---
title: "SuppMat 2: Effects of Network Reconstruction on Food-Web Structure"
authors:
  - name: Tanya Strydom
    id: ts
    orcid: 0000-0001-6067-1349
abstract: |
  Expanded results section.
date: last-modified
bibliography: ../references.bib
---

# Effect of Body Size Sampling Method on Network Metrics

To assess whether the choice of body size sampling distribution (uniform, lognormal, or truncated lognormal) influences the estimated structure of ecological networks, we computed partial eta-squared (η²) values for each network metric within each reconstruction model. This approach isolates the effect of body size distribution while controlling for model-specific variation.

Across all models and network metrics, the effect of body size sampling method was extremely small. Most η² values were effectively zero (<0.01), indicating that the choice of distribution had negligible influence on metrics such as connectance, generality, vulnerability, and various motif counts. Only a few metrics in the ATN model showed slightly higher effects (η² ≈ 0.17 for number of linear chains), but these remained the exception rather than the rule.

These findings justify using any of the tested body size sampling approaches for our simulations, as the structural conclusions drawn from the networks are robust to this methodological choice. Consequently, analyses of network metrics and comparisons across reconstruction models are not confounded by the specific form of the synthetic body size distribution.

# Multivariate analysis of network structure

We quantified food-web structure using a suite of macro-, meso-, and micro-scale network metrics capturing global topology, motif composition, and species-level interaction patterns (Table S1). Differences among reconstruction approaches were assessed using a multivariate analysis of variance (MANOVA), with model identity as a fixed factor and the full set of network metrics as response variables. Pillai’s trace was used to assess overall multivariate significance due to its robustness to violations of multivariate normality.

To identify the multivariate axes driving differences among models, we performed canonical discriminant analysis (CDA) on the MANOVA model. Canonical variates represent orthogonal linear combinations of network metrics that maximize separation among reconstruction approaches. The contribution of individual metrics to each canonical variate was quantified using canonical structure coefficients (correlations between original metrics and canonical scores).

For visualization, canonical scores were plotted using linear discriminant analysis (LDA), which yields an equivalent discriminant subspace under equal group priors. Model separation in canonical space was visualized using convex hulls encompassing all network replicates for each reconstruction approach. Univariate analyses of variance and effect sizes (partial η²) were calculated for individual metrics and are reported in the Supplementary Materials for descriptive comparison.
Pairwise interaction turnover was quantified using link-based beta diversity, which measures dissimilarity in the identity of trophic interactions between networks and captures differences arising from species turnover or changes in interactions among shared species.

## Figure S1. Effect of Body Size Sampling Method on Network Metrics

![](figures/effect_size_bodysize_within_model.png)

Metrics where η² was notably higher are labelled directly on the bars. The figure highlights that, for the majority of network properties and models, η² values are extremely low (<0.01), confirming that the body size distribution choice has negligible impact on network structure. A few exceptions appear for the ATN model, but these are limited to specific metrics (e.g., number of linear chains).

# Effects of Network Reconstruction on Food-Web Structure

## Table S1. Descriptive statistics of network metrics by model

```{r}
library(knitr)
library(tidyverse)

readr::read_csv("tables/Table_S1_descriptive_stats.csv") %>%
kable()

```

## Table S2. Canonical discriminant analysis

```{r}

readr::read_csv("tables/canonical_loadings.csv") %>%
kable()

```

## Figure S1. Canonical Loadings

Canonical loadings for the first two canonical variates (CV1, CV2) from the canonical discriminant analysis of network metrics. Arrows indicate the contribution of each metric to the multivariate separation among reconstruction models. Colours denote the scale of each metric: Macro (green), Meso (orange), Micro (purple). Metric labels are shown for the most influential variables.

![](../figures/canonical_loadings_plot.png)

# Model choice influences inferred extinction dynamics

## Figure S2. Raw temporal trajectories of network structure during extinction simulations.

Panels show mean values of network-level metrics through time for each reconstruction model, grouped by macro-, meso-, and micro-scale properties as in Figure 3. Lines represent raw simulation outputs averaged across replicates. This figure provides the underlying data corresponding to the GAM-predicted trajectories shown in Figure 3.

![](figures/Figure_S3_time_structure.png)

## Table S3. Full generalized additive model (GAM) results for network-level metrics.

Parametric coefficients, model-specific smooth terms, and ANOVA comparisons of shared versus model-specific time effects are shown for each network metric. Estimate/EDF and Std. Error / Ref.df correspond to parametric coefficients or effective degrees of freedom and reference degrees of freedom for smooth terms. t/F value and p-value report statistical significance. Parametric terms represent the baseline effect of each model; smooth terms describe non-linear temporal trajectories of each reconstruction model. ANOVA rows compare the fit of shared versus model-specific smooths. No inference or interpretation is implied in this table; the main text and Figure 3 provide inferential conclusions.

```{r}

readr::read_csv("tables/Table_S7_GAM_results.csv") %>%
kable()

```

## Table S4. ANOVA comparisons of shared versus model-specific GAM smooths for all network-level metrics.

Each row shows the result of comparing a generalized additive model (GAM) with a shared smooth term for time across reconstruction models versus a model-specific smooth term for each reconstruction model. Columns include the F value and p-value of the ANOVA test. Very small p-values are reported as <0.001. These tests indicate whether allowing model-specific temporal trajectories significantly improves model fit; no inferential claims about the direction or magnitude of changes are made in this table.

```{r}

readr::read_csv("tables/Table_S8_GAM_model_comparison.csv") %>%
kable()

```

# References {.unnumbered}

::: {#refs}
:::