Persistence selection between simulated biogeochemical cycle variants for their distinct effects on the Earth system

Abstract

The average long-term impact of Darwinian evolution on Earth's habitability remains extremely uncertain. Recent attempts to reconcile this uncertainty by "Darwinizing" nonreplicating biogeochemical processes subject to persistence-based selection conform with the historicity of the geochemical record but lack mechanistic clarity. Here, we present a theoretical framework showing how: 1) A biogeochemical "cycle-biota-variant" (CBV) can be defined non-arbitrarily as one biologically facilitated pathway for net recycling of an essential element, plus the genotypes driving the relevant interconversion reactions. 2) Distinct CBVs can be individuated if they have climatic or geochemical side effects that feed-back on relative persistence. 3) The separation of spatial/temporal scales between the dynamics of such effects and those of conventional Darwinian evolution can introduce a degree of randomness into the relationship between CBVs and their Earth system impact properties, loosely analogous to that between the biochemical causes and evolutionary effects of genetic mutation. 4) Threshold behavior in climate feedback can accentuate biotic impacts and lead to CBV-level "competitive exclusion". 5) CBV-level persistence selection is observationally distinguishable from genotype-level selection by strong covariance between "internal" CBV properties (genotypes and reactions) and "external" climatic effects, which we argue is analogous to the covariance between fitness and traits under conventional Darwinian selection. These factors cannot circumvent the basic fact that local natural selection will often favor phenotypes that ultimately destabilize large-scale geochemical/climatic properties. However, we claim that our results nevertheless demonstrate the theoretical coherence of persistence-selection between non-replicating life-environment interaction patterns and therefore have broad biogeochemical applicability.

Keywords: Gaia hypothesis; field theory; its-the-song-not-the-singer theory; persistence selection.

Fig. 1.

The general concept of cycle individualization by external impact on biogeochemical processes. A generic biologically essential element J is interconverted between three distinct variants J₁, J₂, J₃ as a physiological byproduct of biological “reactions” R_A, R_B, R_C, R_D (solid arrows depict increasing influence). An intuitive definition of a putatively persistence-selected CBV as one pathway for net recycling of J leads to two distinct CBVs being identifiable, AB (red) and CDB (blue), but also illustrates how process-level interconnectedness (purple, reaction R_B) may render such a definition arbitrary. This is less of a problem given the additional assumption that the combined byproducts of reactions R_A and R_B impact upon a different geoclimatic system X, ultimately feeding back negatively (dashed arrows) on reaction R_C, therefore influencing on CBV relative persistence.

Fig. 2.

A simple timescale separation is sufficient for CBV-level dynamics to make a difference to gene frequencies. The impact of the timescale separation ${\tau }_X$ between the X-cycle (row C) and the biological (row A) and J-cycle (row B) dynamics, upon two single-simulation results (column 1, ${\tau }_X=10$, and column 2, ${\tau }_X=20$) for otherwise identical parameter choices. With sufficient timescale overlap (column 1), the byproduct flux from species A and B reacts with the $X_{\mathit{res}}$ reservoir, until its depletion leads to a discontinuity in the X-cycle (1C), the subsequent state of which suppresses the growth of species C, leading to the displacement of CBV CDB by AB (1D). This change is associated with a decrease in the cross-species mean frequency of the reaction-performing p-allele (1A) but fixation of p_A and p_B. A minor increase in the timescale separation (column 2) prevents any change from the initial equilibrium state.

Fig. 3.

Replicate-averaged steady state solutions of the biogeochemical mode under different boundary conditions. Each color point shows the average of 1,000 simulations equivalent to those given in Fig. 2. The Top row shows the effect of changing the baseline selection and mutation parameters, first under boundary conditions in which the biological byproduct flux is always zero (there is no feedback via the X cycle, $X_{var0}=0$), the second row under conditions in which it is an increasing function of the product of reactions A and B (this feedback does exist, $X_{var0}=1$). The Bottom row shows (for constant selection and mutation coefficients) the effect of incremental variation in the baseline magnitude of the byproduct flux $X_{var0}$ and the suppression function ${\alpha }_0$. Columns A-F show, respectively, the mean level of J-variant (i.e., $\frac{1}{3}\left(J_1+J_2+J_3\right)$), the value of X, the mean (cross species averaged) relative frequency of the reaction-performing p-genotype, the final value of the suppression function $\alpha =f(X)$, and the final normalized relative value of the two CBVs.

Fig. 4.

Correlations between steady state normalized CBVs and suppression function values across different boundary conditions. Rows correspond to those in Fig. 3, i.e., sensitivity analyses to selection and mutation with no X cycle feedback (row 1), selection and mutation with X cycle feedback (row 2), and baseline magnitudes of the byproduct flux $X_{var0}$ and suppression function ${\alpha }_0$ for constant selection and mutation rate (row 3). Within each row, the first two columns show the within-sample correlation—i.e., the correlation between the final values of the variables across the set of replicates for the parameter combination shown on the X and Y axes. The second two columns show a scatterplot of all final steady state values, with a 1st-degree polynomial linear regression line (red) giving the value of the correlation across the entire dataset.