SuppInfo‐Appendix). Add “Default” to the end of these function names to look at them in R or to use the help (e.g. help(entryRateFuncDefault))—functions in the bottom section do not require this

Function name	Description
entryRateFunc	Rate of entry of each state variable to system at time t
removalRateFunc	Rate of exit of each state variable from system at time t
pHFunc	pH value at time t
pHLimFunc	pH limit on growth (varies between 0 and 1 for a given pH value)
extraGrowthLimFunc	Another limit on growth (default value is 1 i.e. no limit). This is included to allow the user to add in any kind of growth limitation as its output is used to scale the maxGrowthRate value)
growthLimFunc	This scales the maximum growth value (value between 0 and 1)
combineGrowthLimFunc	Combining growth on multiple resources
uptakeFunc	Uptake of resource due to microbial growth
productionFunc	Production of metabolites resulting from microbial growth
combinePathsFunc	Combining the results of growth on multiple metabolic pathways
createDF	Creates a data frame from a .csv file
derivsDefault	Describes the ODEs; called by ode
getGroupName	Returns the name of the group from the strain name
makeInflowFromSoln	Returns the exit rate of each state variable (matrix[time,variable])
microPopModel	Simulates growth of microbial populations (main function)
pHcentreOfMass	Finds the mean pH weighted by the pH limitation
plotTraitChange	Plots the average group trait over time (when there are multiple strains per group)
runMicroPopExample	Used to run the scripts for the examples described in Section 2

2 EXAMPLE APPLICATIONS

Here, we give a flavour of how microPop can be used to simulate a wide range of microbial systems. For more information on these examples please refer to the vignette included with the package (vignette(‘microPop’) in R). The scripts for all of these examples are included in the microPop package11 The location of these files can be found by “system.file(’DemoFiles/ExampleFileName.R’, package=‘microPop’). It is also printed to screen when the script is run.”
and in the supporting information with this paper; they are intended to serve as a template for users when defining their own problems. The name of the appropriate script is given in square brackets in each example heading and they can be run in R, using, for e.g. runMicroPopExample(‘human1’) (for the human1.R script (Section 2.1.1)). Most of the plots shown in this paper are automatically generated by microPop and can be tweaked using the “plotOptions” input list in microPopModel.

2.1 Modelling human gut microbiota

The microbial ecosystem in the human colon has been linked to numerous issues in human health. For example, two important functions are harvesting extra energy from our food, thus warranting the name the “forgotten organ” (O'Hara & Shanahan, 2006), and aiding the development of our immune system (Chow, Lee, Shen, Khosravi, & Mazmanian, 2010). The following four examples are based on the model described by Kettle et al. (2015) which uses 10 different microbial groups to represent the microbial community in the human colon (Table 1). Here we use just three of these—Bacteroides, NoButyStarchDeg (starch degraders that do not produce butyrate) and Acetogens—to demonstrate some features of microPop. It should be noted that although we believe the microbial system described here is representative of that in the human colon, in this application the model is set up to simulate an experiment with a fecal sample in a fermentor system, therefore absorption of short chain fatty acids (SCFA) and other interactions with the host are not included. The information describing the inflows and outflows of each state variable for these scenarios is contained in the data frames “resourceSysInfoHuman” and “microbeSysInfoHuman” which are included with the package and are based on the system described by Kettle et al. (2015) and Walker et al. (2005). To look at these simply type “resourceSysInfoHuman” or “microbeSysInfoHuman” at the R prompt. Since these contain information on all 10 groups used in the full simulation by Kettle et al. (2015), the user can also use these when simulating the behaviour of any/all of the 10 groups.

2.1.1 Microbial growth in a constant environment (human1.R)

This is a simple example to show how microPopModel can be run using most of the default settings and intrinsic dataframes. In this scenario, there is no limit on growth due to pH and the Bacteroides group dominate the system (Figure 1).

Figure 1

Human colon application (human1)

2.1.2 How does temporal pH change affect microbial growth? (human2.R)

In this scenario, pH changes from 5.5 to 6.5 halfway through the simulation. This is implemented by altering rateFuncs$pHFunc and setting input argument “pHLimit=TRUE.” Due to their preferred pH ranges (determined by “pHcorners” in the data frames for each group) NoButyStarchDeg now dominate the first half of the simulation, however when the pH rises to 6.5 Bacteroides regain dominance (Figure 2).

