International Conference MPDEE’18

Models in Population Dynamics, Ecology and Evolution

International Conference

Models in Population Dynamics, Ecology, and Evolution (MPDEE’18)

University of Leicester (UK), April 9-13, 2018

Sponsored by the London Mathematical Society and the University of Leicester

Organizers: Andrew Morozov and Sergei Petrovskii

(University of Leicester, UK)

Aims and Scope

The meeting will consider applications of mathematical modelling to explore processes and mechanisms in various biological systems ranging from a cell to the human society. A special focus will be on the interplay between ecology and evolution across time and space. MPDEE’18 is also expected to explore similarities between modelling techniques traditionally applied in ecology and evolution and those used in other life sciences with the purpose to enhance interdisciplinary approaches and to stimulate further advances in population dynamics, ecology and evolution. The meeting will be an open forum for interaction between theoreticians and empirical biologists with the main goal of enhancing communication between the two groups to better link theories with empirical realities.

Organization & structure

Honorary Lectures: Michel Loreau (Moulis, France) Andrew Liebhold (Morgantown, USDA Forest Service, USA)

Plenary Speakers: Elaine Crooks (Swansea, UK) Donald DeAngelis (Miami, USA) Sergey Gavrilets (Knoxville, USA) Mats Gyllenberg (Helsinki, Finland) Rainer Klages (London, UK) John McNamara (Bristol, UK) Hans Metz (Leiden, The Netherlands) Ran Nathan (Jerusalem, Israel) Rachel Norman (Stirling, UK) Andre de Roos (Amsterdam, The Netherlands)

Advisory Scientific Committee: Edward Codling (Colchester, UK) Alexander Gorban (Leicester, UK) Eva Kisdi (Helsinki, Finland) Roberto Kraenkel (Sao Paolo, Brazil) Horst Malchow (Osnabrueck, Germany) Natalia Petrovskaya (Birmingham, UK) Jean-Christophe Poggiale (Marseille, France) Jonathan Sherratt (Edinburgh, UK) Ezio Venturino (Turin, Italy)

Local organizing committee: Oksana Gonchar (University of Leicester, UK) Simran Sandhu (University of Leicester, UK) Anna Zincenko (University of Leicester, UK) Abridged timetable of MPDEE’18 Monday April 9th

8.20-9.00 Registration 9.00-9.10 Welcome talk 9.10-10.00 Plenary talk 1 (Mats Gyllenberg) 10.00-10.50 Plenary talk 2 (Sergey Gavrilets) 10.50-11.20 Coffee break 11.20-13.00 Theoretical Ecology-1 Eco-Evolutionary Models-1 13.00-14.10 Lunch break 14.10-15.50 Theoretical Ecology-2 Population Dynamics of Cells 15.50-16.20 Coffee break 16.20-18.00 Ecological Modelling-1 Evolutionary Models-1

Tuesday April 10th

9.00-9.50 Plenary talk 3 (John McNamara) 9.50-10.40 Plenary talk 4 (Hans Metz) 10.40-11.10 Coffee break 11.10-12.50 Theoretical Ecology-3 Evolutionary Models-2 12.50-14.00 Lunch break 14.00-15.40 Mathematical Methods Evolutionary Models-3 15.40-16.10 Coffee break 16.10-17.50 Epidemiology Eco-Evolutionary Models-2 18.00-20.00 Reception and poster session

Wednesday April 11th

9.00-9.50 Plenary talk 5 (Ran Nathan) 9.50-10.40 Plenary talk 6 (Rainer Klages) 10.40-11.10 Coffee break 11.10-12.50 Movement Ecology Topics in Mathematical Biology 12.50-14.00 Lunch break 14.00-15.40 Spatial Ecology-1 Minisymposium Advances in Adaptive dynamics 15.40-16.10 Coffee break 16.10-17.00 Dispersal and Invasions Modelling Evolutionary Fitness 17.05-18.05 Honorary Lecture (Andrew Liebhold)

Thursday April 12th

9.00-9.50 Plenary talk 7 (André de Roos) 9.50-10.40 Plenary talk 8 (Rachel Norman) 10.40-11.10 Coffee break 11.10-12.50 Topics in Ecology-1 Models of Human Evolution 12.50-14.00 Lunch break 14.00-15.40 Models of Food Webs Ecological Modelling-2 15.40-16.10 Coffee break 16.10-17.00 Community Ecology Models Topics in Ecology-2 17.05-18.05 Honorary Lecture (Michel Loreau)

Friday April 13th

9.00-10.40 Population Dynamics Modelling Spatial Ecology-2 10.40-11.10 Coffee break 11.10-12.00 Plenary talk 9 (Elaine Crooks) 12.00-12.50 Plenary talk 10 - Closing Lecture (Donald DeAngelis) 12.50-13.00 Closing address and the end of the conference

Detailed Conference Program

Monday April 9th

Venue: Bennett Building, ground floor 8.20-9.00 Registration ------

9.00-10.50 Introduction and plenary talks 1, 2

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 9.00-9.10 Introduction and welcome address 9.10-10.00 Plenary talk 1. Mats Gyllenberg (University of Helsinki, Finland). Finite dimensional state representation of physiologically structured populations 10.00-10.50 Plenary talk 2. Sergey Gavrilets (University of Tennessee, Knoxville, USA). Modelling the evolutionary origins and dynamics of social complexity.

------10.50-11.20 Coffee break: Bennett Building, ground floor ------

11.20-13.00 Theoretical Ecology-1

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 11.20-11.45 Axel Rossberg (Queen Mary University of London, UK). On the irrelevance of ecological theory and modelling. 11.45-12.10. Inkyung Ahn (Korea University, South Korea) Predator-prey model with predation- induced dispersal in a heterogeneous environment. 12.10-12.35 Michiel Stock (Ghent University, Belgium). Disentangling ecological networks using graph embedding methods 12.35-13.00 Andrew Hoyle (University of Stirling, UK). Optimising antibiotic dosage regimens to treat bacterial infections.

11.20-13.00 Eco-Evolutionary Models-1

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 11.20-11.45 Theodore Galanthay (Ithaca College, USA). A game-theoretic approach to modeling ecological dynamics. 11.45-12.10. Mathias Gauduchon (Aix-Marseille University, France). Adaptive evolution of trophic networks: gradual construction, emergence of functional diversity. 12.10-12.35. Orestes Gutierrez Al-Khudhairy (Queen Mary University of London, UK). How trophic interactions are constrained over evolutionairy timescales. 12.35-13.00. Ruben Ceulemans (University of Potsdam, Germany) Effects of introducing trait variation on the dynamics of a tritrophic food chain.

------13.00-14.10 Lunch break ------

14.10-15.50 Theoretical Ecology-2

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 14.10-14.35. Géza Meszéna (Eötvös University, Hungary) Sympatric, or allopatric? Adaptive emergence of reproductive isolation in different ecological situations. 14.35-15.00. D’ (Queen Mary University of London, UK) Ecological structurally stability and spatial coexistence mechanisms in model metacommunities. 15.00-15.25. Daniel Bearup (University of Kent, UK) The emergence of mutualistic relationships in communities of competing ecosystem engineers. 15.25-15.50. Jonathan Potts (University of Sheffield, UK) How movement responses can shape demographic dynamics in strongly competing populations.

14.10-15.50 Population Dynamics of Cells

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 14.10-14.35. Vitaly Ganusov (University of Tennessee, USA). Clustering of CD8 T cells around malaria-infected hepatocytes is rapid and is driven by antigen-specific T cells. 14.35-15.00. Vuk Milisic (Université Paris 13, France). Mathematics modelling of cell adhesion forces: from global to local existence, from delay to friction. 15.00-15.25. Yuriy Pichugin (Max Planck Institute for Evolutionary Biology, Plön, Germany) Evolution of simple multicellular life cycles in a dynamic environment. 15.25-15.50. Cordula Reisch (TU Braunschweig, Germany). Impact of geometry variations on solutions of reaction-diffusion models for hepatitis C infections. ------15.50-16.20 Coffee break: Bennett Building, ground floor ------

16.20-18.00 Ecological Modelling-1

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 16.20-16.45. Michael Sieber (Max Planck Institute for Evolutionary Biology, Germany). Prophage- mediated competition between two key members of the Hydra vulgaris microbiota. 16.45-17.10. Robert Manning Smith (Rothamsted Research, UK). Modelling lifestyle change in Arsenophonus phytopathogenicus, from mutualistic insect-endosymbiont to plant pathogen. 17.10-17.35. Tanya Rogers (Northeastern University, USA). Hidden similarities in the asynchronous dynamics of Atlantic blue crab populations 17.35-18.00. Nicola Walker (CEFAS, UK). Can individual-based models provide useful insights into the management of recreational and commercial fisheries?

16.20-18.00 Evolutionary Models-1

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 16.20-16.45. George Constable (University of Bath, UK). Why do most species have so few mating types, yet some have so many? 16.45-17.10. Louise Chevalier (UMR ECOBIOP, INRA, France). A dynamic game theoretical model predicts variance in choosiness when mate availability fluctuates. 17.10-17.35. Xiang-Yi Li (University of Zürich, Switzerland) Evolution of sexual dimorphism by intersexual resource competition. 17.35-18.00. Karan Pattni (University of Liverpool, UK). Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population.

Time for rest and relaxation

Tuesday April 10th

9.00-10.40 Plenary talks 4,5 Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 9.00-9.50 Plenary talk 4. John McNamara (University of Bristol, UK). Phenotypic integration of genetic and epigenetic information from a Darwinian perspective 9.50-10.40 Plenary talk 5. Hans Metz (Leiden University, the Netherlands). Conflict between alleles and modifiers in the evolution of genetic polymorphisms. ------10.40-11.10 Coffee break: Bennett Building, ground floor ------

11.10-12.50 Theoretical Ecology -3

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 11.10-11.35. Josef Hofbauer (University of Vienna, Austria) Permanence via the invasion graph. 11.35-12.00. Nadav Shnerb (Bar Ilan University, Israel) Population and community dynamics under environmental stochasticity. 12.00-12.25. Alberto Pascual-García (ETH-Zürich, Switzerland). Structural stability of complex ecosystems: effective competition theory and the role of mutualistic interactions in biodiversity maintenance. 12.25-12.50. Haim Weissmann (Bar Ilan University, Israel). Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition

11.10-12.50 Evolutionary Models-2

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2). 11.10-11.35. Max Souza. (Universidade Federal Fluminense, Brazil). Fixation: the fingerprint of evolutionary processes. 11.35-12.00. Francisco Herrerías Azcué. (University of Manchester, UK) Stirring does not make populations well mixed - The effect of motion on fixation probability. 12.00-12.25. Nurdan Cabukoglu (University of Leicester, UK). Predator-prey diffusion dependence of reproduction coefficient. 12.25-12.50. Christopher Overton. (University of Liverpool, UK) Deterministic approximations of stochastic dynamics in evolutionary graph theory.

