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

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

In [1]:

library(knitr)
library(tidyverse)

── Attaching core tidyverse packages ──────────────────────── tidyverse 2.0.0 ──
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✔ forcats   1.0.1     ✔ stringr   1.6.0
✔ ggplot2   4.0.2     ✔ tibble    3.3.1
✔ lubridate 1.9.5     ✔ tidyr     1.3.2
✔ purrr     1.2.1     
── Conflicts ────────────────────────────────────────── tidyverse_conflicts() ──
✖ dplyr::filter() masks stats::filter()
✖ dplyr::lag()    masks stats::lag()
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readr::read_csv("tables/Table_S1_descriptive_stats.csv") %>%
kable()

Rows: 6 Columns: 17
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr  (1): model
dbl (16): connectance_mean, connectance_sd, trophic_level_mean, trophic_leve...

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

model	connectance_mean	connectance_sd	trophic_level_mean	trophic_level_sd	generality_mean	generality_sd	vulnerability_mean	vulnerability_sd	S1_mean	S1_sd	S2_mean	S2_sd	S4_mean	S4_sd	S5_mean	S5_sd
ADBM	0.2980289	0.0173274	14.9000	4.394688	0.9018448	0.0950970	0.8893876	0.0559394	0.0000000	0.0000000	1.1891795	0.4682134	1.4537193	0.6319601	1.3887004	0.3871614
ATN	0.2250133	0.0170831	15.7300	6.889176	1.0308906	0.1385251	1.0673261	0.1042244	0.0291176	0.0502323	0.4557063	0.1981065	1.3411211	0.5991332	1.1685892	0.2930910
PFIM	0.1185292	0.0231336	15.6525	6.238513	1.7226598	0.1528536	0.6326936	0.0763279	0.1044935	0.0352603	0.1390467	0.0305457	0.0644215	0.0456966	0.5227883	0.1453698
log ratio	0.1720401	0.0155925	19.9100	10.106545	0.6371490	0.0896016	0.6898121	0.1403929	0.7490114	0.2910247	0.1410731	0.0622885	0.5286292	0.2069172	0.5014183	0.2151592
niche	0.1181557	0.0328685	18.4925	12.145317	1.1245242	0.1685898	0.6482552	0.1672472	0.1924341	0.1096531	0.1088552	0.0890663	0.1434281	0.0855302	0.3231550	0.1852910
random	0.2213846	0.0449628	17.0675	12.154929	0.3263843	0.0833936	1.7046249	0.2168757	0.0107583	0.0127651	0.1808526	0.0937089	1.6233885	0.6556234	0.0296900	0.0213948

Table S2. Canonical discriminant analysis

In [2]:

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

Rows: 8 Columns: 4
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (1): Metric
dbl (3): Can1, Can2, Can3

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Metric	Can1	Can2	Can3
connectance	-0.75	0.36	-0.45
trophic_level	-0.31	-0.75	-0.25
generality	0.73	0.58	0.32
vulnerability	-0.86	-0.20	0.38
S1	0.38	-0.60	-0.48
S2	-0.35	0.62	-0.53
S4	-0.81	0.14	-0.11
S5	-0.12	0.74	-0.52

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.

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.

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.

In [3]:

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

Rows: 104 Columns: 7
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (4): Term, Network metric, Term type, p-value
dbl (3): Estimate / EDF, Std. Error / Ref.df, t / F value