Figure 2

Human colon application (human2)—pH changes from 5.5 to 6.5 halfway through the simulation

2.1.3 How does spatial pH change affect microbial growth? (human3.R)

Here, we approximate the pH change in sections of the human colon by defining the system as two compartments where the first one (at pH 5.5) flows into the second (at pH 6.0). To simulate two compartments, we add a loop to call microPopModel twice. The first call simulates growth in the first compartment over the whole of the simulation time. The results from this are then used to provide the entry rates to the second compartment (using the function makeInputFromSoln) in the second microPopModel call. The results (Figure 3) show that NoButyStarchDeg dominate in first compartment (top row) and Bacteroides begin dominating the second compartment but this changes due to large inflow of NoButyStarchDeg from the previous compartment.

Figure 3

Human colon application (human3)—two compartments with different pH. Top row: first compartment (pH 5.5), bottom row: second compartment (pH 6.0)

2.1.4 How does microbial diversity affect response to pH? (human4.R)

Here we use the “human2” example, where pH changes from 5.5 to 6.5 halfway through the simulation, but include microbial diversity by assigning five strains to each microbial group (via input argument, “numStrains”). We assume that the strains within a microbial group have the same metabolic pathways i.e. those specified in the group data frame, but diversity is incorporated by randomly varying some of their growth parameters (based on Kettle et al., 2015). The extent of the variation, the parameters which are to be randomised and whether trade‐offs are required are all controlled via the “strainOptions” list. Moreover, the user may also specify the parameter values for individual strains using “paramsSpecified” and “paramDataName” also in this list (note, not all parameter values need to be specified—those that are specified will simply overwrite the randomly generated values). Figure 4a shows the results for each strain.

Figure 4

Human colon application (human4)—five strains per group. (a) shows the concentration of each strain. Note, to plot the sum of the strains in each group set “plotOptions$sumOverStrains=TRUE”). (b) shows the concentration of each resource. (c) shows the mean value of the pH trait for each of the three groups computed using Equation 3

Since there are multiple strains per group, it is possible to examine how the mean group trait adapts over time using a biomass‐weighted average at each time step:

(3)

(Norberg et al., 2001) where xt is the average group trait at time t, x_i is the trait value for strain i and m_i(t) is the mass of strain i at time t. For example, when the pH changes, strains which prefer that new pH will flourish while others will be washed out. The centre of mass of the trapezoidal pH limitation can be computed using the function pHcentreOfMass and we define this one parameter as the pH trait. We can compute and plot the change in time of any of the stochastically varying parameters/traits, using the function plotTraitChange (e.g. Figure 4c shows the variation of the pH trait over time for each microbial group). For more details on phenotype adaptation please see Kettle et al. (2015) or Norberg et al. (2001). Since microbial growth can lead to the release of acids, the local pH may vary with microbial growth, thereby affecting the growth rate of the microbiota i.e. there is a system feedback. This may affect community diversity (Kettle, Donnelly, Marion, & Flint, 2014). By including some extra bio‐chemical functions, this can be explicitly included in the system (e.g. Munoz‐Tamayo et al., 2016).

2.2 Methane production from rumen microbiota (rumen.R)

Methane production through feed fermentation by ruminants contributes significantly to greenhouse gas production by agriculture (Cottle, Nolan, & Weidemann, 2011). Here we use microPop to model in vitro rumen fermentation, based on a simplified version of the model by Munoz‐Tamayo et al. (2016). The construction of this model is significantly different to the human colon model in Section 2.1 in several ways. Firstly, and most importantly, there are no substitutable resource; all resources are essential (see Appendix B.1 for an explanation of the different types of resource) and microbial growth is included explicitly in the group stoichiometries (the groups involved are sugar‐utilisers (X_su), amino‐acid utilisers (X_aa) and hydrogen utilisers (X_h2); included data frames “Xh2,” “Xsu” and “Xaa”). Secondly, hydrolysis is treated as a separate process such that polymer substrates must be hydrolised to soluble sugars and amino acids before they are available for microbial uptake. Thirdly, dead microbial cells are recycled into polymers.