------12.50-14.00 Lunch break ------

14.00-15.40 Mathematics Methods

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 14.00-14.25. Jean-Christophe Poggiale (Aix-Marseille University, France). Geometric tools for multiple time scales problems: applications in ecological modelling. 14.25-14.50. Atheeta Ching (University College London, UK). The carrying simplex in non- competitive Lotka-Volterra systems. 14.50-15.15. Matthew Adamson (University of Osnabruck, Germany). Anticipating nonlocal critical transitions in nearly-1D systems. 15.15-15.40. Katherine Heath (University of Oxford, UK). Types of competition in mosquito larvae influence adult population dynamics.

14.00-15.40 Evolutionary Models -3

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 14.00-14.25. Marcel Weiss (University of Cambridge, UK). Studying the causes of phenotype robustness and evolvability in genotype-phenotype maps. 14.25-14.50. Marco Colnaghi (University College London, UK) Quality and quantity: selection over mitochondrial genomes determines female germline development. 14.50-15.15. Alexander Leonard (University of Cambridge, UK) The evolution of symmetric and asymmetric protein binding interfaces. 15.15-15.40. Tim Russell (Royal Holloway, University of London, UK). Fluctuating dynamics in breakage-dependent selection and recombination systems. ------15.40-16.10 Coffee break: Bennett Building, ground floor ------

16.10-17.50 Epidemiology

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1)

16.10-16.35. Thomas Rawson (University of Oxford, UK) .Optimal control approaches for combining medicines and mosquito control in tackling dengue. 16.35-16.00. Amit Chattopadhyay (Aston University, UK). Do we need vaccination? 17.00-17.25. Latifat Erinle-Ibrahim (Tai Solarin University of Education, Ijagun, Nigeria). The mathematical modelling of the effect of treatment on the transmission of pneumonia infection. 17.25-17.50. Jitendra Singh (PPN College Kanpur, India). The effect of density dependent emigration on the spread of infectious diseases: A Modelling study

16.10-17.50 Eco-Evolutionary Models-2

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 16.10-16.35. Kalle Parvinen (University of Turku, Finland). Evolution of dispersal in metapopulation models. 16.35-17.00. Peter Czuppon (Max Planck Institute for Evolutionary Biology, Germany). Does ecology affect evolutionary processes? Fixation behavior under stochastically fluctuating population size. 17.00-17.25. Elias Ehrlich (University of Potsdam, Germany). Trait-fitness relationships determine how trade-off shapes affect species coexistence. 17.25-17.50. Leonardo Miele (University of Leeds, UK) Eco-Evolutionary dynamics and the emergence of life cycles in microbial populations.

------18.00-20.00 Poster session and wine reception: Bennett Building, ground floor ------

Time for rest and relaxation

th Wednesday April 11

9.00-10.40 Plenary talks 6,7 Venue: Bennett Building, Bennett Building, Lecture Theatre 1 (BEN LT1) 9.00-9.50 Plenary talk 5. Ran Nathan (University of Jerusalem, Israel). Progress, emerging challenges and new opportunities in movement ecology: Ten years after PNAS 9.50-10.40 Plenary talk 6. Rainer Klages (Queen Mary University of London, UK). Statistical physics and anomalous dynamics of foraging.

------10.40-11.10 Coffee break: Bennett Building, ground floor ------

11.10-12.50 Movement ecology

Venue: Bennett Building, Lecture Theatre 1 (BEN LT 1). 11.10-11.35. Edward Codling (University of Essex, UK). Modelling the efficiency of animal navigation strategies. 11.35-12.00. Paulo Tilles (University of Leicester, UK). On stochastic animal movement across temporal scales. 12.00-12.25. Andy Reynolds (Rothamsted Research, UK). Langevin dynamics encapsulate the microscopic and emergent macroscopic properties of midge swarms. 12.25-12.50. Eslene Bikoumou (University of Portsmouth, UK). How do foraging animals adapt their behaviour when competing (or cooperating) in a shared environment?

11.10-12.50 Topics in Mathematical Biology

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2). 11.10-11.35. Yuval Zelnik (CNRS, Moulis, France). The three regimes of spatial recovery. 11.35-12.00. Michael Stich (Mathematics, Aston University, UK) Evolutionary search processes in simple replicator populations. 12.00-12.25. Aviad Heifetz (Open University of Israel, Israel). Feeding at the nest in polygamous groups as a public-good game with intra-sex competition. 12.25-12.50. Rajneesh Dwevedi (Amity University, Noida, India). Modelling of breeding population of Painted Stork, Mycteria leucocephala: A 37-year long study in Keoladeo National Park

------12.50-14.00 Lunch break ------

14.00-15.40 Spatial Ecology -1

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 14.00-14.25. Horst Malchow (Osnabrück University, Germany). Spatial coexistence of competitors in a variable environment. 14.25-14.50. Merlin Christopher Köhnke (Osnabrück University, Germany). Wave pinning in a variable environment. 14.50-15.15. Helena Stage (University of Manchester, UK). Anomalous metapopulation dynamics on scale-free networks. 15.15-15.40. Bernd Blasius (ICBM, University of Oldenburg). Yule-Simon process determines the worldwide spread of alien species over centuries.

14.00-15.40 Minismposium dvances in daptive dnamics’.

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 14.00-14.25. Stefan Geritz (University of Helsinki, Finland) Resident-invader dynamics of similar strategies in non-constant environments. 14.25-14.50. Sébastien Lion (CEFE CNRS, Montpellier, France) Spatial evolutionary ecology: short- and long-term theory. 14.50-15.15. Åke Brännström (Umeå University, Sweden). Adaptive dynamics for spatially- structured population. 15.15-15.40. Louise Lassalle (University of Amsterdam, the Netherlands). Evolution of life history vartiations in a physiologically structured population.

------15.40-16.10 Coffee break: Bennett Building, ground floor ------

16.10-17.00 Dispersals and Biological Invasions

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 16.10-16.35. Robert West (University of Leeds, UK). The influence of external and internal noise on the cyclic Lotka-Volterra model. 16.35-17.00. Natalia Petrovskaya (University of Birmingham, UK). Detection and classification of spatial patterns arising during invasive spread: is seeing believing?

16.10-17.00 Modelling Evolutionary Fitness

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 16.10-16.35. Oleg Kuzenkov (Lobachevsky State University, Russia). Towards constructing a mathematically rigorous framework for modelling evolutionary fitness. 16.35-17.00. Simran Sandhu (Mathematics, University of Leicester) Revealing evolutionary optimal strategies in self-reproducing systems via a new computational approach.

------

17.05-18.05 Honorary Lecture

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1)

17.05-18.05 Andrew Liebhold (Forest Service Northern Research Station, USA). Modelling invasions from start to finish.

Time for rest and relaxation

th Thursday April 12

9.00-9.50 Plenary talks 7,8

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 9.00-9.50 Plenary talk 7. André de Roos (University of Amsterdam, The Netherlands). Linking individual life history and population dynamics using physiologically structured population models. 9.50.10-10.40. Plenary talk 8. Rachel Norman (University of Stirling, UK). Using mathematical models to understand tick borne pathogen dynamics and control in a multi-host system with multiple transmission routes. ------10.40-11.10 Coffee break: Bennett Building, ground floor ------

11.10-12.50 Topics in Ecology -1

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1).

11.10-11.35. Henri Laurie (University of Cape Town, South Africa). A population of DEB individuals can be analysed using supply/demand analysis to determine the most sensitive parameters. 11.35-12.00. Angela Martiradonna (Institute for Applied Mathematics, CNR, Italy). Optimal spatiotemporal control of Ailanthus altissima (Mill.) Swingle in the Alta Murgia National Park. 12.00-12.25. Rik Verdonck (SETE, Moulis, France). Phase-related behaviour in the desert locust: classification versus characterization. 12.25-12.50. Slimane Ben Miled (University of Tunis el Manar, Tunisia). HermaDEB: An IBM for energy allocation in hermaphrodites.

11.10-12.50 Models of Human Evolution

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2). 11.10-11.35. John Bryden (Royal Holloway University of London, UK) Groups, words and how humans transmit language: insights in language dynamics from Twitter. 11.35-12.00. Mauricio González-Forero (University of St Andrews, UK). Inference of ecological and social drivers of human brain-size evolution 12.00-12.25. Martina Testori. (University of Southampton, UK) How psychopathic people help us to survive (or not)? 12.25-12.50. Belgin Seymenoglu (University College London, UK) Invariant manifolds of the selection-recombination model from population genetics.

------12.50-14.00 Lunch break ------

14.00-15.40 Models of Food Webs

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 14.00-14.25. Alexey Ryabov (University of Oldenburg, Germany). Imperfect prey selectivity of predators promotes biodiversity and irregularity in food webs. 14.25-14.50. Kai Uwe von Prillwitz (University of Oldenburg, Germany). Mid-domain effect for food chain length 14.50-15.15. Max Lindmark (Swedish University of Agricultural Sciences, Sweden). Species interactions determine effects of warming on stability in a stage-structured food chain. 15.15-15.40. Markus Stark (University of Potsdam, Germany). How spatial networks affect food web structure and persistence.

14.00-15.40 Ecological Modelling-2

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 14.00-14.25. Daniele Bevacqua (INRA, Avignon, France). A model for temporal dynamics of brown rot spreading in fruit orchards. 14.25-14.50. Andrew Dean (University of Liverpool, UK). Toxin-mediated competition in bacterial communities. 14.50-15.15. Sami Lehtinen (University of Helsinki, Finland). Understanding the Venus flytrap through mathematical modelling. 15.15-15.40. Kevin Liautaud (CNRS, Moulis, France). Uniting individualistic and organismic visions of nature with competition theory.

------15.40-16.10 Coffee break: Bennett Building, ground floor ------

16.10-17.00 Community Ecology Models

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 16.10-16.35. Jean-François Arnoldi (CNRS, Moulis, France). Generic assembly patterns in complex ecological communities. 16.35-17.00. Matthieu Barbier (CNRS, Moulis, France). Dimensionality reduction of complex food web dynamics. 16.10-17.00 Topics in Ecology -2

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 16.10-16.35. Jaqueline Maria da Silva (University of Leicester, UK). A study about seeds dispersion and vegetation dynamics. 16.35-17.00. Paola Correa (Pontificia Universidad Catolica de Chile, Chile). Towards a metastability approach: Outbreaks of mice in Australia ------

17.05-18.05 Honorary Lecture

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1)

17.05-18.05 Michel Loreau (CNRS, Moulis, France).Biodiversity and stability of ecological systems: A new look at an old debate

Time for rest and relaxation

th Friday April 13

09.00-11.05 Population Dynamics Modelling

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1 ) 09.00-09.25. Malay Banerjee (IIT Kanpur, India). Consequences of Allee effect in predator growth on prey-predator dynamics. 09.25-09.50. Jehan M.K. Al-Ameri (University of Leicester, UK) Fast numerical evaluation of periodic solutions for a class of nonlinear systems and its applications for parameter estimation problems. 09.50-10.15. Anna Zincenko (University of Leicester, UK). An economic-demographic dynamical system. 10.15-10.40. Anuraj Singh (IIITM Gwalior, India). Complex dynamics in a fractional-ordered prey- predator model.

