Inferring Intraspecific Competition from Leaf Gall Spatial Patterns

Introduction

In ecological systems, spatial distribution patterns yield vital clues regarding underlying biological interactions, including intraspecific competition, mutualism, microhabitat heterogeneity, and resource partitioning. Broadly, three canonical spatial dispersion patterns occur in natural populations:

1. Random Distribution: Typically characterizes resource-rich, homogeneous environments where individuals establish independently without strong competitive interference or social attraction.
2. Regular (Uniform) Distribution: Characterized by even, maximized inter-individual distances, typically generated by direct competitive antagonism, territorial exclusion, or local resource depletion.
3. Aggregated (Clustered) Distribution: Characterized by spatial clumping around microenvironmental resource patches, localized dispersal vectors, or social aggregation.

In this study, we analyzed the spatial dispersion of insect-induced leaf galls across 12 leaves of the scholar tree (Alstonia scholaris) using the classical Clark–Evans Nearest Neighbour Method (Clark and Evans, 1954).

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Materials and Methods

Materials

• 12 freshly collected leaves of Alstonia scholaris displaying insect galls
• Standard millimeter graph sheets
• Transparent acetate overlays and fine archival markers
• Vernier caliper (0.01 mm resolution)

Methods

Leaf boundaries and individual gall coordinates were traced onto transparent acetate overlays. Lamina surface area ($A$) was calculated by grid counting against calibrated $1.0{\text{ cm}}^2$ graph paper.

Using a Vernier caliper, the distance $r_i$ from each gall $i$ to its nearest spatial neighbour was measured in millimetres and converted to centimetres.

Mathematical Formulation

1. Gall Density ($\lambda$):

   $$\lambda =\frac{N}{A}$$

   Where $N$ is total gall count and $A$ is lamina area (${\text{cm}}^2$).

2. Observed Mean Nearest Neighbour Distance (${\overline{r}}_O$):

   $${\overline{r}}_O=\frac{1}{N}\sum _{i=1}^N{r}_i$$

3. Expected Mean Distance for a Poisson Random Distribution ($r_E$):

   $$r_E=\frac{1}{2\sqrt{\lambda }}=\frac{1}{2}\sqrt{\frac{A}{N}}$$

4. Clark–Evans Dispersion Ratio ($R$):

   $$R=\frac{{\overline{r}}_O}{r_E}$$

5. Dispersion Classification:

   • Clustered / Aggregated: $R<0.5$
   • Random: $0.5\le R\le 1.5$ (theoretical expectation $R=1.0$)
   • Regular / Uniform: $R>1.5$ (theoretical maximum hexagonal packing $R\approx 2.1491$)

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Data

Leaf Area and Gall Enumeration

Leaf ID	Leaf Area (cm²)	Number of Galls
Leaf 1	41	15
Leaf 2	49	6
Leaf 3	38	8
Leaf 4	54	14
Leaf 5	44	17
Leaf 6	48	24
Leaf 7	86	9
Leaf 8	50	5
Leaf 9	53	17
Leaf 10	31	15
Leaf 11	33	9
Leaf 12	35	10

Leaf Area vs. Clark–Evans Dispersion Ratio ($R$)

Leaf ID	Leaf Area (cm²)	Observed ${\overline{r}}_O$ (cm)	Expected $r_E$ (cm)	$R$ (Ratio)	Inferred Pattern
Leaf 1	41	0.9047	0.8266	1.0945	Random
Leaf 2	49	1.2300	1.4289	0.8602	Random
Leaf 3	38	1.0475	1.0909	0.9599	Random
Leaf 4	54	0.7636	0.9815	0.7779	Random
Leaf 5	44	0.7506	0.8046	0.9328	Random
Leaf 6	48	0.8087	0.7071	1.1440	Random
Leaf 7	86	1.4900	1.5459	0.9638	Random
Leaf 8	50	2.7860	1.5811	1.7621	Regular
Leaf 9	53	0.7665	0.8824	0.8686	Random
Leaf 10	31	0.7467	0.7188	1.0388	Random
Leaf 11	33	0.7411	0.9574	0.7735	Random
Leaf 12	35	1.2510	0.9354	1.3364	Random

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Results

Gall abundance vs. leaf area ($r_s=-0.0633$)	Nearest neighbour distance vs. gall count ($r_s=-0.5800$)
Clark-Evans $R$ vs. leaf area ($r_s=-0.1189$)	Distribution classifications across the 12 sampled leaves

Statistical Correlation Analyses

1. Leaf Area vs. Gall Abundance:
   Spearman's rank correlation coefficient $r_s=-0.0633$ confirms no correlation between leaf size and total gall infestation.
2. Gall Abundance vs. Mean Nearest Neighbour Distance:
   Spearman's rank correlation coefficient $r_s=-0.5800$ demonstrates a statistically significant negative relationship ($p<0.05$): higher gall infestation directly forces tighter physical packaging.
3. Scale Invariance of Dispersion Ratio:
   Spearman's rank correlation between leaf area and Clark–Evans ratio $r_s=-0.1189$ confirms that spatial dispersion pattern is scale-invariant across leaves.

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Discussion and Conclusion

Across the 12 examined leaves:

• 11 leaves (91.7%) exhibited $R$ values firmly within the random distribution envelope ($0.5\le R\le 1.5$, centered near $\overline{R}\approx 1.0$).
• 1 leaf (8.3%, Leaf 8) displayed a regular distribution ($R=1.7621$).
• 0 leaves exhibited clustered distributions ($R<0.5$).

The predominant random distribution pattern indicates that Alstonia scholaris leaf laminas act as homogeneous oviposition substrates for the gall-inducing insects. Oviposition appears to be Poisson-distributed across available lamina tissue rather than clustered around localized structural features or spaced through aggressive territorial deterrence.

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References

1. Clark, P.J. and Evans, F.C. (1954). Distance to nearest neighbor as a measure of spatial relationships in populations. Ecology, 35(4), pp. 445–453.
2. Dale, M.R. and Fortin, M.J. (2014). Spatial Analysis: A Guide for Ecologists. Cambridge University Press.