For demonstration purposes, we have simplifed the original model by Munoz‐Tamayo et al. (2016) as follows: we consider only constituents dissolved in the rumen fluid (thereby removing gas transfer from the fluid to the rumen head space), we have removed carbon chemistry (we only consider dissolved inorganic carbon) and we have removed the calculation of pH from acid‐base reactions. Also, we use units of mass rather than moles. Figure 5 shows a schematic diagram of the system and notation of state variables is given in the figure caption.22 microPop code for the original (unsimplified model) is available on request for academic purposes.

Figure 5

The rumen system based on the model by Munoz‐Tamayo et al. (2016) consists of polymers (non‐structural carbohydrates (Z_nsc), cell wall carbohydrates (Z_ndf) and proteins (Z_pro) which are hydrolised to the soluble components: sugars (S_su) and amino acids (S_aa). The microbial groups are sugar‐utilisers (X_su), amino‐acid utilisers (X_aa) and hydrogen utilisers (X_h2). They convert their respective substrates to short chain fatty acids, SCFA, (acetate, butyrate and propionate), hydrogen (S_h2), ammonia (S_nh3), inorganic carbon (S_IC) and methane (S_ch4). Dead microbial cells are recycled to the polymer compartments (arrows not shown)

Since polymers are not used directly by any of the microbial groups (and are therefore not mentioned in the MFG data frames) they will not be automatically added as state variables by microPopModel. Thus to include hydrolysis we add Z_nsc, Z_ndf and Z_pro to the microPop data frame for X_su. We then explicitly state the parameters needed for hydrolysis and recycling of dead cells into polymers as these are not included in the input files. Furthermore, removalRateFunc is redefined to include the reduction rate for polymers and the entryRateFunc includes the equivalent increase for soluble sugars (S_su) and soluble amino acids (S_aa). Similarly the death of microbial cells is included in removalRateFunc and the increase in polymers from the dead cells is included in entryRateFunc.

Using the same settings as Munoz‐Tamayo et al. (2016), we investigate how increasing the initial concentrations of the feed polymers, Z_nsc, Z_ndf and Z_pro, affects the concentration of methane in the rumen (S_ch4). Thus we set the initial polymer concentrations at 1 g/l and then increase each one in turn to 20 g/l (Figure 6). Increasing Z_ndf and Z_pro leads to increasing methane concentrations as expected, however, the second row in Figure 6 shows that, somewhat counter‐intuitively, the amount of methane produced decreases as initial concentrations of Z_nsc increases over a threshold between 15 and 20 g/l. S_IC (soluble inorganic carbon) and (soluble hydrogen, not shown) both increase with Z_nsc, therefore the cause of this appears to be the decrease in ammonia (S_nh3) (third column in Figure 6), which rapidly falls to zero for high initial values of Z_nsc. This is because Z_nsc is hyrolysed at a much faster rate (0.2 h⁻¹) than Z_ndf (0.05 h⁻¹) so increased Z_nsc leads to increased S_su and rapid growth of X_su and hence rapid uptake of S_nh3. The depletion of S_nh3 inhibits the growth of X_h2 and thus mitigates methane production in this simple model example.

Figure 6

Methane concentration in the rumen for initial concentrations between 1 and 20 g/l (legend in centre column) of the feed polymers Z_nsc, Z_ndf and Z_pro (while one polymer concentration is changed the other two are held at 1 g/l). Note change in scale for S_nh3 for Z_pro

2.3 At what depth do phytoplankton grow best? (phyto.R)

Here we show how microPop can be used in a simple 1D application to investigate the depth at which phytoplankton blooms occur, given their growth relies on nutrients welling up from below and sun light entering from above. By simulating the competing growth of three different (theoretical) microbial groups we show how the groups form a vertical assemblage based on their different requirements for light and nutrient (loosely based on work by Kettle & Merchant, 2008). The light level at depth, z (m), is given by,

(4)

where k_L is the light attenuation coefficient (we use k_L = 0.5 m⁻¹). Nutrient upwelling is modelled by assuming that the inflow of nutrient, I_N (g l⁻¹ day⁻¹), increases with depth such that

(5)

where v_N is the gradient of inflow rate of nutrient with depth (g l⁻¹ day⁻¹ m⁻¹).