09.00-11.05 Spatial Ecology-2

Venue: Bennett Building, Lecture Theatre 2 (BEN LT2) 09.00-09.25. Yuri Tyutyunov (SSC RAS, Rostov-on-Don, Russia). Spatial demogenetic models of population dynamics. 09.25-09.50. John Ellis (University of Birmingham, UK). An IBM study of spatial patterns arising in the density dependent population movement. 09.50-10.15. Christopher Terry (University of Oxford, UK). Identifying significant trophic interaction modifications for the population dynamics of ecological communities. 10.15-10.40. TBA.

------10.40-11.10 Coffee break: Bennett Building, ground floor ------

11.10-12.50 Plenary talks 9, 10

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1) 11.10-12.00. Plenary talk 9. Elaine Crooks (Swansea University, UK) Invasion speeds in a competition-diffusion model with mutation. 12.00-12.50 Plenary talk 10 (Closing Lecture). Donald DeAngelis (University of Miami, USA) Carrying capacity in a heterogeneous environment: experiments and resolution of a paradox. ------

12.50-13.00 Closing address and end of meeting.

Venue: Bennett Building, Lecture Theatre 1 (BEN LT1)

Honorary and Plenary Talks

(in alphabetic order)

Elaine Crooks, Department of Mathematics, Swansea University, UK

Invasion speeds in a competition-diffusion model with mutation

Abstract

We consider a reaction-diffusion system modelling the growth, dispersal and mutation of two phenotypes. This model was proposed by Elliott and Cornell (2012), who found evidence that for a class of dispersal and growth coefficients and a small mutation rate, the two phenotypes spread into the unstable extinction state at a single speed that is faster than either phenotype would spread in the absence of mutation. Under suitable smallness conditions on the effect of mutation and inter-morph competition, we prove that the spreading speed of the two phenotypes is indeed determined by the linearisation about the extinction state, and then deduce both that the spreading speed is a non- increasing function of the mutation rate, implying that greater mixing between phenotypes leads to slower propagation, and determine the ratio at which the phenotypes occur in the leading edge in the limit of vanishing mutation.

This is joint work with Luca Börger and Aled Morris (Swansea University, UK).

Donald DeAngelis, Department of Biology, University of Miami, USA

Carrying Capacity in a Heterogeneous Environment: Experiments and Resolution of a Paradox

Abstract

Spatial models, such as the logistic and related equations, show that populations diffusing in environments with heterogeneously distributed local carrying capacity can under some conditions reach higher total equilibrium size than if non-diffusing, and higher size than if the same total carrying capacity is uniformly distributed. It is shown here that this apparently paradoxical result does not hold when energetic constraints on population growth are taken into account. When spatial models of diffusing consumers are extended to include an exploitable resource, they show that higher equilibrium total population size can be reached when the population is diffusing than not, but that a homogeneous distribution with the same total resource input leads to the same or higher total population size than if the inputs were spread heterogeneously. We tested our theoretical predictions using experiments in the budding yeast Saccharomyces cerevisiae, in which a limiting nutrient was spatially distributed to create both heterogeneous and homogeneous carrying capacities, and cultures were propagated with and without spatial diffusion. The experiment confirmed the mathematical results.

This is joint work with Bo Zhang2, David Van Dyken2 and Wei-Ming Ni3,4

1Wetland and Aquatic Research Center, U. S Geological Survey, Gainesville, FL, USA 2Department of Biology, University of Miami, Coral Gables, FL, USA 3School of Mathematics, University of Minnesota, MN, USA 4Center for Partial Differential Equations, East China Normal University, P. R. China

Sergey Gavrilets, University of Tennessee, Knoxville, USA

Modelling the evolutionary origins and dynamics of social complexity

Abstract

Intensive research by generations of evolutionary biologists and other life-scientists has led to major advances in our understanding of how new species arise and evolve — the central theme of Darwin’s revolutionary book “On the Origin of Species” (1859). I believe the time is ripe for these advances to be applied to humans, a species to which we naturally attach special importance. It is now well recognized that understanding modern human behavior, psychology, culture, and certain economic and political processes is hardly possible without also considering factors and processes that were shaping our recent evolution. Deciphering the problems of human origins and subsequent social and cultural evolution requires a concerted effort of researchers from a diverse set of disciplines including biology, anthropology, psychology, economics, history as well as mathematics and computational science. If we, as scientists, are successful in this endeavor, the societal impact will be enormous. I will illustrate some advances in this area based on close integration of empirical and theoretical approaches.

Mats Gyllenberg, Department of Mathematics and Statistics, University of Helsinki, Finland

Finite dimensional state representation of physiologically structured populations

Abstract

In a physiologically structured population model, individuals are characterised by certain variables, collectively called their i-state. The world in which these individuals live is characterised by another set of variables, collectively called the environmental condition. The model consists of submodels for (i) the dynamics of the i-state, i.e., growth/maturation, (ii) survival and (iii) reproduction, with the relevant rates described as a function of (i-state, environmental condition). When the environmental condition is an input, i.e., a given function of time, the population model is linear. Density dependence and interaction with other populations is captured by feedback via the environment, i.e., by letting the environmental condition be influenced by output, for which yet another submodel has to be specified. This yields a systematic methodology for formulating a community model by combining building blocks that use a linear population model to define a nonlinear input-output map.

For some combinations of submodels the structured (= infinite dimensional) population model may be replaced by a finite dimensional ODE without loss of relevant information. In this talk I will give necessary and sufficient conditions for when such a reduction is possible, given ertain restrictions. These restrictions are: (i) one-dimensional i-state, (ii) deterministic i-state dynamics, (iii) the completeness of the catalogue concerns the combined effect of growth and survival, (iv) the reproduction submodel is restricted a posteriori.

This is joint work with Odo Diekmann1 and Hans Metz2.

1Utrecht University, the Netherlands 2Institute of Biology Leiden, Leiden University, the Netherlands

Rainer Klages, Queen Mary University of London, UK; Institute for Theoretical Physics, University of Cologne, Germany; Institute of Theoretical Physics, Technical University of Berlin, Germany

Statistical Physics and Anomalous Dynamics of Foraging

Abstract

A question that attracted a lot of attention in the past two decades is whether biologically relevant search strategies can be identified by statistical data analysis and mathematical modelling [1]. A famous paradigm in this field is the Lévy Flight Foraging Hypothesis. It states that under certain mathematical conditions Lévy dynamics, which defines a key concept in the theory of anomalous stochastic processes, leads to an optimal search strategy for foraging organisms. This hypothesis is discussed controversially in the current literature. I will review examples and counterexamples of experimental data and their analyses confirming and refuting it. Related to this debate is own work about biophysical modelling of bumblebee flights under predation threat [2] and biological cell migration [3], both based on experimental data analysis, which I briefly outline.

References

[1] R. Klages, Search for food of birds, fish and insects, chapter in: A.Bunde et al. (Eds.), Diffusive Spreading in Nature, Technology and Society (Springer, Berlin, 2018), p.49-69 [2] F.Lenz et al., Phys. Rev. Lett. 108, 098103 (2012) [3] P.Dieterich et al., PNAS 105, 459 (2008)

Andrew M. Liebhold, US Forest Service Northern Research Station, Morgantown West Virginia, USA

Modelling invasions from start to finish

Abstract

Biological invasions comprise one of the most serious current environmental problems worldwide and evidence indicates that trends of continuing globalization will tend to intensify the problem. Understanding the processes driving invasions and devising strategies for mitigating these problems represent serious challenges for ecologists. Mathematical models have played crucial roles in providing insight into the invasion problem and provide unique possibilities for developing effective invasion management efforts. Here, I review some types of models that have been useful for work on various phases of the invasion process.

Though the vast majority of species in the world have never established outside of their native range, there is evidence that successive invasions deplete the supply of invasive species. I present a model that captures this information and provides a framework for predicting future invasions under varying levels of future trade.

When invading populations initially arrive, they typically exist at very low densities and the dynamics of such populations may be strongly affected by stochasticity and Allee effects. I will illustrate how models that capture Allee effects can be used to explore strategies for eradicating invading populations.

The spread phase of biological invasions results from the coupling of population growth with dispersal. Considerable work has focused on models to capture the dynamics of spread of invading populations. I discuss how these models can be used to draw inference on effective barrier zone strategies for containment of spread during invasions.

Michel Loreau, Centre for Biodiversity Theory and Modelling Theoretical and Experimental Ecology Station CNRS & Paul Sabatier University, Moulis, France

Biodiversity and stability of ecological systems: A new look at an old debate

Abstract

The relationship between the diversity and stability of ecological systems has been a hotly debated issue in ecology over the past century. Recent theoretical and experimental work provides a completely new perspective and a potential resolution of this debate. In contrast to classical theory, which is based on stability measures that are largely divorced from empirical data, new theory based on invariability predicts different diversity–stability relationships at the population and ecosystem levels. It also provides a consistent hierarchical framework for studying ecosystem stability across multiple spatial scales. This new theory agrees with empirical and experimental data and shows that biodiversity plays an important stabilising role in ecosystems at multiple scales, thereby ensuring the steady provision of ecosystem services to human societies.

John McNamara, Department of Mathematics, University of Bristol, UK

Phenotypic integration of genetic and epigenetic information from a Darwinian perspective

Abstract It is often useful to think of developmental systems as integrating available sources of information about current conditions to produce organisms. Genes and inherited physiology provide cues, as does the state of the environment during development. The integration systems themselves are under genetic control and subject to Darwinian selection, so we expect them to evolve to produce organisms that fit well with current ecological (including social) conditions. I will illustrate these concepts using a series of models, identifying how the weights put on specific types of cue depend on environmental properties. I will also comment on the synergy, or lack of it, between different cues. Genes as cues are of particular interest, and I illustrate the possibility that genes can act as cues of relatedness and can affect social behaviour through epistatic modifiers. Finally, I show that clustered genes coding for ecological specialism and unlinked generalist genes coding for phenotypic plasticity differ in their evolutionary interest, so that there can be genetic conflict.

