The theory of Janzen-Connell effects in corals: How dispersal and clonal growth shape pathogen-mediated coexistence

Technical Summary: The Theory of Janzen-Connell Effects in Corals

Problem Statement
Coral reefs exhibit high species diversity within limited space, a paradox that classic ecological theory struggles to explain given the lack of distinct limiting resources beyond space and light. The Janzen-Connell (JC) hypothesis, which posits that specialist natural enemies (pathogens) suppress conspecific recruitment near adult hosts, offers a potential mechanism for this coexistence. However, applying standard JC models to corals is problematic due to two key biological departures from the assumptions used in tropical tree models:

1. Dispersal Mismatch: Coral larvae disperse over kilometer scales (effectively "global" at the reef scale), whereas microbial pathogens act over centimeter scales (highly localized).
2. Indeterminate Growth: Unlike trees with fixed canopy areas, corals exhibit indeterminate clonal growth, allowing colonies to expand into adjacent empty space.

It remains unclear whether these departures strengthen or weaken pathogen-mediated coexistence. Furthermore, experimental support for JC effects in corals is limited and mixed, necessitating a theoretical assessment of their plausibility.

Methodology
The authors developed a stochastic, spatially explicit lattice model to simulate coral dynamics on a 2D grid.

• Model Structure: The lattice consists of sites that are either empty or occupied by an adult coral. The model tracks single-species and two-species dynamics.
• Demographic Processes:
  • Death: Occurs at a constant per capita rate ($D$).
  • Clonal Growth: Adults expand into adjacent empty sites at rate ($G$).
  • Recruitment: Larvae are produced at rate ($F$) and disperse via a bipartite kernel: a fraction ($m$) disperses globally (well-mixed pool), and $(1-m)$ disperses locally to the parent's site and immediate neighbors.
  • Pathogen Dynamics: Pathogens are produced by adults and disperse similarly: a fraction ($s$) disperses globally, and $(1-s)$ disperses locally. Recruitment success is suppressed linearly by the local and global pathogen load, modulated by a suppression intensity parameter ($\gamma$).
• Analytical Approach: To avoid the computational cost and stochastic noise of individual-based simulations, the authors employed pair approximation. This method derives deterministic ordinary differential equations (ODEs) for the frequencies of nearest-neighbor site configurations (e.g., empty-occupied pairs). This approach retains spatial information necessary to capture distance-dependent JC effects while allowing for rapid numerical analysis and invasion stability analysis.
• Invasion Analysis: Coexistence was assessed by calculating the invasion growth rate ($\lambda$) of a rare species in the presence of a resident species at equilibrium. A positive $\lambda$ indicates stable coexistence.

Key Contributions

1. Continuous Variation of Dispersal: Unlike previous models that treated dispersal as binary (local vs. global) or spatially implicit, this study continuously varies both host dispersal ($m$) and pathogen dispersal ($s$) in a closed, spatially explicit system.
2. Integration of Clonal Growth: This is the first analysis to explicitly model how indeterminate clonal growth interacts with JC dynamics.
3. Analytical Approximation: The authors derived an analytical expression for the invasion growth rate using perturbation expansion, providing insight into the interaction terms between dispersal parameters.

Results

• Host and Pathogen Dispersal: Both host dispersal ($m$) and pathogen dispersal ($s$) generally promote coexistence.
  • Host Dispersal: Long-distance dispersal helps species escape the high pathogen loads near their parents. This contrasts with environmental heterogeneity models where local dispersal is favored; here, the "enemy-free space" is located far from the parent.
  • Pathogen Dispersal: Contrary to spatially implicit models (e.g., Stump and Chesson, 2015) which predicted no effect of pathogen dispersal under global host dispersal, this spatially explicit model shows that increasing pathogen dispersal ($s$) promotes coexistence even when host dispersal is global.
  • Mechanism: In a spatially explicit context, locally dispersing pathogens often land on their source colony (where adults are immune), rendering them ineffective. Global dispersal spreads pathogens to empty sites, increasing the average pathogen pressure on recruitment sites. This intensifies density-dependent feedbacks, disproportionately harming the abundant resident species and aiding the rare invader.
• Clonal Growth: The effect of clonal growth ($G$) is highly context-dependent and non-monotonic.
  • Equalizing Mechanism: When an invader has lower fecundity than the resident, clonal growth can compensate for this deficit, acting as an equalizing mechanism that aids coexistence.
  • Crowding Out: However, because clonal growth bypasses pathogen suppression (adults are immune), high rates of clonal growth can "crowd out" the stabilizing JC effects. If growth dominates recruitment, the system loses the density-dependent feedbacks essential for coexistence, potentially driving the invasion growth rate toward zero.
• Interaction Effects: The relationship between dispersal and coexistence can be U-shaped under intermediate pathogen pressure, where both the equalizing effect of limited dispersal and the stabilizing effect of global dispersal compete.

Significance and Claims
The paper claims to provide a theoretical framework for understanding how the unique biology of corals—specifically the mismatch between larval and pathogen dispersal scales and the presence of clonal growth—modulates the Janzen-Connell mechanism.

• Validation of JC Plausibility: The results suggest that JC effects can theoretically sustain coral diversity even with global larval dispersal, provided that pathogen dispersal is sufficiently global to reach empty recruitment sites.
• Contradiction of Previous Theory: The finding that pathogen dispersal promotes coexistence under global host dispersal contradicts predictions from spatially implicit models, highlighting the necessity of spatially explicit modeling for systems with localized enemies.
• Context-Dependence: The study emphasizes that the net effect of coral life-history traits on diversity is not uniform; it depends on the balance between long-range larval dispersal (which aids escape from enemies) and short-range pathogen dispersal (which creates the enemy-free space), as well as the relative strength of clonal growth versus recruitment.
• Empirical Unknowns: The authors conclude that whether these mechanisms boost or weaken coexistence in real coral communities depends on empirical parameters not yet fully quantified: the magnitude of conspecific vs. heterospecific suppression, size-dependent demographic rates, and the specific dispersal kernels of pathogens and larvae. They advocate for reciprocal experimental designs to resolve these unknowns.