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Mapping the Trade-Offs That Shape Mammalian Brain Network Architecture

Adrian DendorferiD, Alexa MousleyiD, Francisco Páscoa dos SantosiD, Duncan Edward AstleiD, Kayson FakhariD

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Abstract

A brain's wiring must satisfy conflicting pressures, from the outside world (be capable) and from the inside (stay within finite resources). These pressures often have opposing requirements. Prior work studies these trade-offs mostly between 2-3 pressures at a time, and thus cannot say how many pressures shape brain wiring or for which trade-off brains decide. To see all possible trade-offs at once and to uncover the set of most important pressures, we generate 25,000 synthetic brain networks and describe each by 29 network properties. We then place 635 human (ages 6-22) and 224 mammalian (12 taxonomic orders) brain networks in this property space. The space is triangular, and follows three pressures: computational capability, robustness to damage, and metabolic efficiency. No network is optimal at all three, and biological brains cluster in one small niche of this triangle. There, they accept higher metabolic cost to gain both robustness and capability. Development and evolution move brains in the same direction; additionally, human maturation first raises capability, and later optimizes for efficiency. This study underscores the triangular trade-off between metabolic efficiency, computational capacity and robustness, and the narrow region brains occupy in this trade-off triangle, visible only from a multi-property, cross-species perspective.

In-depth summary

Claude Opus 5.5 · xhigh effort · 7 Nov 2026 · from the full text of version 1 (11 Oct 2026) · CC BY 4.0

Across 25,000 generative-model networks scored on 29 properties, 635 human and 224 mammalian connectomes cluster in one narrow niche, trading wiring economy for computational capability and robustness.

Earlier network-morphospace studies fixed two or three objectives in advance (information processing against wiring cost, later plus segregation), so they can demonstrate that objectives conflict without establishing how many independent pressures act on connectomes. Here the objectives are read off a principal component analysis of 29 ungrouped properties over synthetic, reference and empirical networks, which resolves three competing goals rather than a single front.

Key results

  1. ShownHuman and mammalian connectomes occupy one bounded region of the property space, fully enclosed by the cloud of generative network model (GNM) networks, with moderate values on many properties rather than an extreme on any; mammals whose brain volumes differ by over four orders of magnitude converge there.

    PCA of 29 z-scored properties over 25,963 networks (25,000 GNM, 635 HCP-D, 224 MaMI, 101 baselines, 3 communication-optimised): PC1 57.49 %, PC2 14.65 %, PC3 4.51 % of variance. Erdős-Rényi networks occupy the minimum-PC1 extreme, diffusion-optimised and minimum-wiring networks the low-PC2 extreme; routing- and propagation-optimised networks lie near the MaMI cluster. · Multi-Objective Property Space; Property space construction via PCA

  2. SuggestedLoadings resolve three tensions: integration vs segregation (PC1), wiring cost vs computational capacity (PC2), robustness vs all other objectives (PC3); treating PC1 as architecture rather than a goal, the authors read three competing goals (economy, capability, robustness) that span a triangle.

    PC1: small-worldness, global and propagation efficiency vs modularity, maximum clique size, controllability spread. PC2: spectral gap, long-range fraction, wiring cost vs linear and non-linear memory capacity, modularity. PC3: targeted-attack robustness, synchronizability vs critical size/threshold, wiring cost. Summed goal loadings reproduce the PC2 split; robustness projects weakly onto PC1-PC2. · Competing Objectives and the Property Scheme

  3. ShownKnown pairwise fronts reappear; on a rank-normalised simplex of economic efficiency, global efficiency and memory capacity, connectomes sit near the efficiency-memory edge, far from the economy vertex, spending wiring for capability, yet below some synthetic networks in summed rank.

    Global efficiency vs modularity medoids: HCP-D ≈ 0.43 vs ≈ 0.50, MaMI ≈ 0.47 vs ≈ 0.40; routing-optimised ≈ 0.53 vs ≈ 0.22. Economic efficiency (1 − fLR, fLR = long-range edge fraction): HCP-D ≈ 0.55, MaMI ≈ 0.51; minimum-wiring 1.00 with global efficiency ≈ 0.38. Summed rank: low-γ GNM networks exceed every empirical connectome; propagation-optimised is highest and most balanced of the references. · Recovering Established Trade-Offs…; Pairwise and Ternary Trade-Off Analyses

  4. SuggestedDevelopment and phylogeny both register most on one axis of a synthetic-only PCA (PC2GNM): with age, connectomes move toward computational capacity, then after an inflection at 16.0 years toward integration; mammalian orders form two clusters that track cortical folding or brain volume, not the phylogenetic tree.