Hans Metz, Institute of Biology Leiden, Leiden University, the Netherlands

Conflict between alleles and modifiers in the evolution of genetic polymorphisms

Abstract

The Canonical Equation of adaptive dynamics is a differential equation for the adaptive change of observable traits over evolutionary time, derivable through subsequent limits from individual-based trait-differentiated population models including rare mutations with small effect. In this talk I describe an example of how this CE can be used to arrive at a somewhat unexpected biological conclusion. In diploid Mendelian populations the average offspring number in the branching process by which a mutant allele invades into some resident population can be decomposed into a micro-gametic and a macro-gametic contribution (in humans through sperm or eggs). The standard population genetics assumption is that these two contributions are equal. However, realistically speaking this is generically never the case. I therefore do not assume equality. Focus on some protected polymorphism, i.e., a polymorphism such that each of the two alleles has average offspring number larger than 1 in the ecological and genetic environment produced by a population of homozygotes of the other allele.

We can then write down two different CEs for the evolutionary change of the polymorphism, one for the case where only the focal alleles evolve, the other for the case where only the rest of the genome evolves (usually referred to as modifier evolution). Not only are the CE's different, they also have different equilibria. Hence there is an intra-genomic conflict between the two sorts of players. Of course, for the description of reality both CE's have to be combined into one, with the contributions of the two mechanisms weighted with the respective relative mutation frequencies. As the rest of the genome will in general produce more relevant mutations than the focal alleles, we may expect that overall the modifiers will win. However, when the population has settled at a modifier dominated ESS, still once in a while a mutant in the focal alleles will produce a change in phenotypes that will quickly be undone again by the modifiers. The effect will be a continual turnover of the genome with no visible effect. Although from an ecological perspective the inferred arms race should be generic, it does not occur in the standard simplified models from the literature: if one argues backwards to see under which conditions it will not occur, the main commonly used simplifications pop out. For the connection with the real world the most interesting case is when there are two separate sexes with their own genotype to phenotype maps (males can have different values of the trait than females). This leads to the prediction that hermaphroditic species (e.g. most seed plants, but also quite some animals) should have faster genome turnover than species with separate sexes.

Ran Nathan, Alexander Silberman Institute of Life Sciences, the Hebrew University of Jerusalem, Jerusalem, Israel

Progress, emerging challenges and new opportunities in movement ecology: Ten years after PNAS

Abstract

The emerging field of movement ecology largely benefited from the recent development in wildlife tracking technologies, enhanced computation abilities and powerful data analysis tools. Movement ecology studies have utilized those technological advances, along with new conceptual/theoretical frameworks, to elucidate movement patterns, the underlying movement processes and their ecological and evolutionary consequences. Despite these significant advances, some of the key questions on how movement shapes the ecology, behavior and evolution of organisms across multiple spatial and temporal scales remain unresolved. In this talk, I will highlight some of the most exciting developments and challenges in movement ecology since the introduction of this paradigm in a Special Feature published in PNAS ten years ago. These include (i) reexamination of previous dogmas, conceptions and assumptions that have long underlined ecological, behavioral and evolutionary research; (ii) promises and difficulties in the forthcoming Big Data revolution generated by the recent burst of high-throughput tracking technologies; and (iii) new opportunities to address big unanswered questions such as Why do young inexperienced animals die and how they improve performance with age and experience? How do animals find their way in the dark? and What are the most important “things” in life?

Rachel A Norman, Department of Computing Science and Mathematics, University of Stirling, UK

Using mathematical models to understand tick borne pathogen dynamics and control in a multi-host system with multiple transmission routes

Abstract

In this talk I will introduce Louping ill virus as an example of a tick borne pathogen which is transmitted through multiple pathways and by multiple hosts. I will present some key results from over 20 years of model development at different scales including the predicted effects of different control methods and the predicted changes in risk due to climate change.

André M. de Roos, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, The Netherlands.

Linking individual life history and population dynamics using physiologically structured population models

Abstract

Many problems in ecology and evolution revolve around the question how individual life history influences population and community dynamics or vice versa how the population and community setting influences selection and adaptation of individual life histories. Physiologically structured population models are well suited to address such questions as this class of models represents the reproduction, development and mortality of individuals during their life history as dependent on the state of the individual itself and the environment it lives in. These structured population models hence consistently translate the individual life history to the population level and in turn account for density dependent, population feedback on life history through changes in the environment that the individual experiences. In recent years, a general methodology has been developed to carry out demographic, equilibrium (bifurcation) and evolutionary analysis of physiologically structured population models, which in its simplest form boils down to the numerical evaluation of the Lotka- Euler integral equation for computing population growth rates. I will give an introduction to the general methodology and illustrate its application with a few examples.

Theme sessions and minisymposia talks

(in alphabetic order)

Matthew Adamson, Institute of Environmental Systems Research, University of Osnabruck, Germany

Anticipating nonlocal critical transition in neatly-1D systems Abstract

Much research in recent years has been devoted to the construction of generic methods for anticipating critical transitions from time series data. While a lot of progress has been made in this direction, there are shortcomings in the currently existing toolbox. At present, most indicators for critical transitions are only available for systems at equilibrium, whereas many systems in nature are inherently fluctuating. Time-series based indicators can also be difficult to interpret in real time: while it may be easy to see that a given indicator is rising, it is more difficult to infer how likely a transition is given such a rise, or to predict when it will occur. From the point of view of decision making in the prevention of critical transitions, such information is vital, and to provide this we may need to go beyond purely generic methods, and consider certain more or less specific properties of systems. In this talk, I’ll present a method for anticipating critical transitions in systems for which large parts of the dynamics can be reconstructed using 1D maps – a common property of systems in biology and ecology known as nearly-one-dimensionality. Using this property, we can predict nonlocal bifurcations of limit cycles and boundary crises of strange attractors, as well as more widely studied transitions such as saddle-node bifurcations. The method has the further advantage that it gives concrete predictions for the time of a transition, as well as the expected resilience of the system in the run-up.

Inkyung Ahn, Department of Mathematics, Korea University, South Korea

Predator-prey model with predation-induced dispersal in a heterogeneous environment

(joint work with Wonhyung Choi1)

Abstract

In this presentation, we discuss predator-prey models with a nonuniform random dispersal induced by predation in a spatially heterogeneous environment. We consider a ratio-dependent model with predation-induced dispersal to understand the effect of a nonuniform random dispersal on the fitness of each species in a heterogeneous region. Our conclusion is that a nonuniform dispersal induced by predation increases the fittness of a species in a spatially heterogeneous environment. To verify this, the stability of semi-trivial solutions for a model with nonuniform random diffusion on the predator is investigated. Subsequently, the stability conditions of such a model are compared to those of a model with linear diffusion. Our mathematical study is based on the eigenvalue analysis for the linearized operator derived from the model and bifurcation theory

1Department of Mathematics, Korea University, South Korea

Jehan M.K. Al-Ameri, Department of Mathematics, University of Leicester, UK

Fast Numerical Evaluation of Periodic Solutions for a Class of Nonlinear Systems and its Applications for Parameter Estimation Problems

(joint work with Ivan Tyukin1)

Abstract

Fast numerical evaluation of forward models is central for a broad range of inverse problems. Here we propose a method for deriving computationally efficient representations of periodic solutions of parameterized systems of nonlinear ordinary differential equations. These representations depend on parameters of the system explicitly, as quadratures of parameterized computable functions. The method applies to systems featuring both linear and nonlinear parametrization, and time-varying right-hand-side. In addition, it opens possibilities to invoke scalable parallel computations and suitable function approximation schemes for numerical evaluation of solutions for various parameter values. Application of the method to the problem of parameter estimation of nonlinear ordinary differential equations is illustrated with a numerical example for the Morris-Lecar system.

1Department of Mathematics, University of Leicester, UK

Jean-François Arnoldi, Centre for Biodiversity Theory and Modelling, Paul Sabatier University, France Generic assembly patterns in complex ecological communities

(joint work with Matthieu Barbier1, Guy Bunin2, Michel Loreau1)

Abstract

In a recent paper (PRE 2017), Guy Bunin used a cavity method adapted from spin-glass models to prove that the equilibrium properties of large random Generalized Lotka Volterra models (GLV) are entirely determined by a few elementary statistics of species interactions. With Matthieu Barbieri, Guy Bunin and Michel Loreau we used Guy's analytical approach to demonstrate emerging genericity in complex ecosystem models. We did so by comparing their dynamical behaviour to those of random GLV, seen as their disordered limit. We found that many models generate collective behaviours that are in fact equivalent to those of their disordered limit. We found an intuitive criterion for this to hold: heterogeneities in species traits and interactions should be sufficiently well-mixed throughout the community. This can hold regardless of many model details, including interaction type, functional response and diverse network metrics. The structures that lead to discrepancies between models and their disordered limit exhibit large-scale differentiated neighbourhoods within the web of interactions, e.g. functional groups. By combining disorder and simple structures we could expand the random model to capture relevant features while retaining maximal genericity. This paves a way towards understanding and in a sense, defining large-scale structures in networks of species' interactions, without relying on empirically unavailable details.

1 Centre for Biodiversity Theory and Modelling. Paul Sabatier University, France 2 Department of Physics. Technion-Israel Institute of Technology, Israel

Malay Banerjee, Department of Mathematics & Statistics, IIT Kanpur, India

Generic assembly patterns in complex ecological communities

(joint work with Deeptajyoti Sen1)

Abstract

Different types of prey-predator models with Allee effect either in prey population or in predator population are investigated by several researchers. Some of the formulations are mathematically tractable but not justified ecologically. Prey-predator models with specialist predator and Allee effect in predator growth have received comparatively less attention than Allee effect in prey growth. Main objective of this talk is to present a prey-predator model with Allee effect in predator growth with appropriate ecological justification behind its formulation where the predator is specialist. Apart from preliminary stability and local bifurcation results the complete global bifurcation scenario is explored. The talk will be concluded with the discussion on ecological interpretation of obtained results and possibility of extension of this formulation in case of generalist predator.

1Department of Mathematics & Statistics, IIT Kanpur, India

Matthieu Barbier, Station d’Ecologie Expérimentale, CNRS, Moulis, France

Dimensionality reduction of complex food web dynamics Abstract

Previous work has shown that many-species Lotka-Volterra (and similar) systems can, if sufficiently disordered, be reduced to a single stochastic equation with few generic parameters. This approach can be extended to more ordered systems, in particular food webs, by adding structure in the equation (e.g. correlations, multiple groups). Our question is then: how to attain the most parsimonious description of a (real or generated) complex food web? I will demonstrate the use of coarse-graining ideas inspired by physics and information geometry, to perform clustering based on predicting outcomes of the dynamics, rather than on the static structure of the interaction network.

