Biophysical optimality of the golden angle in phyllotaxis
Takuya Okabe · Scientific Reports · 2015 · Mathematical and numerical model of plant development
Original publication · Original publication · Original publication
Recorded summary
An energy-cost model identifies the golden angle as an optimum for transitions between phyllotactic fractions and reproduces several common and less common leaf-arrangement sequences.
Recorded limitations
The proposed evolutionary explanation depends on the chosen transition-cost model. Agreement with known patterns does not measure the assumed energy costs or establish the genetic mechanism.
Evidence and provenance
Chapter Trust Factor uses a minimum of three distinct qualifying studies. Publication records retain their own evidence and assessment.
Study design and assessment
- design
- Mathematical and numerical model of plant development
- assessment
- is Randomized Controlled Trial
- false
- blinding
- Not applicable to a clinical-trial grade
- basis
- Mathematical and numerical model of plant development. No human randomized controlled trial is reported.
- sources
https://www.nature.com/articles/srep15358
- category
- peer-reviewed
- peer Reviewed
- true
- trust Factor
- score
- 1
- scope
- Paper
- status
- assessed
- randomized Controlled Trial
- false
- blinding
- not-confirmed
- peer Reviewed
- true
- basis
- Mathematical and numerical model of plant development. No human randomized controlled trial is reported.
- sources
https://pubmed.ncbi.nlm.nih.gov/26471765/ · https://www.nature.com/articles/srep15358
- review Scope
- Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
- assessed At
- 2026-10-27
- jadad
- status
- not-applicable
- score
- Not recorded
- reason
- Not a human randomized controlled trial.
- evidence
- evidence Type
- Mathematical and numerical model of plant development
- evidence Class
- proposed_biological_model
- measurement
- Phyllotactic fractions and divergence-angle cost function
- measured Genes
- None recorded
- pathways
- None recorded
- relationship Note
- Background literature only. This paper does not test or validate an OXTR–Fibonacci relationship.
- clinical Evidence
- false
- review Depth
- Abstract and selected source passages: Results; Discussion; Methods.
- full Paper Appraisal
- Not completed; review depth states the material assessed.
Topics and recorded topic scores
- key
- general:fibonacci-biological-patterns
- title
- Biological patterns and developmental mechanisms
- collection
- general
- trust Score
- 1
Citation snapshot and identifiers
- id
- nature-fibonacci-srep15358
- doi
- 10.1038/srep15358
- pmid
- 26471765
- citation Snapshot
- count
- 31
- source
- Crossref cited-by count
- retrieved At
- 2026-10-24
- url
- https://api.crossref.org/works/10.1038/srep15358
- field
- is-referenced-by-count
- source Indexed At
- 2026-10-16T19:42:48Z
- coverage Note
- Count reflects Crossref-deposited references and can differ from publisher or other database totals. It is not a quality or clinical-evidence score.
- citations By Collection
- general
- 31
Complete approved library record
- id
- nature-fibonacci-srep15358
- aliases
- None recorded
- title
- Biophysical optimality of the golden angle in phyllotaxis
- journal
- Scientific Reports
- publisher Family
- nature
- publisher Family Label
- Nature Portfolio
- neurotransmitters
- None recorded
- year
- 2015
- authors
- Takuya Okabe
- design
- Mathematical and numerical model of plant development
- kind
- Journal article
- identity Conflict
- Not recorded
- doi
- 10.1038/srep15358
- pmid
- 26471765
- urls
https://www.nature.com/articles/srep15358 · https://doi.org/10.1038/srep15358 · https://pubmed.ncbi.nlm.nih.gov/26471765/
- collections
general
- categories
Fibonacci mathematics · Biological pattern formation
- targets
- None recorded
- priority
- 1
- quotes
- None recorded
- summary
- An energy-cost model identifies the golden angle as an optimum for transitions between phyllotactic fractions and reproduces several common and less common leaf-arrangement sequences.
- limitation
- The proposed evolutionary explanation depends on the chosen transition-cost model. Agreement with known patterns does not measure the assumed energy costs or establish the genetic mechanism.
- citation Count
- 31
- citation Snapshot
- count
- 31
- source
- Crossref cited-by count
- retrieved At
- 2026-10-24
- url
- https://api.crossref.org/works/10.1038/srep15358
- field
- is-referenced-by-count
- source Indexed At
- 2026-10-16T19:42:48Z
- coverage Note
- Count reflects Crossref-deposited references and can differ from publisher or other database totals. It is not a quality or clinical-evidence score.
- study Design Assessment
- is Randomized Controlled Trial
- false
- blinding
- Not applicable to a clinical-trial grade
- basis
- Mathematical and numerical model of plant development. No human randomized controlled trial is reported.
- sources
https://www.nature.com/articles/srep15358
- category
- peer-reviewed
- peer Reviewed
- true
- paper Trust Assessment
- score
- 1
- scope
- Paper
- status
- assessed
- randomized Controlled Trial
- false
- blinding
- not-confirmed
- peer Reviewed
- true
- basis
- Mathematical and numerical model of plant development. No human randomized controlled trial is reported.