    17 per-year HCP-D consensus networks: age vs PC1GNM r = 0.521 (p = 0.032), PC2GNM r = −0.552 (p = 0.022); inflection stable for λ ≥ 5. Mean PERMANOVA (permutational multivariate ANOVA) pseudo-F: PC2GNM 11.63, PC4GNM 9.79, others ≤ 3.20. Primates/Carnivora/Cetartiodactyla (Mahalanobis dM = 0.22) and Rodentia/Chiroptera (dM = 0.18) not separated internally (p > 0.05); between clusters all p = 0.001, F > 10. · Developmental Maturation and Phylogenetic…; Developmental Trajectory and Phylogenetic…

  5. ShownThe cost-homophily wiring rule reproduces biological connectomes less closely than it reproduces the minimum-wiring and communication-optimised networks, and best-fit (η, γ) coordinates leave most mammalian orders unseparated, so the parameter space is a coarser embedding than the property space.

    Residual DeltaCon distance (mean over the 100 best-fitting grid cells): HCP-D 8.77 ± 0.05, MaMI 8.07 ± 0.08 vs minimum-wiring 5.26 ± 0.19, diffusion-optimised 6.28 ± 0.16, propagation-optimised 7.06 ± 0.12. HCP-D medoid η ≈ −3.06, γ ≈ −0.01; 62.5 % of MaMI vs 6.1 % of HCP-D best fits have η > 0, attributed to MaMI preprocessing. · GNM Morphospace; Comparing Networks: DeltaCon

Methods, data and reproducibility

A generative network model (GNM) adding edges with probability set by distance (exponent η) and neighbourhood overlap (exponent γ) was swept over a 50 × 50 grid with 10 replicates, giving 25,000 100-node networks at 10 % density; these, the connectomes and reference networks were scored on 29 properties and embedded by PCA, and each connectome was matched to its closest GNM network with DeltaCon.

  • Human Connectome Project Development (HCP-D) structural connectomes, ages 6-22; DSI Studio GQI deterministic tractography, Schaefer-100 parcellation, binarised at 10 % density · human · n = 635 individuals (17 per-year consensus networks)
  • Mammalian MRI (MaMI) ex vivo diffusion-MRI connectomes from 12 taxonomic orders, downsampled from 200 to 100 nodes; order analyses used the five orders with n > 20 · multiple mammalian species (12 orders) · n = 224 (one disconnected animal removed)
  • Synthetic GNM networks (distance-homophily rule, minimum-spanning-tree seed, Schaefer-100 coordinates, 10 % density, 50 × 50 (η, γ) grid × 10 replicates) · n = 25,000
  • Erdős-Rényi random networks (100 nodes, 495 edges) · n = 100
  • Minimum-wiring network (495 shortest-distance node pairs) · n = 1
  • Communication-optimised reference networks (routing, diffusion, propagation), grown with YANAT from a ring lattice to 10 % density · n = 3
Methods & tools
DSI Studio, netneurotools, NetworkX, generativenetworkmodels, YANAT, echoes, bctpy, GraphRicciCurvature, netrd (DeltaCon), scikit-learn, scikit-bio, SciPy
Assay conditions & compute
Comparing all HCP-D connectomes against the 25,000 synthetic networks with DeltaCon took approximately 23 CPU-core hours, vs slightly more than 13 CPU-core days that KS-based energy distance would have needed; hardware not stated.
Reproducibility gaps
Code, the 25,000 synthetic and reference networks and property matrices are promised at publication (Zenodo); HCP-D connectomes not redistributed (HCP data use terms); no Zenodo identifier printed for MaMI; no library versions. Supplementary animation on GitHub (ad045/14_4D_property_space).
Limitations (6)
  • All connectomes come from diffusion-MRI tractography, which suffers crossing-fibre and false-positive errors, so findings concern tractography-reconstructed networks rather than true anatomical wiring. · stated by the authors
  • The 29-property set is a choice, some properties rest on single stochastic estimates (e.g. one Louvain partition for modularity), and the hand assignment of properties to goals, architectural settings and emergent behaviours yields groups that are not orthogonal. · stated by the authors
  • HCP-D (in vivo, Schaefer-100) and MaMI (ex vivo, k-means endpoint parcellation) differ in acquisition and reconstruction, so the offset between their clouds is not read biologically; 62.5 % of MaMI best fits land at η > 0, which the authors attribute to MaMI preprocessing. · stated by the authors
  • Cortical folding scales with brain volume independently of taxonomic order, so order differences may partly or solely reflect volume-dependent geometry; HCP-D age labels may also be offset by up to one year. · stated by the authors
  • The developmental trajectory rests on 17 per-year consensus networks from one cohort; the two significant age correlations (p = 0.032, p = 0.022) come from ten components tested, with no multiple-comparison correction described. · noted in this summary
  • Every synthetic network is grown on human Schaefer-100 coordinates at 10 % density, and MaMI distances are rescaled to the human distribution, so the space of possible architectures is defined by a single (human) cortical geometry. · noted in this summary

Read this if you study connectome organisation with generative network models or morphospaces and want a 29-property, cross-species view of which wiring trade-offs human and mammalian brains settle on.

Citations
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