Daniel Bearup, School of Mathematics, Statistics and Actuarial Science, University of Kent, UK

The emergence of mutualistic relationship in communities of competing ecosystem engineers

Abstract

Ecosystem engineers, species which significantly modify their habitats, play a disproportionate role in shaping the composition, and character, of the ecological communities of which they are a part. In particular, by creating and maintaining an atypical habitat (e.g. a coral reef), they support communities that are uniquely adapted to that habitat. Studies of these species have focused either on capturing the effect of ecosystem engineering activity on its own survival (or invasion) chances, or on interactions between ecosystem engineers with antithetical preferred habitats. Far less is known about how these species interact when they engineer compatible habitats.

In this study, we use a simple mathematical model, inspired by the classical competitive Lotka- Volterra system and the more recent work of Hastings and Cuddington, to investigate such interactions. While a species is always able to attain a higher population in a single species community, greater habitat improvements (and indeed higher total populations) can be attained in multi-species communities. Furthermore, species spread is often fastest in such communities. Thus ecosystem engineering facilitates a form of mutualism.

Slimane Ben Miled, Institut Pasteur de Tunis, University of Tunis el Manar, Tunisia

An IBM for energy allocation in hermaphrodites

Abstract

Size-advantage hypothesis models (SAH) allow an understanding of which sex occurs first and when the sex is changed in hermaphrodite species, through the optimal allocation of energy in terms of male versus female roles. Whereas sex allocation depends directly on how an organism allocates energy throughout its lifetime, the dynamic energy budget (DEB) theory describes the uptake and use of energy and nutrients, as well as the physiological organization throughout an organism's life cycle, including growth, maintenance, reproduction, and aging. We propose a model to bridge the gap between metabolic models and the sexual allocation model. We describe an individual-based model used to study the size at the time of a sex change/maximum size, i.e., Lratio and the most important physiological factors influencing size at the time of a sex change, Lchange. We prove that the fraction that determines how much to invest in somatic maintenance and growth, κ, the cost of the structure relative to the energy allocated to the soma, and the somatic maintenance rate coefficient are the most influential factors. We also show that the ratio between male and female gamete costs has very little influence on Lratio and Lchange.

Daniele Bevacqua, National Institute of Agronomic Research (INRA), France

A model for temporal dynamics of brown rot spreading in fruit orchards

Abstract

Brown rot, caused by Monilinia spp., is a major disease of stone fruits and, in favourable environmental conditions and in the absence of fungicide treatments, it causes important economic losses. In the present work, we propose a modification of classical susceptible, exposed, infectious and removed (SEIR) compartmental models to grasp the peculiarities of the progression of brown rot epidemics in stone fruit orchards in the last stage of the fruit growth (i.e. from the end of the pit hardening to harvest time). Namely, we took into account i) the lifespan of airborne spores, ii) the dependence of the latent period on the cuticle crack surface area, which itself varies in time with fruit growth, iii) the impossibility of recovery in infectious fruit, and iv) the abrupt interruption of disease development by the elimination of the host fruit at harvest time. We parametrized the model by using field data from a peach Prunus persica orchard infected by M. laxa and M. fructicola in Avignon (southern France). The basic reproduction number indicates that the environmental conditions met in the field were extremely favourable to disease development and the model closely fitted the temporal evolution of the fruit abundance in the different epidemiological compartments.

The model permits us to highlight crucial mechanisms undergoing brown rot build up and to evaluate the consequences of different agricultural practices on the quantity and quality of the yield. We found that winter sanitation practices (which decrease the initial infection incidence) and the control of the fruit load (which affects the host fruit density and the single fruit growth trajectory) can be effective in controlling brown rot in conjunction with or in place of fungicide treatments.

Eslene Bikoumou, University of Portsmouth, UK

How do foraging animals adapt their behaviour when competing (or cooperating) in a shared environment?

Abstract

How do foraging animals adapt their behaviour when competing (or cooperating) in a shared environment? How individual animals occupy and partition space has important consequences for the dynamics and distribution of populations on a large scale. The understanding of territorial behaviour is valuable in both the field of animal behaviour and has applications in ecology and conservative biology. The appropriate framework with which to model animal conflict is game theory.

Game theory is the standard tool used to model strategic interactions in evolutionary biology and social science. Traditionally, game theory studies the equilibria of simple games. The ideas and methods of evolutionary game theory have been applied in a wide range of situations, including animal contests. The idea behind game theory is that we can simulate the outcome of particular strategies by playing them as if they were evolutionary games. The contestants or players in this game are individual animals who can choose a particular strategy; i.e. 'fight', 'display' or 'retreat'. The consequences of a given strategy are measured by the pay-off of that strategy which mainly corresponds to a gain in fitness.

Our interest in statistical animal foraging mainly comes from the work of ecologists on home ranges. We want to understand how and why home ranges separate out and at which point this happens. Before we delve into our work, we want to know what other researchers have done as the questions we are trying to answer are bound to have been looked at in lots of ways but maybe not in the same form.

Many animals feed on patchy renewable resources and develop routes to visit such patches in stable sequences. These routes are known as “Traplines”, a term coined by Canadian fur trappers in the 1930’s. Our aim is to analyse the competitions that take place between different foragers as they try to optimize their traplines.

A well-known traplining species is the hummingbird. These birds have been observed visiting feeding locations in stable sequences, and must compete with each other to find a productive and energy-rich line. We have modelled humming bird behaviour by viewing traplines as strategies in a large and complex game. In this context, a stable configuration of lines is a “Nash Equilibrium”. While some species are territorial, aggressively defending sites from competitors, others engage instead in “defence through depletion” in which they aim to avoid direct conflict by visiting food- rich sites repeatedly in a sequence that enables them to gain the most from the accumulated resources. By arriving at a time when large rewards have accumulated and then leaving again before a competitor arrives they deplete the rewards available to the latecomer and effectively dissuade them from visiting the site.

We have come up with a model as an attempt to characterise the behaviour of foraging animals. In our model, we wanted to look at the idea of traplining in a different way such that the foragers can change their strategies by adding a site to the lines or remove a site from their lines.

Bernd Blasius, Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, Germany

Yule-Simon process determines the worldwide spread of alien species over centuries

Abstract

The Yule-Simon process is a generic model to describe a population of elements that are growing according to a rich-get-richer (or preferential attachment) mechanisms [1, 2]. It is one of the simplest models able to generate heavy-tailed size distributions and it has been applied to describe a range of empirical distributions, such as the number of biological species in general, citation numbers of scientific papers, word usage in a language, income distributions, and the node degree in scale-free networks. Here we investigate the historical spread of alien species over the globe and show that the spreading dynamics is determined by a Yule-Simon process over many centuries. Our analysis is based on a recently published data set of over 40,000 first records of an established alien species in a region [3]. We find that the distribution of first records per species follows a broad distribution with a power-law tail that remains identical over different historical epochs. The spreading dynamics can be described in remarkable similarity to the historical data by a Yule- Simon process where new alien species emerge at a constant rate and new first records of species in different regions are determined by a preferential attachment mechanism. Despite the huge complexity underlying biological invasions, our simple model is able to capture the dynamics of the spreading process (e.g., the temporal rate of emerging alien species) in terms of a single fitting parameter, suggesting that the process of bioinvasion on a global scale is driven by a universal process.

References

[1] Yule GU (1925). A mathematical theory of evolution based on the conclusions of Dr. J. C. Willis. Philos. Trans. R. Soc. London B 213: 21-87.

[2] Simon HA, (1955). On a class of skew distribution functions. Biometrika 42: 425-440.

[3] Seebens H, Blackburn TM, Dyer EE, Genovesi P, Hulme PE, Jeschke JM, Pagad S, Pyšek P, Winter M, Arianoutsou M, Bacher S, Blasius B, et al. (2017). No saturation in the accumulation of alien species worldwide. Nature Communications 8: 14435.

Åke Brännström, Department of Mathematics and Mathematical Statistics, Umeå University, Sweden

Adaptive dynamics for spatially-structured population

Abstract

Determining selection in spatially-structured populations can be tricky as a simple arithmetic average of local selection pressures usually gives the wrong answer. In this talk, I will show how selection can be determined for a class of spatial models that include reaction-diffusion equations and certain meta-population models. My presentation builds on joint work published as Wickman et al. (2017).

References

J Wickman, S Diehl, B Blasius, CA Klausmeier, AB Ryabov, Å Brännström. Determining selection across heterogeneous landscapes: a perturbation-based method and its application to modeling evolution in space. The American Naturalist 189 (4), 381-395

John Bryden, Royal Holloway University of London, UK

Groups, words and how humans transmit language: insights in language dynamics from Twitter

(joint work with Vincent Jansen1)

Abstract

Within a community, individuals tend to group together with those with which they share characteristics. At the same time, much of our characteristics and preferences are influenced by those that we interact with. These two processes create dynamics which give rise to clusters of individuals which share certain characteristics [1]. In human networks we have found evidence of such processes in the language that we use [2,3]. We have shown that on Twitter tribes of users tend to form, and the network emerging from user communication can be structured into a hierarchy of communities, and that the members of such tribes have similar word usage, and use specific words [2]. Consequently, communities can be characterised by their words. We can also show that word usage is passed on from speaker to speaker, demonstrating that language use spreads among those engaged in conversation [4] This suggests a mechanism for transmission whereby for each word someone encounters there is a chance they will use it more often. This mechanism for transmission can be used to study language patterns and evolution within populations.

1Royal Holloway University of London, UK

References [1] Bryden, J., Funk, S., Geard, N., Bullock, S. and Jansen, V.A.A., 2011. Stability in flux: community structure in dynamic networks. Journal of The Royal Society Interface, 8, 1031-1040. http://doi.org/10.1098/rsif.2010.0524

[2] Bryden, J., Funk, S. and Jansen, V.A.A., 2013. Word usage mirrors community structure in the online social network Twitter. EPJ Data Science, 2(1), 3. http://doi.org/10.1140/epjds15

[3] Tamburrini, N., Cinnirella, M., Jansen, V.A.A. and Bryden, J., 2015. Twitter users change word usage according to conversation-partner social identity. Social Networks, 40, pp.84-89. http://doi.org/10.1016/j.socnet.2014.07.004

[4] Bryden, J, Wright, S, and Jansen V.A.A. (2018) How humans transmit language: Horizontal transmission matches word frequencies amongst peers on Twitter. J. R. Soc. Interface. 15: 20170738. https://doi.org/10.1098/rsif.2017.0738

Nurdan Cabukoglu, Department of Mathematics, University of Leicester, UK

Kinesis Model: Diffusion depending on Reproduction Coefficient

(joint work with Alexander N. Gorban1)

Abstract

Kinesis is the non-directional movement as a response to the changing conditions. Migration and dispersal of animals depend on the natural selection. The dispersal strategy should increase Darwinian fitness. In this study, the new kinesis model with diffusion coefficient depending on fitness has been introduced. The kinesis strategy controlled by the locally and instantly evaluated wellbeing can be described in simple words: Animals stay longer in good conditions and leave quicker bad conditions. If the well-being is measured by the instant and local reproduction coefficient then the minimal model of kinesis can be written as follows:

ir i( u1 ,..., u k , s ) (1) tuxtDe i(,) 01 i  (  uruusu i )  i (,...,,), k i th where: ui is the population density of i species, s represents the abiotic characteristics of the living conditions (can be multidimensional), ri is the reproduction coefficient, which depends on all

and on s, D0i  0 is the equilibrium diffusion coefficient (defined for = 0), the coefficient

i  0 characterises dependence of the diffusion coefficient on the reproduction coefficient. Equations (1) describe dynamics of the population densities for arbitrary dynamics of s. For the complete model the equations for environment s should be added. The space distribution strategy is

ri summarised in the diffusion coefficient Dii D0 e , which depends only on the local in space and time value of the reproduction coefficient. Diffusion depends on well-being measured by this coefficient. We can see that the new models add one new parameter per species to the equations.

