Community assembly: alternative stable states or alternative transient states?

Abstract

The concept of alternative stable states has long been a dominant framework for studying the influence of historical contingency in community assembly. This concept focuses on stable states, yet many real communities are kept in a transient state by disturbance, and the utility of predictions for stable states in explaining transient states remains unclear. Using a simple model of plant community assembly, we show that the conditions under which historical contingency affects community assembly can differ greatly for stable versus transient states. Differences arise because the contribution of such factors as mortality rate, environmental heterogeneity and plant-soil feedback to historical contingency changes as community assembly proceeds. We also show that transient states can last for a long time relative to immigration rate and generation time. These results argue for a conceptual shift of focus from alternative stable states to alternative transient states for understanding historical contingency in community assembly.

Figure 1

Illustrative example of community assembly where assumption 1 is valid: beta diversity is higher in one scenario (a) than in the other (b) for both transient and stable states, except at very early stages of assembly. Temporal changes in alpha, beta and gamma diversity are presented with means (dark lines) and standard deviations (pale lines). Transient dynamics (from t=1 – 150) and stable states (t=1580 – 1600) are shown. In (c), beta diversity is presented for both scenarios to facilitate comparison between them.

Figure 2

Illustrative example of community assembly where assumption 1 is violated: beta diversity differs between the scenarios during transient dynamics, but not at stable states. Symbols are as in Fig. 1.

Figure 3

Illustrative example of community assembly where assumption 1 is violated: beta diversity differs between the scenarios at stable states, but not during transient dynamics. Symbols are as in Fig. 1.

Figure 4

Illustrative example of community assembly where assumption 1 is violated: beta diversity shows temporal reversal between the scenarios (see text for detail). Symbols are as in Fig. 1.

Figure 5

Summary of all possible pair-wise comparisons of the scenarios shown in Fig. S2.

Figure 6

Vegetation recovery in the model defined by dx/dt= rx (1 – x/K) –cx²/(x² + 1) (see text for parameter details). In (a), black line indicates stable equilibrium, dotted line indicates unstable equilibrium, and arrows indicate the direction of change in vegetation biomass under a given value of c. Two alternative stable states exist for a certain range of c (indicated by shading), as indicated by two stable equilibria for a given c value. In (b) and (c), trajectories of vegetation biomass recovery from 50 different initial values (i.e. 1/100, 2/100, 3/100, 4/100, … 49/100 and 50/100 of the equilibrium value) are shown for each of the two values of c (c₁ and c₂) indicated in (a). In (d), temporal changes in maximum variation in vegetation biomass between recoveries from different initial values are shown under c₁ and c₂.

Figure 7

Alpha (a, d, g, j), beta (c, f, i, l) and gamma (b, e, h, k) diversity (means and standard deviations) as a function of environmental heterogeneity (h), positive feedback strength ( f ) and timing of observation (t). Mortality rate (m) is 0.1 for all cases.