The DOI matches its Crossref record; 16 of the 17 references it cites were found in a registry or an index.
Zigzagging: Theoretical insights on climbing strategies
Abstract
Human and animal trails on steep hillsides often exhibit dramatic switchbacks and shortcuts. Helbing et al. have recently examined the emergence of human trail systems on flat terrains while Minetti and Margaria established the effect of gradients on human metabolic efficiency. In this paper we use these ideas to develop a semi-quantitative theoretical model of the behaviour of humans moving on a terrain with relief. The model determines the direction of movement by minimising metabolic cost per unit of distance in a desired direction. The structure of the theory resembles the Landau Theory of Phase Transitions, much used in theoretical physics. We find that both hairpin bends (switchbacks) and shortcuts appear as efficient strategies for downhill walkers, while uphill walkers retain switchbacks. For weakly inclined slopes, the best strategy involves walking directly uphill or downhill. For sufficiently steep slopes, however, we find that the best strategy should undergo a transition to a broken symmetry solution corresponding to the switchback trail patterns typical of rugged environments. The critical slope at which this transition takes place should be less steep for uphill and downhill walkers. The theory should be amenable to empirical investigation. Amongst other applications, this model will enable us to generalize the work of previous authors to real landscapes, eventually permitting the reconstruction of ancient patterns of movement in archaeological landscapes.
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In the citing paper
“Of the two energy-based cost functions tested, that is Herzog (2014c) and Llobera and Sluckin (2007), it is only however Herzog (2014c) that can produce the model outcomes that follow the Roman road (Fig. 10A).”
From Explaining known past routes, underdetermination, and the use of multiple cost functions (2024) · cites this paper as Llobera and Sluckin (2007)
In the citing paper
“Although the hypothesis could be formulated as 'humans minimise steeper slope gradients when traveling by wheeled vehicles', the critical gradient parameter within the cost function is not given a predefined value defined by the cost function but instead to be estimated from the past route being explained.”
From Explaining known past routes, underdetermination, and the use of multiple cost functions (2024) · cites this paper as Llobera and Sluckin (2007)
In the citing paper
“The use of Llobera and Sluckin's (2007) energy expenditure cost function over the more familiar time-based Tobler's Hiking Function (Tobler, 1993) reflects previous success in its ability to model Roman roads (e.g.Fonte et al., 2017;Güimil-Fariña & Parcero-Oubiña, 2015;Parcero-Oubiña et al., 2019).”
From Probabilistic modelling for incorporating uncertainty in least cost path results: a postdictive roman road case study (2021) · cites this paper as Llobera and Sluckin's (2007)
In the citing paper
“The cost of movement has been modelled based again only on the effect of terrain slope and calculated using the metabolic walking costs function proposed in (Llobera & Sluckin, 2007).”
From Exploring the inherent affordability for movement in past landscapes (2027) · cites this paper as Llobera & Sluckin, 2007
In the citing paper
“The cost of movement has been modelled based only on the effect of terrain slope and calculated using the metabolic walking costs function proposed in Llobera & Sluckin, 2007.”
From Exploring the inherent affordability for movement in past landscapes (2027) · cites this paper as Llobera & Sluckin, 2007
In the citing paper
“Furthermore, previous work [11, 29–31] has identified the existence of a critical gradient; the angle at which it is faster to zig-zag up a hill, rather than ascend directly. This occurs at a walking slope of around 15—21 degrees, so models which failed to predict the critical gradient occurring below 21 degrees were removed.”
From Improved prediction of hiking speeds using a data driven approach (2023) · cites this paper as [31]
In the citing paper
“The modified Tobler function has a critical slope for cost-saving zig-zagging of 27%, as defined by Llobera & Sluckin's (2007) equation 20.”
From Budget travel in the Mediterranean: a methodology for reconstructing ancient journeys through least cost networks (2022) · cites this paper as Llobera & Sluckin's (2007)
In the citing paper
“Costs of walking are mostly estimated in terms of energy consumption [Llobera and Sluckin 2007;Minetti et al. 2002] or time [Ericson and Goldstein 1980;Irmischer and Clarke 2017;Langmuir 2004;Tobler 1993].”
From Issues in replication and stability of least-cost path calculations (2022) · cites this paper as Llobera and Sluckin 2007
In the citing paper
“Even though movecost offers a wide range of functions for calculating accumulated slope-dependent anisotropic cost surfaces, we have chosen to use the traditionally most successful function to represent mobility in pre-industrial contexts [55], alongside the function whose results aligned best with fossilised stretches of paths identifiable on satellite imagery (Tobler, see Figure 12), a tried-and”
From Andean landscape legacies: comprehensive remote sensing mapping and GIS analysis of long-term settlement and land use for sustainable futures (NW argentina) (2024) · cites this paper as [55]
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Metadata
- Authors
- Llobera, M., & Sluckin, T. J.
- Affiliations
- University of Washington (US)
- University of Southampton (GB)
- Corresponding author
- Llobera, M.
- Venue
- Journal of Theoretical Biology
- Publisher
- Elsevier BV
- Published
- 2007-11
- Volume
- 249
- Issue
- 2
- Pages
- 206-217
- ISSN
- 0022-5193 (ISSN-L)
- OpenAlex
- W2049192609
- Cited by
- 103
- References
- 17
- Citations by year
- 2026: 9 · 2025: 15 · 2024: 4 · 2023: 10 · 2022: 9 · 2021: 7 · 2020: 5 · 2019: 8 · 2018: 1 · 2017: 4 · 2016: 2 · 2015: 4 · 2014: 6 · 2013: 6 · 2012: 6
- FWCI
- 9.27
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Journal of Theoretical Biology (publishedVersion)
- PubMed (publishedVersion)
- ePrints Soton (University of Southampton) (submittedVersion)
- UCL Discovery (University College London) (submittedVersion)
- Funders
- University of Washington
- Leverhulme Trust
- Arts and Humanities Research Council
- Topics
- Social Sciences › Safety Research › Evacuation and Crowd Dynamics
- Social Sciences › Urban Studies › Urban Design and Spatial Analysis
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Theoretical and Computational Physics
- Keywords
- switchbacks, hiking trails, trail formation, metabolic cost, symmetry breaking, Landau theory, critical slope, archaeological landscape
- MeSH terms
- Altitude, Animals, Biomechanical Phenomena, Energy Metabolism, Humans, Models, Biological, Motor Activity, Walking
About these checks
Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
Statistics and arithmetic are recomputed, not judged.
Confidence bands are shown only for fields calibrated on our annotated test set. None is calibrated yet, so no band is shown.
What counts as a claim ›How we measure confidence ›How we check this ›
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