This is the kinesis constant ai . It can be defined as

1 dDii() r ai  D0ii dr

In the first approximation, Di D0 i(1 a i r i ). This model (1) can be considered as the minimal model of purposeful kinesis. The model has been explored with many numerical experiments. It has been shown the conditions that kinesis may be beneficial for assimilation of patches of food or of periodic fluctuations. However, kinesis may not be always beneficial. For species with the Allee effect it can delay invasion and spreading. It is proven that kinesis cannot modify stability of homogeneous steady states.

1Department of Mathematics, University of Leicester, UK

Ruben Ceulemans, University of Potsdam, Germany

Effects of introducing trait variation on the dynamics of a tritrophic food chain

(joint work with Ursula Gaedke1, Christian Guill1)

Abstract

Trait-based models have proven successful in capturing complex eco-evolutionary feed-backs in predator-prey systems, which greatly facilitated our understanding of their dynamic behaviour. Here, we aim at extending these insights to more diverse communities by introducing trait variation within each trophic level in a tritrophic food chain, where prey species can be defended against predator species and predator species can increase their prey selectivity. These traits interact in a uni-directional way: the defended species (d) can only be consumed by the generalist species (g), and the specialist species (s) can only consume the undefended species (u). In this way, the chain is transformed into a more complex food web with eight nodes. Notably, the species on the intermediate trophic level inhabit a two-dimensional trait space as they are both predator and prey. The difference in species traits is varied gradually, so that effects on the dynamics can be studied over a continuous spectrum.

An important feature of the model is the existence of two alternative stable states: one where the nutrients are well exploited and biomass production is high, whereas on the other one the mean free nutrient concentration is high and biomass production is low. We show that increasing the trait difference leads to an increase in the basin of attraction of the high production attractor. Conversely, a reduction in the amount of trait diversity can lead to its disappearance by a crisis.

Additionally, the increase in dynamical complexity due to the introduction of trait variation is characterized. We observe that a sufficient amount of trait diversity imposes a second timescale, on which species with different traits move out-of-phase relative to each other. While this leads to more convoluted phase relationships between species of neighbouring trophic levels, the fundamental quarter-phase lag rule characteristic of predator-prey interactions can be recovered by taking these trait differences and their interaction into consideration.

1Ecology and Ecosystem Modelling Group, University of Potsdam, Germany

Amit Chattopadhyay, Aston University, UK

Do we need vaccination?

Abstract

The issue of whether or not to have vaccination has seen a resurgence of late. Here, we present an epidemiological SIRV model based study that analyses the impact of vaccination in containing infection spread, in a 4-tiered population compartment comprised of susceptible, infected, recovered and vaccinated agents. As an advancement over popular epidemiological models which assume lifelong protection through vaccination, our model highlights the impact of a realistic waning immunisation on an endemic situation, resulting from a conversion of vaccinated and recovered agents to susceptible ones. Two asymptotic stationary states exist, a "disease-free equilibrium" and an "endemic equilibrium", with the transitions between these states controlled by the vaccination and relative conversion rates, expressed in terms of the basic reproduction number. We find that vaccination of newborns and adults lead to different consequences in containing an epidemic situation. For a homogeneous isotropic population, interacting through diffusion, a transition to the endemic state occurs through the propagation of a traveling infection wave, akin to that in the Fisher-Kolmogorov theory. The spatiotemporal stability of the disease-free equilibrium state of the spatial model could be represented through a spatial variant of the basic reproduction number that converges to its namesake for the diffusion-free state in the limit of zero wavenumber (k = 0) but has a parabolic dependence on k at all other values. Results emphasise the merit of vaccination, especially for migrant population groups.

Louise Chevalier, ECOBIOPOP, University of Pau and Pays Adour, France

A dynamic game theoretical model predicts variance in choosiness when mate availability fluctuates

(joint work with Jacques Labonne1,François-Xavier Dechaume Moncharmont2)

Abstract

Evolution of mate choosiness is a central topic in the Darwinian framework and has stimulated many experimental approaches in sexual selection. The optimal choosiness may depend on the quality of both the chooser and the potential partner, but it should also account for the complexity of intra-sexual competition for mate, mutual choice and fluctuation of partner availability. Most existing models, however, have focused on single-sex discrimination, treating mate choice as an optimization problem for either males or females alone. Johnstone (1997) thus developed a game theoretical model of mutual mate choice to calculate the Evolutionary Stable Strategy (ESS) of choosiness flexibility when individuals pair only once per breeding season under constant and even operational sex ratio (OSR). Yet, OSR is rarely even in natural populations. On the contrary, it fluctuates and depends on adult sex ratio (ASR) and the duration of the refractory period (i.e. time to become available for another reproduction). The results of Johnstone’s seminal work have yet to be generalized to this larger picture that encompasses different options to multiple mating for both sexes. In the present work, we develop his model by integrating biased ASR and variable refractory period, while still considering the dynamic mutual mate choice framework under scramble competition and the variation in quality for each sex.

Our results evidence for a predominant role of refractory period (via multiple mating) over ASR, controlling the choosiness of both sexes, different combinations of periods between sexes producing different outcomes in ESS of choosiness. When males and females mate more than once, variance in choosiness is substantial and is correlated to variance in quality. Additionally, patterns of positive homogamy demonstrated by Johnstone hold in many cases, although with decreasing strength with the biased ASR. This theoretical investigation confirms that evolution of optimal flexible choosiness leads to positive assortative mating and explains maintenance of variance in choosiness within populations.

1 UMR 1224 ECOBIOP, INRA - UNIV PAU & PAYS ADOUR, Saint-Pée sur Nivelle, France

2 UMR CNRS 6282 Biogéosciences, University Bourgogne Franche-Comté, Dijon, France

Edward Codling, Department of Mathematical Sciences, University of Essex, UK

Modelling the efficiency of animal navigation strategies

(joint work with Joe Bailey1, Jamie Wallis1,2, Nikolai Bode3)

Abstract

In this talk I will discuss a simple theoretical navigation problem that is relevant to animal movement at a range of scales (from large scale migration to short scale search and target-finding). I will first consider a biased and correlated random walk (BCRW) model for individual movement that balances direct navigation with forward persistence. I will show how an approximation for the navigational efficiency can be derived mathematically and will demonstrate the counter-intuitive result that giving higher weighting to indirect navigational cues (such as persistence) rather than direct cues may in many cases be the most efficient navigation strategy. I will subsequently show how simulations can be used to extend the model to consider collective group navigation such as in migrating flocks of birds or schools of fish. I will demonstrate how using indirect navigation cues such as persistence or copying the direction of movement of group neighbours (or some combination of both) can lead in many cases to more efficient collective navigation. I will briefly discuss the implications of these results within the context of the evolution of efficient animal navigation strategies.

1Department of Mathematical Sciences, University of Essex, UK 2Institute of Biomedical Engineering, University of Oxford, UK 3Faculty of Engineering, University of Bristol, UK

Atheeta Ching, University College London, UK

The carrying simplex in non-competitive Lotka-Volterra systems

Abstract

For some competitive Kolmorogov systems, there is an invariant Lipschitz manifold called the carrying simplex which is an attractor in the positive orthant; in fact, all trajectories are asymptotic to one on this manifold. Many other properties of the carrying simplex have been proven such as how its convexity affects the behaviour of the system. This carrying simplex exists in types of competitive Lotka-Volterra population models where it is the boundary of the basin of repulsion of the origin and contains all non-trivial limit sets. Our work explores non-competitive systems, investigating whether this manifold still exists and which properties still hold. We also find an analytic formula for the carrying simplex in the two species case.

Marco Colnaghi, Genetics, Evolution and Environment, University College London, Centre for Computation, Mathematics and Physics in the Life Sciences and Experimental Biology, University College London, UK

The strange dynamics of mitochondrial mutants: how the female germline generates quality and massive ploidy

(joint work with Andrew Pomiankowski1, Nick Lane1)

Abstract

Mitochondria provide the energy and metabolic precursors needed for normal cell function. The frequent turnover and replication of mitochondrial DNA makes it uniquely vulnerable to the accumulation of mutations. This problem is compounded by the high copy number of mitochondria in cells, which results in individual mutations having negligible effect on cell fitness. So mutants are not easily eliminated by selection and can be amplified to high numbers through stochastic processes, with the resulting high mutation loads being responsible for a range of severe diseases. But the process of inheritance of mitochondrial genomes is still far from understood. The simple hypothesis that mitochondrial mutants segregate randomly during female germline development is undermined by experimental studies showing complex collective dynamics, with evidence that developmental processes lead to a reduction in mutation load. In this talk, I will present a new model for the inheritance of mitochondrial genomes that considers three hypotheses on the underlying germline dynamics: a) a bottleneck in mitochondrial numbers during development, b) elimination of dysfunctional organelles during cytoplasmic transfer to the Balbiani body, and c) purifying selection on oocytes as they mature before ovulation. Using a combination of Markov models and numerical methods, we infer the distribution of mitochondrial mutations in oocytes, and compare the predictions of these different models with data on mutation levels and the incidence of mitochondrial diseases in humans. Our results beautifully explain the dynamics of female germline development, notably Balbiani body formation, the loss of 80% oogonia as apoptotic nurse cells, the proliferation of mitochondria in maturing oocytes, and the observed patterns of mitochondrial disease. We show that the female germline is fashioned by the requirement to minimise the new mitochondrial mutations while maximising mitochondrial numbers in the mature oocyte.

1 Genetics, Evolution and Environment, UCL, United Kingdom

George W. A. Constable, Department of Mathematical Sciences, University of Bath, UK

Why do most species have so few mating types, yet some have so many?