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Term	Network metric	Term type	Estimate / EDF	Std. Error / Ref.df	t / F value	p-value
(Intercept)	connectance	parametric	0.298	0.001	241.811	<0.001
Model: Body-size ratio	connectance	parametric	-0.126	0.002	-72.283	<0.001
Model: ATN	connectance	parametric	-0.073	0.002	-41.891	<0.001
Model: Niche	connectance	parametric	-0.180	0.002	-103.197	<0.001
Model: PFIM	connectance	parametric	-0.179	0.002	-102.983	<0.001
Model: Random	connectance	parametric	-0.077	0.002	-43.973	<0.001
Smooth: time by ADBM	connectance	smooth	2.921	2.995	22.563	<0.001
Smooth: time by Body-size ratio	connectance	smooth	2.927	2.996	13.810	<0.001
Smooth: time by ATN	connectance	smooth	2.958	2.999	27.042	<0.001
Smooth: time by Niche	connectance	smooth	2.249	2.618	2.719	0.112
Smooth: time by PFIM	connectance	smooth	2.987	3.000	113.849	<0.001
Smooth: time by Random	connectance	smooth	2.604	2.882	4.720	0.016
ANOVA: shared vs model-specific smooths	connectance	anova	NA	NA	32.045	<0.001
(Intercept)	trophic_level	parametric	3.583	0.032	110.465	<0.001
Model: Body-size ratio	trophic_level	parametric	2.666	0.046	58.124	<0.001
Model: ATN	trophic_level	parametric	-0.388	0.046	-8.450	<0.001
Model: Niche	trophic_level	parametric	0.448	0.046	9.771	<0.001
Model: PFIM	trophic_level	parametric	-1.105	0.046	-24.099	<0.001
Model: Random	trophic_level	parametric	2.312	0.046	50.402	<0.001
Smooth: time by ADBM	trophic_level	smooth	2.740	2.948	15.265	<0.001
Smooth: time by Body-size ratio	trophic_level	smooth	2.918	2.995	72.135	<0.001
Smooth: time by ATN	trophic_level	smooth	2.642	2.903	11.011	<0.001
Smooth: time by Niche	trophic_level	smooth	2.925	2.996	46.779	<0.001
Smooth: time by PFIM	trophic_level	smooth	1.496	1.811	6.427	0.007
Smooth: time by Random	trophic_level	smooth	2.994	3.000	607.810	<0.001
ANOVA: shared vs model-specific smooths	trophic_level	anova	NA	NA	78.029	<0.001
(Intercept)	generality	parametric	0.902	0.004	200.915	<0.001
Model: Body-size ratio	generality	parametric	-0.265	0.006	-41.698	<0.001
Model: ATN	generality	parametric	0.129	0.006	20.329	<0.001
Model: Niche	generality	parametric	0.223	0.006	35.079	<0.001
Model: PFIM	generality	parametric	0.821	0.006	129.304	<0.001
Model: Random	generality	parametric	-0.575	0.006	-90.653	<0.001
Smooth: time by ADBM	generality	smooth	2.949	2.998	101.687	<0.001
Smooth: time by Body-size ratio	generality	smooth	2.847	2.981	25.350	<0.001
Smooth: time by ATN	generality	smooth	2.979	3.000	230.268	<0.001
Smooth: time by Niche	generality	smooth	1.001	1.001	0.391	0.532
Smooth: time by PFIM	generality	smooth	2.996	3.000	366.841	<0.001
Smooth: time by Random	generality	smooth	2.933	2.996	48.486	<0.001
ANOVA: shared vs model-specific smooths	generality	anova	NA	NA	122.123	<0.001
(Intercept)	vulnerability	parametric	0.889	0.006	141.193	<0.001
Model: Body-size ratio	vulnerability	parametric	-0.200	0.009	-22.403	<0.001
Model: ATN	vulnerability	parametric	0.178	0.009	19.974	<0.001
Model: Niche	vulnerability	parametric	-0.241	0.009	-27.068	<0.001
Model: PFIM	vulnerability	parametric	-0.257	0.009	-28.815	<0.001
Model: Random	vulnerability	parametric	0.815	0.009	91.514	<0.001
Smooth: time by ADBM	vulnerability	smooth	2.595	2.877	10.151	<0.001
Smooth: time by Body-size ratio	vulnerability	smooth	2.909	2.993	49.940	<0.001
Smooth: time by ATN	vulnerability	smooth	2.912	2.994	45.848	<0.001
Smooth: time by Niche	vulnerability	smooth	2.824	2.976	20.777	<0.001
Smooth: time by PFIM	vulnerability	smooth	2.944	2.997	40.497	<0.001
Smooth: time by Random	vulnerability	smooth	1.412	1.697	0.222	0.695
ANOVA: shared vs model-specific smooths	vulnerability	anova	NA	NA	33.392	<0.001
(Intercept)	S1	parametric	0.000	0.003	0.000	1
Model: Body-size ratio	S1	parametric	0.749	0.004	194.021	<0.001
Model: ATN	S1	parametric	0.029	0.004	7.543	<0.001
Model: Niche	S1	parametric	0.192	0.004	49.847	<0.001
