The reversible exchange reaction of the form B ^{_1}}_{_{-1}}}} A ^{_2}}_{_{-2}}}} C has rate equations given by the following: {dt} = k_{-1}[B]-k_1[A]-k_2[A]+k_{-2}[C] \\ {dt} = k_1[A]-k_{-1}[B] \\ {dt} = k_2[A]-k_{-2}[C] Note that, for the purposes of this analysis, the inter-conversion of the major isomers is ignored. This is a valid assumption if the rate of inter-conversion of B ↔ C is small. We estimate from cursory analysis of the data that the rate constants for this process are at least two orders of magnitude smaller than the pathway that proceeds through the minor isomer, A. However, a steady-state approximation for the system of rate equations is not valid for the minor isomer because its concentration changes appreciably and is not significantly different from those concentrations of either major isomer. Thus, the differential equations in (2)-(4) are solved explicitly. The exact solutions to these equations are: A(t) = B_0[k_{-2}}{mn}-(k_{-2}-m)}{m(m-n)}^{-mt}-(k_{-2}-n)}{n(m-n)}^{-nt}] \\ B(t) = B_0[k_{-2}}{mn}+(m-k_2-k_{-2})}{m(m-n)}^{-mt}+(k_2+k_{-2}-n)}{n(m-n)}^{-nt}] \\ C(t) = B_0[k_{2}}{mn}-k_{2}}{m(m-n)}^{-mt}+k_{2}}{n(m-n)}^{-nt}] Where, m = {2}(p+q)\\ n = {2}(p-q)\\ p = k_1+k_{-1}+k_2+k_{-2}\\ q = (p^2-4(k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}))^{2} The values of _m_ and _n_ generally differ by less than an order of magnitude within the range of rate constant values expected for Reaction (1). Thus, fits to time-dependent data in the form of y(t)=y₀ + Λe−λt + Ke−κt tend to converge to the form y(t)=y₀ + αe−βt. We take advantage of this to approximate k−1 by fitting data for major isomer _B_ with a single exponential such that equation (6) may be rearranged as: B(t) = B_0[k_{-2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}+[k_2+k_{-1}k_{-2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}]^{-x_1t}] Similarly, the integrated rate laws for isomers A and C may be rewritten as: A(t) = B_0[k_{-2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}+[k_{-2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}]^{-x_2t}]\\ C(t) = B_0[k_{2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}+[k_{2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}]^{-x_3t}] Note that in equations (12) and (14), x₁ and x₃ are roughly equivalent to k−1 and k−2, respectively. x₂ does not have an obvious analogue. At equilibrium, for a normalized data set, the following relations also hold: 1 =[A]+[B]+[C]\\ [B]_e =}{k_{-1}}[A]_e={K_1}[A]_e\\ [C]_e ={k_{-2}}[A]_e=K_2[A]_e Where K₁ and K₂ are the equilibrium constants for the first and second step of Reaction (1), respectively. Substituting Eqns (16) and (17) into (15) and rearranging yields the following relationship: [A]_e = k_{-2}B_0}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}} Then, in solving for Eqn (3) at equilibrium, [B]_e = k_{1}k_{-2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}+k_2+k_{-1}k_{-2}}{k_{-1}k_2+k_{1}k_{-2}+k_{-1}k_{-2}}^{-k_{-1}t} Thus, by inspection of Eqns (12) and (19), x₁ ≈ k−1. Equation (4) may be similarly rearranged and integrated to solve assuming equilibrium conditions, where x₃ ≈ k−2. Unfortunately, equations (12)-(14) cannot be expressly used to determine exact values for k₁, k−1, k₂, and k−2 explicitly because those variables are coupled due to the simplifying assumption that a three-component exponential fit to the experimental data converges to a two-component exponential fit when values of m and n are similar. It is, however, relatively straightforward to determine K₁ and K₂ by fitting the experimental data with a function of the form y(t)=y₀ + αe−βt to obtain y₀ and β for A, B, and C at each temperature. It then follows that K_1={y_0(A)} and K_2={y_0(A)} Finally, K₁ and K₂ may be used to estimate the remaining two unknowns, k₁, k₂, from the estimated values of k−1, and k−2.

INTRODUCTION Biofilms are diverse and complex microbial consortia, and, the biofilm lifestyle is the rule rather than the exception for microbes in many environments. Large and small-scale biofilm architectural features play an important role in their ecology and influence their role in biogeochemical cycles . Fluid mechanics impact biofilm structure and assembly , but it is less clear how other abiotic factors such as resource availability affect biofilm assembly. Aquatic biofilms initiate with seed propagules from the planktonic community . Thus, resource amendments that influence planktonic communities may also influence the recruitment of microbial populations during biofilm community assembly. In a crude sense, biofilm and planktonic microbial communities divide into two key groups: oxygenic phototrophs including eukaryotes and cyanobacteria (hereafter “photoautotrophs”), and heterotrophic bacteria and archaea. This dichotomy, admittedly an abstraction (e.g. non-phototrophs can also be autotrophs), can be a powerful paradigm for understanding community shifts across ecosystems of varying trophic state . Heterotrophs meet some to all of their organic carbon (C) requirements from photoautotroph produced C while simultaneously competing with photoautotrophs for limiting nutrients such as phosphorous (P) . The presence of external C inputs, such as terrigenous C leaching from the watershed or C exudates derived from macrophytes , can alleviate heterotroph reliance on photoautotroph derived C and shift the heterotroph-photoautotroph relationship from commensal and competitive to strictly competitive . Therefore, increased C supply should increase the resource space available to heterotrophs and increase competition for mineral nutrients decreasing nutrients available for photoautotrophs (assuming that heterotrophs are superior competitors for limiting nutrients as has been observed ). These dynamics should result in the increase in heterotroph biomass relative to the photoautotroph biomass along a gradient of increasing labile C inputs. We refer to this differential allocation of limiting resources among components of the microbial community as niche partitioning. While these gross level dynamics have been discussed conceptually and to some extent demonstrated empirically , the effects of biomass dynamics on photoautotroph and heterotroph membership and structure has not been directly evaluated in plankton or biofilms. In addition, how changes in planktonic communities propagate to biofilms during community assembly is not well understood. We designed this study to test if C subsidies shift the biomass balance between autotrophs and heterotrophs within the biofilm or its seed pool (i.e. the plankton), and, to measure how changes in biomass pool size alter composition of the plankton and biofilm communities. Specifically, we amended marine mesocosms with varying levels of labile C input and evaluated differences in photoautotroph and heterotrophic bacterial biomass in plankton and biofilm samples along the C gradient. In each treatment we characterized plankton and biofilm community composition by PCR amplifying and DNA sequencing 16S rRNA genes and plastid 23S rRNA genes.