(joint work with Hanna Kokko1)

Abstract

Why do sexually reproducing species frequently contain just two self-incompatible mating types? This question has not been robustly answered for isogamous species. Basic deterministic theory suggests that since rare mating types experience a selective advantage (by virtue of their many potential partners), novel types should always successfully invade and the number of mating types consistently grows. However, in nature, species with thousands of mating types are exceedingly rare. Several competing theories attempt to explain the predominance of a low (usually two) number of mating types, yet lack an explanation for how many are possible and in which species to expect high numbers. In this talk, I will show that if the number of mating types results from a mutation-extinction balance, then the rate of sexual reproduction plays a crucial role. If sex is facultative and rare (a very common combination in isogamous species), mating type diversity will remain low. I will also demonstrate that the empirical literature supports the role of drift and the rate of sex as a determinant of mating type dynamics. Since current theories addressing the evolution of mating type number do not account for sex being facultative, I will conclude by describing how the predictions of alternative hypotheses may be altered in the light of rare sex.

1 Department of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland

Paola Correa, Pontificia Universidad Catolica de Chile, Chile

Towards a metastability approach: Outbreaks of mice in Australia

(joint work with Derek Corcoran1, Sergio Estay1, Peter Brown1, Mauricio Lima1)

Abstract

Populations of mice in Australia keep low densities most of the time, but sudden population outbreaks cause important economic damages in cereal crops. The outbreaks of mice have irregular dynamics and so far no one has been able to find a satisfactory explanatory mechanism. The aim of this study, was to identify, which are the basic principles and mechanisms responsible for epidemic outbreaks in Walpeup, Victoria, using a time series from 1983 to 2004. We fitted two type of models, single species logistic growth including exogenous factors, focused on mice populations (Mus musculus), and predator-prey models with functional response focused on population of mice and generalist predator (Elanus axillaris ). For the first approximation, we used single species models with humidity, precipitation, evaporation, temperature and productivity of wheat crop as exogenous factors (alone and mixed), but none of the models accurately predicted the outbreaks. On the other hand, we evaluated the existence of alternative equilibrium points related with metastability, through phase portraits and stochastic simulations. The predator-prey approach explained transitional states between lower and high densities, allowing us to identify the mechanisms that generate the outbreaks and establish management measures in the future to reduce their economic impact.

1Pontificia Universidad Catolica de Chile, Chile

Peter Czuppon, Max Planck Institute for Evolutionary Biology, Plön, Germany

Does ecology affect evolutionary processes? Fixation behavior under stochastically fluctuating population size

(joint work with Chaitanya Gokhale1 and Arne Traulsen1)

Abstract

We study the fixation probability of a mutant type when introduced into a resident population. We implement a stochastic competitive Lotka-Volterra model with frequency dependent competition and allow for stochastically varying population sizes. Using techniques from population genetics, evolutionary game theory and theoretical ecology we are able to disentangle the eco-evolutionary effects on the fixation probability. We approximate this quantity under weak selection in both, the evolutionary and the ecological, components. Our main result shows that the location of potential internal fixed points play a crucial role in the formula and their stability determine the evolutionary success of the mutant trait. Hence, the qualitative behavior of the fixation probability can be reduced to the corresponding replicator equation while this is not true in case of fixed population sizes.

1Max Planck Institute for Evolutionary Biology, Plön, Germany

Jaqueline Maria da Silva, Federal University of Jequitinhonha and Mucuri Valleys, Brazil; Department of Mathematics, University of Leicester, UK

Modelling seed dispersal phenomena in a tropical forest (joint work with Sergei Petrovskii1)

Abstract

The study of the vegetation growth is very important to understand the dynamics of flooded ecosystems in some tropical forests. In Amazon floodplains areas, the seed dispersion process is strongly influenced by the annual flood. Seed dispersion and germination occur in the beginnings of a plant’s life cycle, and variations in them strongly affect the distribution, structure, and dynamics of tree populations. Although researchers face lot difficulties to collect data in the Amazon floodplains, due to environmental conditions, a few information about the production and deployment of seeds by trees, as well as their germination, is available. Existing models for vegetation dynamics in the literature usually consider environmental factors as age, height, seed distribution, mortality, shadowing and the flood in an integrated manner.

In this work, we propose a computational, non-deterministic but probabilistic, model to study the impact of seed dispersion and germination on the behaviour of tree-populations. This model is data meagre, that is, it requires the collection of very little data to estimate its parameters that are mostly probabilities and rates. The model is for generic populations of trees. Annual flood effects will be considered implicitly, through the data and parameters used, that originate from field research in flooded areas and by considering in the algorithm some details of the tree-growth and the seed- dispersion processes that are characteristic of the flooded areas. It also considers a simplified, minimally necessary, age structure and light incidence. Despite being probabilistic, the model behaves similarly to usual population models with finite carrying capacity.

1 Department of Mathematics, University of Leicester, United Kingdom

Andrew Dean, Department of Mathematical Sciences, University of Liverpool, UK

Toxin-mediated competition in bacterial communities

(joint work with Mal Horsburgh1, Bakhti Vasiev1)

Abstract

The rise of antimicrobial resistance is one of the greatest challenges facing the global community in the twenty-first century. One possible solution is the exploitation of natural competition between microbial species in order to combat pathogens. For example, the human skin microbiome invariably contains the commensal bacteria Staphylococcus epidermidis and S. hominis, whose presence may aid in preventing colonisation by the potentially pathogenic S. aureus. However, the dynamics involved in such interactions are complex and difficult to study in sufficient detail in the laboratory. We have therefore developed an ODE model of a simple bacterial ecosystem incorporating both passive competition for resources and active inhibition via toxin production. We analyse this model under various ecological scenarios in conjunction with existing empirical data.

We are thus able to elucidate the interplay between passive and active competition and its effect on the populations under consideration, paying particular attention to a species' ability to defend against invasions from a competitor and the role of resistance in such interactions.

1Institute of Integrative Biology, University of Liverpool, UK

Jacob Dinner O'Sullivan, Queen Mary University, UK

Structurally instability and spatial coexistence mechanisms in model metacommunities

(joint work with Axel G. Rossberg1)

Abstract

Ecologists remain deeply divided about the plausibility the Ecological Limits Hypothesis, which predicts dynamic diversity equilibria at the highest levels of biological organisation. Conservation of large scale assemblages strongly determined by ecological limits would require fundamentally distinct management strategies to those appropriate for metacommunities far from equilibria. Therefore, improving our understanding of ecological assembly mechanisms is vital. To that end we have developed a spatially explicit competitive metacommunity assembly model in which species interact and disperse within a complex, multi-dimensional landscape. Our theoretical metacommunities converge on regional diversity equilibria which are best understood through the emerging mathematical framework we call the theory of Ecological Structural Stability, applied here for the first time to spatially explicit networks in heterogeneous landscapes.

Using the mathematical predictions of Ecological Structural Stability we show our model metacommunities converge on regional diversities that strongly depend on the distribution of realised interaction strengths, which in turn depend on the spatial aggregation of conspecific biomass. We find that saturated assemblages controlled by ecological limits to species richness at both local (community) and metacommunity scales manifest macroecological patterns that are considered effectively universal in the empirical literature - in particular the left-skewed log-normal species abundance distribution and sub-linear species area relation.

In summary our model communities resolve realistic macroecological patterns that are well described by the emerging theory of Ecological Structural Stability, suggesting natural assemblages may well be best understood as dynamic, structurally unstable systems, with major implications for the design and management of conservation programmes and sustainable harvesting.

1Queen Mary University, UK

Rajneesh Dwevedi, Amity Institute of Wildlife and Forest Sciences, Amity University, Noida, India

Modeling of breeding population of Painted Stork, Mycteria leucocephala: a 37-year long study in Keoladeo National Park.

(joint work with Vishal Deo2, Janmejay Sethy1, Renuka Gupta2 and Mahendiran Mylswamy4)

Abstract

Keoladeo National Park is a world heritage site and a unique ecosystem. Ecology of this ecosystem is dependent on the water received during monsoon. Ajan Dam and monsoon is the main source of water for the park. Park supports large aggregation of colonial birds including Painted Storks (Mycteria leucocephala). Painted Storks is a flagship species of wetland ecosystem and lies on the top of the food chain. Hence, the population level of this species is a good indicator of overall health of the ecosystem. Breeding population of Painted Stork has been monitored over 37 years in the form of different ecological studies conducted at Keoladeo National Park. Authors analyzed this breeding population (pair) data to study changes over 37 years. Genearlized Additive Models (GAM), including Poisson (PO), Zero Inflated Poisson (ZIP) and Negative Binomial (NBI and NBII), was tested for their suitability to predict population fluctuations. Water released in the park from Ajan Dam; regional monsoon rainfall; and time, was used as the predictor of the breeding population. Package GAMLSS in program ‘R’ was used for the analysis. Models were tested for best fit using AIC, SBC and Log Likelihood values. Worm plot was used to test for adequacy of the model. Negative Binomial II GAM was found best, to predict the population fluctuation (AIC = 362.65, SBC = 368.74, logLik = -176.32). Breeding population showed significant negative trend with time (t = -3473.27, p = 0.00). Water released was found to have significant positive effect on the breeding population (t = 5.49, p = 0.00).

1Amity Institute of Wildlife and Forest Sciences, Amity University, Noida, India 2Department of Statistics, Ramjas College, University of Delhi, Delhi, India 3Department of Biology, Lady Irwin College, University of Delhi, Delhi, India 4Wetland Ecology Division, Salim Ali Centre for Ornithology and Natural History, Coimbatore, India

Elias Ehrlich, Institute for Biochemistry and Biology, Department of Ecology and Ecosystem Modelling, University of Potsdam, Germany

Trait-fitness relationships determine how trade-off shapes affect species coexistence

(joint work with Lutz Becks1, Ursula Gaedke2)

Abstract

Trade-offs between functional traits are ubiquitous in nature and can promote species coexistence depending on their shape. Classic theory predicts that convex trade-offs facilitate coexistence of specialized species with extreme trait values (extreme species) while concave trade-offs promote species with intermediate trait values (intermediate species). We show here that this prediction becomes insufficient when the traits translate non-linearly into fitness which frequently occurs in nature, e.g. an increasing length of spines reduces grazing losses only up to a certain threshold resulting in a saturating or sigmoid trait-fitness function. We present a novel, general approach to evaluate the effect of different trade-off shapes on species coexistence. We compare the trade-off curve to the invasion boundary of an intermediate species invading the two extreme species which is calculated based on measurable trait-fitness relationships. If at least one of these relationships is not linear, the invasion boundary becomes non-linear implying that convex and concave trade-offs not necessarily lead to different coexistence patterns. Therefore, we suggest a new ecological classification of trade-offs into extreme-favouring and intermediate-favouring which differs from a purely mathematical description of their shape. We apply our approach to a well-established model of an empirical predator-prey system with competing prey types facing a trade-off between edibility and half-saturation constant for nutrient uptake. We show that the survival of the intermediate prey depends on the convexity of the trade-off. Overall, our approach provides a general tool to make a priori predictions on the outcome of competition among species facing a common trade-off in dependence of the shape of the trade-off and the shape of the trait-fitness relationships.