To define this system in microPop, we consider nutrient to be the only resource since light is not depleted through microbial use and therefore does not need to be included as a state variable. Nutrient upwelling is incorporated via entryRateFunc and light limitation via extraGrowthLimFunc (the output from this function is used to scale the maximum growth rate in a similar way to pHLimFunc). There is no wash out rate for resources but we set a small wash out rate for the phytoplankton of 0.005 day⁻¹ (see “systemInfoMicrobesPhyto”) to represent death rate.

We divide a depth of 20 m into 1 m layers and run microPop for each layer for a simulation time of 3 months. The simulation begins with phytoplankton spread evenly through the depth of the water column (e.g. this may occur after vertical mixing caused by high winds). Thereafter, there is no mixing (calm conditions) and the phytoplankton are stationary in the water but grow at different rates according to the light and nutrient levels at that particular depth. In Case 1 (when running runMicroPopExample(‘phyto’) the user will be prompted to enter a case number) we simulate the growth of just one phytoplankton group. Figure 7a shows how the magnitude and depth of the bloom changes.

Figure 7

(a) Concentration of Phyto1 at nine day intervals when it is the only group present (K_N = 1e‐6 g/l, K_L = 0.8 light units). (b) Concentration of all three groups at monthly intervals with Phyto1 in black (K_N = 1e‐6 g/l, K_L = 0.8 light units), Phyto2 in red (K_N = 1e‐4 g/l, K_L = 0.4 light units) and Phyto3 in green (K_N = 1e‐2 g/l, K_L = 0.2 light units)

In Case 2, we add in two more groups, all with the same starting concentration. The three groups have different requirements for nutrient and light as determined by their half saturation values for nutrient and light (K_N and K_L respectively). Figure 7b shows how over time the groups occupy different levels in the water column.

2.4 Bacteriophages and resistance (phages.R)

Although not the main intended use of microPop, bacteriophages (viruses which attack bacteria) can be included in microPop in a simplistic way. In this example, we consider two (theorectical) groups of bacteria (called Bacteria1 and Bacteria2) and two bacteriophages called Virus1 and Virus2. Both bacteria have the same substrate (nutrient) and the same parameters with the only difference that Bacteria2 has a higher maximum growth rate than Bacteria1. Virus1 attacks Bacteria1, and Virus2 attacks Bacteria2. The two viruses have the same parameter values and differ only in their choice of host cell (bacterial group). We consider a simple system with a constant dilution rate of 0.1 day⁻¹. All variables have a starting value of 1 and the only inflow is nutrient.

In order to infect a host cell, the bacteriophage attaches itself to the bacterial cell wall and then injects its genetic material into the host cell, causing the host cell to eventually die and release a large number of new phage particles. To model this within microPop, we make some simplifying assumptions. Firstly, since one phage attacks one bacterial cell, the “consumption” rate does not follow a Monod Equation but it is more like a predator–prey model where the rate of change of the number of cells of the virus, V, due to viral attack on B bacterial cells is

(6)

where α is the specific reproduction rate (number of new virus cells made from one viral cell per bacterial cell per day). Within microPop we put the maxGrowthRate of V1 on B1 equal to α and redefine growthLimFunc so the “limitation” is now simply B rather than the Monod equation (this is multiplied by V later in derivsDefault). The rate of change of the number of bacterial cells due to death by virus attack is

(7)

where Y is the yield i.e. the number of new virus cells per bacterial cell (note α = Yb where b is the binding rate (units of V⁻¹ day⁻¹)).

We now consider bacterial mutations by incorporating mutation of Bacteria1 to a resistant strain via entryRateFunc so that a fraction of the Bacteria1 population is converted to a resistant group (‘resistantBacteria1’, ) per day (f_B). Thus the rate of change of due to mutation is

(8)

and the loss rate from B₁ is the negative of this (also included via entryRateFunc). This model is a very simplified version of that of Cairns, Timms, Jansen, Connerton and Payne (2009) where we have removed the time delay and the infected stage.