Model: PFIM	S1	parametric	0.104	0.004	27.068	<0.001
Model: Random	S1	parametric	0.011	0.004	2.787	0.005
Smooth: time by ADBM	S1	smooth	1.000	1.000	0.000	1
Smooth: time by Body-size ratio	S1	smooth	2.999	3.000	3454.642	<0.001
Smooth: time by ATN	S1	smooth	2.473	2.798	5.453	0.001
Smooth: time by Niche	S1	smooth	2.980	3.000	197.148	<0.001
Smooth: time by PFIM	S1	smooth	2.952	2.998	41.261	<0.001
Smooth: time by Random	S1	smooth	1.000	1.000	0.011	0.916
ANOVA: shared vs model-specific smooths	S1	anova	NA	NA	772.574	<0.001
(Intercept)	S2	parametric	1.189	0.004	282.637	<0.001
Model: Body-size ratio	S2	parametric	-1.048	0.006	-176.145	<0.001
Model: ATN	S2	parametric	-0.733	0.006	-123.268	<0.001
Model: Niche	S2	parametric	-1.080	0.006	-181.560	<0.001
Model: PFIM	S2	parametric	-1.050	0.006	-176.486	<0.001
Model: Random	S2	parametric	-1.008	0.006	-169.460	<0.001
Smooth: time by ADBM	S2	smooth	2.998	3.000	3739.389	<0.001
Smooth: time by Body-size ratio	S2	smooth	2.941	2.997	49.584	<0.001
Smooth: time by ATN	S2	smooth	2.990	3.000	607.421	<0.001
Smooth: time by Niche	S2	smooth	2.860	2.984	22.303	<0.001
Smooth: time by PFIM	S2	smooth	2.757	2.954	13.956	<0.001
Smooth: time by Random	S2	smooth	2.915	2.994	35.738	<0.001
ANOVA: shared vs model-specific smooths	S2	anova	NA	NA	553.156	<0.001
(Intercept)	S4	parametric	1.454	0.005	271.314	<0.001
Model: Body-size ratio	S4	parametric	-0.925	0.008	-122.084	<0.001
Model: ATN	S4	parametric	-0.113	0.008	-14.860	<0.001
Model: Niche	S4	parametric	-1.310	0.008	-172.920	<0.001
Model: PFIM	S4	parametric	-1.389	0.008	-183.346	<0.001
Model: Random	S4	parametric	0.170	0.008	22.391	<0.001
Smooth: time by ADBM	S4	smooth	2.999	3.000	4569.752	<0.001
Smooth: time by Body-size ratio	S4	smooth	2.994	3.000	444.599	<0.001
Smooth: time by ATN	S4	smooth	2.999	3.000	4034.456	<0.001
Smooth: time by Niche	S4	smooth	2.854	2.983	24.949	<0.001
Smooth: time by PFIM	S4	smooth	2.786	2.964	23.029	<0.001
Smooth: time by Random	S4	smooth	2.999	3.000	4479.574	<0.001
ANOVA: shared vs model-specific smooths	S4	anova	NA	NA	990.095	<0.001
(Intercept)	S5	parametric	1.389	0.005	283.303	<0.001
Model: Body-size ratio	S5	parametric	-0.887	0.007	-127.994	<0.001
Model: ATN	S5	parametric	-0.220	0.007	-31.752	<0.001
Model: Niche	S5	parametric	-1.066	0.007	-153.709	<0.001
Model: PFIM	S5	parametric	-0.866	0.007	-124.911	<0.001
Model: Random	S5	parametric	-1.359	0.007	-196.042	<0.001
Smooth: time by ADBM	S5	smooth	2.998	3.000	1900.335	<0.001
Smooth: time by Body-size ratio	S5	smooth	2.995	3.000	593.637	<0.001
Smooth: time by ATN	S5	smooth	2.996	3.000	940.100	<0.001
Smooth: time by Niche	S5	smooth	2.976	3.000	167.436	<0.001
Smooth: time by PFIM	S5	smooth	2.980	3.000	286.415	<0.001
Smooth: time by Random	S5	smooth	1.000	1.000	0.028	0.867
ANOVA: shared vs model-specific smooths	S5	anova	NA	NA	279.442	<0.001

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.

In [4]:

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

Rows: 8 Columns: 4
── Column specification ────────────────────────────────────────────────────────
Delimiter: ","
chr (3): Term, Network metric, p-value
dbl (1): F value

ℹ Use `spec()` to retrieve the full column specification for this data.
ℹ Specify the column types or set `show_col_types = FALSE` to quiet this message.

Term	Network metric	F value	p-value
ANOVA: shared vs model-specific smooths	connectance	32.045	<0.001
ANOVA: shared vs model-specific smooths	trophic_level	78.029	<0.001
ANOVA: shared vs model-specific smooths	generality	122.123	<0.001
ANOVA: shared vs model-specific smooths	vulnerability	33.392	<0.001
ANOVA: shared vs model-specific smooths	S1	772.574	<0.001
ANOVA: shared vs model-specific smooths	S2	553.156	<0.001
ANOVA: shared vs model-specific smooths	S4	990.095	<0.001
ANOVA: shared vs model-specific smooths	S5	279.442	<0.001

SuppMat 2: Effects of Network Reconstruction on Food-Web Structure