Dr Samuel Johnson BSc MSc PhD

Dr Samuel Johnson

School of Mathematics
Associate Professor in Applied Mathematics

Contact details

School of Mathematics
Watson Building
University of Birmingham
B15 2TT

Dr Johnson's research focuses on complex systems, and in particular on the relationship between structure and dynamics. Many of the questions his work addresses relate to ecology, neuroscience or society.


  • PhD in Physics (Interplay between Network Topology and Dynamics in Neural Systems), University of Granada, 2011
  • Certificate of Teaching Aptitude in Mathematics, University of Granada, 2008.
  • MSc in Physics and Mathematics (specialising in mathematical biology), University of Granada, 2008
  • BSc in Physics, University of Granada, 2006


Sam Johnson studied Physics and Mathematics at the University of Granada, Spain, where he did a PhD entitled 'Interplay between Network Topology and Dynamics in Neural Systems', under the supervision of Joaquin Torres and Joaquin Marro. He was a postdoc at the University of Oxford working with Nick Jones before taking up a Marie Curie research fellowship at Imperial College London. After a brief period in a joint position between DNV GL and the University of Bath, he became a Warwick Zeeman Lecturer at the University of Warwick in 2014. In 2017 he took up his current position at the University of Birmingham as Lecturer in Applied Mathematics.


Semester 2

LM Advanced Mathematical Biology


Research activity

Sam has many research interests, most of which can be placed under the umbrella of 'complex systems'. Some of the topics he is currently working on are as follows.

Trophic structure of directed networks: Together with colleagues in Granada, Sam recently studied a network property called 'trophic coherence', (Johnson et al., PNAS, 2014). This and subsequent work (with colleagues Miguel Ángel Muñoz, Virginia Dominguez, Janis Klaise and Nick Jones) has shown that trophic coherence is related to many aspects of complex systems, including the prevalence of cycles and feedback loops, ecological stability, motif distributions and spreading processes such as epidemics and neuronal avalanches. It has also opened several questions, such as: Does trophic coherence account for the existence of large, complex ecosystems? Can trophic structure be used to identify node function in systems like gene regulatory networks? Is there a general theory relating feedback and stability in complex, dynamical systems.

Human ecology: Work with Weisi Guo, Xueke Lu and Guillem Mosquera has show that the prevalence of violence around the world is related to the spatial distribution of cities according to a remarkably simple and robust law. We are currently looking into the causes of this effect though a combination of data analysis and agent based modelling and looking for ways in which our results can be applied.

Brain development: The neural network underlying all mental activity comes into being in a curious way: at birth it has a great many synapses (connections between neurons), about half of which are 'pruned' throughout infancy. Recent work with Ana Paula Millán, Joaquin Torres and Joaquin Marro describes a mechanism which could explain this phenomenon with a simple neural network model. We are now studying this process with more realistic neural modelling, looking into its effects in other complex systems. 

Other activities

Adviser to Polymaths R&D Ltd

Member of the Conflict Research Society


Recent publications


Rodgers, N, Tiňo, P & Johnson, S 2023, 'Influence and influenceability: global directionality in directed complex networks', Royal Society Open Science, vol. 10, no. 8, 221380. https://doi.org/10.1098/rsos.221380

Rodgers, N, Tino, P & Johnson, S 2023, 'Strong connectivity in real directed networks', Proceedings of the National Academy of Sciences, vol. 120, no. 12, e2215752120. https://doi.org/10.1073/pnas.2215752120

Rodgers, N, Tino, P & Johnson, S 2022, 'Network hierarchy and pattern recovery in directed sparse Hopfield networks', Physical Review E, vol. 105, no. 6, 064304 , pp. 64304. https://doi.org/10.1103/PhysRevE.105.064304

Budd, C, Calvert, K, Johnson, S & Tickle, SO 2021, 'Assessing risk in the retail environment during the COVID-19 pandemic', Royal Society Open Science, vol. 8, no. 5, 210344. https://doi.org/10.1098/rsos.210344

Millán, AP, Torres, JJ, Johnson, S & Marro, J 2021, 'Growth strategy determines the memory and structural properties of brain networks', Neural Networks, vol. 142, pp. 44-56. https://doi.org/10.1016/j.neunet.2021.04.027

Johnson, S 2020, 'Digraphs are different: Why directionality matters in complex systems', Journal of Physics: Complexity, vol. 1, no. 1, 015003. https://doi.org/10.1088/2632-072X/ab8e2f

Mackay, RS, Johnson, S & Sansom, B 2020, 'How directed is a directed network? How directed is a directed network?', Royal Society Open Science, vol. 7, no. 9, 201138. https://doi.org/10.1098/rsos.201138

Pilgrim, C, Guo, W & Johnson, S 2020, 'Organisational Social Influence on Directed Hierarchical Graphs, from Tyranny to Anarchy', Scientific Reports, vol. 10, no. 1, 4388. https://doi.org/10.1038/s41598-020-61196-8

Botero, JD, Guo, W, Mosquera, G, Wilson, A, Johnson, S, Aguirre-Garcia, GA & Pachon, LA 2019, 'Gang confrontation: The case of Medellin (Colombia)', PLoS ONE, vol. 14, no. 12, e0225689. https://doi.org/10.1371/journal.pone.0225689

Pagani, A, Mosquera, G, Alturki, A, Johnson, S, Jarvis, S, Guo, W, Varga, L & Alan G, W 2019, 'Resilience or robustness: Identifying topological vulnerabilities in rail networks', Royal Society Open Science, vol. 6, no. 2, 181301. https://doi.org/10.1098/rsos.181301

Millan, AP, Torres, J, Johnson, S & Marro, J 2018, 'Concurrence of form and function in developing networks and its role in synaptic pruning', Nature Communications, vol. 9, no. 1, 2236. https://doi.org/10.1038/s41467-018-04537-6

Klaise, J & Johnson, S 2018, 'Relaxation dynamics of maximally clustered networks', Physical Review E, vol. 97. https://doi.org/10.1103/PhysRevE.97.012302

Johnson, S & Jones, NS 2017, 'Looplessness in networks is linked to trophic coherence', National Academy of Sciences. Proceedings, vol. 114, no. 22, pp. 5618-5623. https://doi.org/10.1073/pnas.1613786114


Johnson, S 2024, 'Epidemic modelling requires knowledge of the social network', Journal of Physics: Complexity, vol. 5, no. 1, 01LT01. https://doi.org/10.1088/2632-072X/ad19e0

Review article

Eastwood, N, Stubbings, WA, Abdallah, MA-E, Durance, I, Paavola, J, Dallimer, M, Pantel, JH, Johnson, S, Zhou, J, Hosking, JS, Brown, J, Ullah, S, Krause, S, Hannah, D, Crawford, S, Widmann, M & Orsini, L 2022, 'The Time Machine framework: monitoring and prediction of biodiversity loss', Trends in Ecology & Evolution, vol. 37, no. 2, pp. 138-146. https://doi.org/10.1016/j.tree.2021.09.008

View all publications in research portal