- sources
https://pubmed.ncbi.nlm.nih.gov/26471765/ · https://www.nature.com/articles/srep15358
- review Scope
- Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
- assessed At
- 2026-10-27
- citations By Collection
- general
- 31
- topics
- key
- general:fibonacci-biological-patterns
- title
- Biological patterns and developmental mechanisms
- collection
- general
- trust Score
- 1
- journal Key
- scientificreports
- journal Label
- Scientific Reports
- chapter Entries
- id
- general-nature-fibonacci-srep15358
- title
- Biophysical optimality of the golden angle in phyllotaxis
- journal
- Scientific Reports
- year
- 2015
- authors
- Takuya Okabe
- doi
- 10.1038/srep15358
- pmid
- 26471765
- urls
https://www.nature.com/articles/srep15358 · https://doi.org/10.1038/srep15358 · https://pubmed.ncbi.nlm.nih.gov/26471765/
- design
- Mathematical and numerical model of plant development
- summary
- An energy-cost model identifies the golden angle as an optimum for transitions between phyllotactic fractions and reproduces several common and less common leaf-arrangement sequences.
- limitation
- The proposed evolutionary explanation depends on the chosen transition-cost model. Agreement with known patterns does not measure the assumed energy costs or establish the genetic mechanism.
- citation Count
- 31
- citation Snapshot
- count
- 31
- source
- Crossref cited-by count
- retrieved At
- 2026-10-24
- url
- https://api.crossref.org/works/10.1038/srep15358
- field
- is-referenced-by-count
- source Indexed At
- 2026-10-16T19:42:48Z
- coverage Note
- Count reflects Crossref-deposited references and can differ from publisher or other database totals. It is not a quality or clinical-evidence score.
- categories
Fibonacci mathematics · Biological pattern formation
- targets
- None recorded
- evidence
- evidence Type
- Mathematical and numerical model of plant development
- evidence Class
- proposed_biological_model
- measurement
- Phyllotactic fractions and divergence-angle cost function
- measured Genes
- None recorded
- pathways
- None recorded
- relationship Note
- Background literature only. This paper does not test or validate an OXTR–Fibonacci relationship.
- clinical Evidence
- false
- review Depth
- Abstract and selected source passages: Results; Discussion; Methods.
- full Paper Appraisal
- Not completed; review depth states the material assessed.
- record Id
- nature-fibonacci-srep15358
- quotes
- None recorded
- source Pages
- None recorded
- paper Trust Assessment
- score
- 1
- scope
- Paper
- status
- assessed
- randomized Controlled Trial
- false
- blinding
- not-confirmed
- peer Reviewed
- true
- basis
- Mathematical and numerical model of plant development. No human randomized controlled trial is reported.
- sources
https://pubmed.ncbi.nlm.nih.gov/26471765/ · https://www.nature.com/articles/srep15358
- review Scope
- Existing publication-specific assessments and bibliographic indexing; no blanket full-text appraisal.
- assessed At
- 2026-10-27
- study Design Assessment
- is Randomized Controlled Trial
- false
- blinding
- Not applicable to a clinical-trial grade
- basis
- Mathematical and numerical model of plant development. No human randomized controlled trial is reported.
- sources
https://www.nature.com/articles/srep15358
- category
- peer-reviewed
- peer Reviewed
- true
- collection
- general
- chapter Number
- 9
- topic Id
- fibonacci-biological-patterns
- topic Title
- Biological patterns and developmental mechanisms
- trust Score
- 1
- evidence
- evidence Type
- Mathematical and numerical model of plant development
- evidence Class
- proposed_biological_model
- measurement
- Phyllotactic fractions and divergence-angle cost function
- measured Genes
- None recorded
- pathways
- None recorded
- relationship Note
- Background literature only. This paper does not test or validate an OXTR–Fibonacci relationship.
- clinical Evidence
- false
- review Depth
- Abstract and selected source passages: Results; Discussion; Methods.
- full Paper Appraisal
- Not completed; review depth states the material assessed.
- jadad
- status
- not-applicable
- score
- Not recorded
- reason
- Not a human randomized controlled trial.
- condition Evidence
- None recorded
- conditions
- None recorded
- topic Trust Scores
1
- full Text
- status
- open-license
- retrieval Available
- true
- url
- https://www.nature.com/articles/srep15358
- rights
- license
- http://creativecommons.org/licenses/by/4.0/
- authors
- Takuya, Okabe
- title
- Biophysical optimality of the golden angle in phyllotaxis
- doi
- 10.1038/srep15358
- copyright
- 2015 The Author(s)
- source
- https://www.nature.com/articles/srep15358
- transformation
- Article sections extracted to plain text; navigation and recommendation sections removed. Equations, tables and image content may be incomplete; use the source for technical interpretation.
- sha256
- e992eb3c84c037c4fe1fc85e513ff359b9a506639a3340b61a8d986c0833ccf4
- checked At
- 2026-10-24