We run microPop for four different system scenarios (when running runMicroPopExample(‘phages’) the user will be prompted to choose from case 1 to 4); the results are shown in Figure 8. To begin with we look at the system without viruses and see the two bacteria competing for nutrient, since Bacteria2 has the highest growth rate it dominates the system (case 1; Figure 8a). We now add in Virus2 which attacks Bacteria2, allowing Bacteria1 to dominate the system causing Bacteria2, and hence Virus2, to die out (case 2; Figure 8b). If we now add in Virus1, so that we have both bacterial groups and both viral groups, we see more complex dynamics emerge (case 3; Figure 8c). In the fourth case, we add in random mutations from Bacteria1 to resistant Bacteria1 which is resistant to Virus1 and therefore survives at the expense of the other bacterial groups (case 4; Figure 8d).

Figure 8

(a) Case 1: Two bacterial groups compete for one substrate (Nutrient); no viruses present. (b) Case 2: A virus (Virus1) which attacks Bacteria1 is added to the system. (c) Case 3: As in (b) but a virus (Virus2) which attacks Bacteria2 is also added to the system. (d) Case 4: As in (c) but Bacteria1 randomly mutates into a group (at a rate f_BB₁(t) where f_B = 0.001 day⁻¹) which is identical to Bacteria1 apart from it has resistance to Virus1

3 RUNNING microPop

To install the package use “install.packages(‘microPop’)” within R, then “library(microPop).” As previously mentioned the main function in the package is microPopModel and this is used to run a simulation. The input arguments to this function are used to completely define the system and its output is a list containing two elements—one is the solution to the ODEs i.e. a matrix of the values of the state variables over time (‘solution’) and the other is a list containing all of the information used to produce the solution (‘parms’). In the simplest case, the user need only specify four of the input arguments to microPopModel (the others have defaults) these four are:

• ‘microbeNames’—a vector of the names of the microbial groups in your system, e.g. c(‘Bacteroides’, ‘Methanogens’). Note that a data frame with the same name must be available for each group specified.
• ‘times’—a vector defining the time sequence at which output is required, e.g. seq(0,10,0.1).
• ‘resourceSysInfo’—this is a data frame or the name of a csv file describing the inflow, outflow, start values and molar masses of the substrates and products associated with the microbial groups specified in microbeNames. See help(resourceSysInfo) for details.
• ‘microbeSysInfo’—this is a data frame or the name of a csv file describing the inflow, outflow and start values of the microbial groups specified in microbeNames. See help(microbeSysInfo) for details.

Figure 9 shows this in detail, using the example given in help(microPopModel). Details of all the input arguments can be found via the function help and in the vignette included with the package.

Figure 9

Schematic showing how to call microPopModel (black box) for the example shown in help(microPopModel). See Section 3 for more details. The csv (comma separated values) files are shown in Libre office but can be created in Microsoft Excel or any text editor. The automatically generated plots are shown at the bottom. Note that here the group data frame (‘Archea’) is defined but this is not necessary if the user wishes to use any of the group data frames already included in the package (Table 1). Also note that this example uses the default rate functions. For information on how to change these please look at the Example Applications in Section 2 and the code in Scripts (Supporting Information)

ACKNOWLEDGEMENTS

We thank the Scottish Goverment's Rural and Environment Science and Analytical Services Division (RESAS) for funding this research. Also many thanks to Rafael Munoz‐Tamayo for his rumen model matlab code and to the three anonymous reviewers.

AUTHORS' CONTRIBUTIONS

H.K. conceived the idea, wrote the package code and led the writing of the manuscript. G.H. contributed extensively to testing and improving the package structure. P.L. and H. J. F. contributed to all aspects of microbiology. All authors contributed critically to the drafts and gave final approval for publication.

DATA ACCESSIBILITY

All code and data is included in microPop v1.3 on github with DOI: https://doi.org/10.5281/zenodo.842797 (Kettle, Holtrop, Louis, & Flint, 2017).