1Department of Evolutionary Ecology, Max Planck Institute for Evolutionary Biology, Plön, Germany

2Institute for Biochemistry and Biology, Department of Ecology and Ecosystem Modelling, University of Potsdam, Germany

John Ellis, Department of Mathematics, University of Birmingham, UK

An IBM study of spatial patterns arising in the density dependent population movement

(joint work with Natalia Petrovskaya1)

Abstract

It is well known that many invertebrate species will often congregate together to form clusters and are thus not evenly distributed across an area. Good understanding of mechanisms behind clustering patterns is important in many ecological problems, the problem of pest monitoring and control being one of them. In our work, a one-dimensional individual-based model was used to simulate the clustering behaviour where two distributions were used to approximate the species random movement: the normal distribution and a power law distribution. It will be shown in the talk that the properties and stability of the clusters formed by these movement regimes can vary considerably depending on the parameters and type of motion. The results of the simulation show that motion generated by the normal distribution produces clearly defined stable clusters whereas movement generated by a power law distribution creates a system with a fluctuating number of clusters.

1Department of Mathematics, University of Birmingham, UK

Latifat Erinle-Ibrahim, Department of Mathematics, Tai Solarin University of Education, Nigeria

The Mathematical modelling of the effect of treatment on the transmission of the pneumonia infection

(joint work with Wasiu O. Adebimpe1, Adedapo C. Loyinmi2, Idowu K. O.1)

Abstract This paper was designed to study the effect of treatment on transmission of pneumonia infection. When studying the transmission dynamics of infectious diseases with an objective of suggesting control measures, it is important to consider the stability of equilibrium points. In this paper we have established basic reproduction number, effective reproduction number, existence and stability of the equilibrium points. Using Lyapunov function we are able to determine that the disease-free equilibrium is unstable. The results are presented in graphs and it is discovered that the spread of the infection will greatly affected by the rate of treatment and natural immunity.

1 Department of Mathematics, Tai Solarin University of Education, Ijebu-Ode, Nigeria 2 Department of Physical Sciences, Landmark University, Omu-Aran, Nigeria

Theodore E. Galanthay, Ithaca College, United States

A game-theoretic approach to modelling ecological dynamics

(joint work with Ross Cressman1 and Vlastimil Křivan2)

Abstract

The Hawk-Dove game theoretic model attempts to explain the evolution of aggression between animals. This model has two parameters that represent Reward and Cost. Recent work [1] introduced theory to incorporate interaction times into two-player matrix games. We apply that theory to develop a series of models to connect the classical Hawk-Dove model to more mechanistic ecological models. We use these models to study the evolution of aggression [2].

1Department of Mathematics, Wilfrid Laurier University, Waterloo, Canada 2Department of Theoretical Ecology, Institute of Entomology, Biology Centre, České Budějovice, Czech Republic

References

[1] Křivan, V. and Cressman, R., Interaction times change evolutionary outcomes: Two player matrix games, Journal of Theoretical Biology (2017): 199-207.

[2] Křivan , V., Galanthay, T., and Cressman, R., Beyond replicator dynamics: From frequency to density dependent models of evolutionary games, (submitted to Journal of Theoretical Biology).

Vitaliy V. Ganusov, Genome Science and Technology, University of Tennessee Department of Microbiology, University of Tennessee, USA

Clustering of CD8 T cells around malaria-infected hepatocytes is rapid and is driven by antigen-specific T cells

(joint work with Reka K. Kelemen1,2 , Harshana Rajakaruna3, Ian A. Cockburn4)

Abstract

Malaria, a disease caused by parasites of the Plasmodium genus, begins when Plasmodium- infected mosquitoes inject malaria sporozoites while searching for blood. Sporozoites migrate from the skin via blood to the liver, infect hepatocytes, and form liver stages. In mice, vaccine-induced activated or memory CD8 T cells are capable of locating and eliminating all liver stages in 48 hours, thus preventing the blood-stage disease. However, rules of how CD8 T cells are able to locate all liver stages within a relatively short time period remains poorly understood. We recently reported formation of clusters consisting of variable numbers of activated CD8 T cells around Plasmodium yoelii (Py)-infected hepatocytes. Using a combination of experimental data and mathematical models we now provide additional insights into mechanisms of formation of these clusters. First, we show that a model in which cluster formation is driven exclusively by T-cell- extrinsic factors, such as variability in \attractiveness" of different Py-infected cells, cannot explain distribution of cluster sizes in different experimental conditions. In contrast, the model in which cluster formation is driven by the positive feedback loop (i.e., larger clusters attract more T cells) can accurately explain the available data. Second, while both Py-specific CD8 T cells and T cells of irrelevant specificity (non-specific T cells) are attracted to the clusters, we found no evidence that non-specific T cells play a role in cluster formation. Third and finally, mathematical modelling suggested that formation of clusters occurs rapidly, within few hours after adoptive transfer of T cells, thus illustrating high efficiency of T cells in locating their targets in complex peripheral organs such as the liver. Taken together, our analysis provides novel information into the mechanisms driving the formation of clusters of antigen-specific CD8 T cells in the liver.

1 Vienna graduate school of population genetics, Institute of Population Genetics, Austria 2 Genome Science and Technology, University of Tennessee, Knoxville, United States 3 Department of Microbiology, University of Tennessee, Knoxville, United States 4 Department of Pathogens and Immunity, John Curtin School of Medical Research, Australian National University, Australia

Mathias Gauduchon, MIO (Mediterranean Institute of Oceanography), Aix-Marseille University, France

Adaptive evolution of trophic networks: gradual construction, emergence of functional diversity

(joint work with Benjamin Girardot1 and Jean-Christophe Poggiale1)

Abstract

Trophic interactions are always central in ecosystems functioning. Beyond the mere diversity of a community, the very structure of the trophic networks species conform to, determines population dynamics and fluxes in the ecosystem and as so inevitably need to be handled by ecosystem modelers. Yet, even if empirical knowledge is abundant on the qualitative as well as on quantitative aspects of trophic networks structuration, theoretical studies about the evolutionary mechanisms underlying their emergence remain scarce and modelers often use some algorithmic methods to provide realistic trophic networks in order to study some of their properties, as their stability, resilience, etc.

Here we present an evolutionary model that allows for the adaptive emergence of specific trophic relationship between species. We use the theoretical framework of Adaptive Dynamics and study adaptation of several individual phenotypic traits: individual body size, preferred prey body size and specialization index. From a single species, several “evolutionary branching “ steps permit for the set-up of diversified community. Furthermore, the evolutionary model shapes trophic networks with complex structures with apparition of marked trophic levels and adaptation of species from specialized to very generalist predators. Red Queen dynamics, as well as multistable evolutionary states of trophic communities are also highlighted.

1MIO (Mediterranean Institute of Oceanography), Aix-Marseille University, France

Stefan Geritz, Department of Mathematics and Statistics, University of Helsinki, Finland

Resident-Invador Dynamics of similar strategies in non-constant environments

(joint work with Yuhua Cai1)

Abstract

If an initially rare strategy y can invade a resident population of strategy x, but not vice versa, does this mean that y will actually take over the population and become the new resident itself? It is known that in general this need not happen, as is illustrated by examples of unprotected coexistence and the \resident strikes back" phenomenon. Is it possible, then, to say anything at all about the outcome of an invasion event on the basis of invasion considerations alone, i.e., without looking into the interior of the resident-invader population state space? For a general, model-independent theory of adaptive dynamics this is an important question. Previous studies have shown that if the strategies of the invader and the resident are sufficiently similar (as one would expect to be the case if single mutations have only a small phenotypic effect), then the generically possible types of resident-invader dynamics are few and can be classified in terms of invasion only (see references below). In this presentation we generalize previous result to resident-invader dynamics in generally non-constant environment, including stochastic and deterministic environmental drivers as well as internally generated limit cycles.

1Department of Mathematics and Statistics, University of Helsinki, Finland

References [1] S.A.H. Geritz, M. Gyllenberg, F.J.A. Jacobs & K. Parvinen (2002) Invasion dynamics and attractor inheritance. J. Mathematical Biology 44, 548-560.

[2] S.A.H. Geritz (2005) Resident-invader dynamics and the coexistence of similar strategies. J. Mathematical Biology 50, 67-82.

[3] F. Dercole & S.A.H. Geritz (2016) Unfolding the resident-invader dynamics of similar strategies. J. Theoretical Biology 394,231-254.

[4] R.S. Cantrell, C. Cosner & K.Y. Lam (2017) Resident-invader dynamics in infinite dimensional systems. J. Differential Equations 263, 4565-4616.

Mauricio González-Forero, School of Biology, University of St Andrews, UK

Inference of Ecological and Social drivers of human brain-size evolution

(joint work with Andy Gardner)

Abstract

The human brain is unusually large. It tripled in size from Australopithecines to modern humans and became almost six times larger than expected for a placental mammal of human size. Brains incur high metabolic costs and accordingly a long-standing question is why the large human brain evolved. The leading hypotheses propose benefits of improved cognition for overcoming ecological, social, or cultural challenges. However, these hypotheses are typically assessed using correlative analyses, and establishing causes for brain-size evolution remains difficult. Here we introduce a metabolic approach that enables causal assessment of social hypotheses for brain-size evolution. Our approach yields quantitative predictions for brain and body size from formalised social hypotheses given empirical estimates of the brain’s metabolic costs. Our model predicts the evolution of adult Homo sapiens brain and body sizes when individuals face a combination of 60% ecological, 30% cooperative, and 10% between-group competitive challenges, and suggests that between-individual competition has been unimportant. Moreover, the model indicates that brain expansion in Homo was not driven by social but by ecological challenges, perhaps strongly promoted by culture. Our metabolic approach thus allows for causal assessments that refine, refute, and unify hypotheses for brain-size evolution.

Orestes Gutierrez Al-Khudhairy, Queen Mary University of London, United Kingdom

How trophic interaction are constrained over evolutionary time-scales

(joint work with Axel Rossberg1)

Abstract

From the study of even the simplest predator-prey models it is clear that, all else equal, trophic interaction strength (attack rates) must fall within a certain range of values to allow predators to survive and prevent bringing the abundance of its prey close to zero, in transients, oscillatory states, or the equilibrium solution. From studies of assembly models of large multi-level [2] and two-level food webs [1], it is known that when attack rates are permitted to evolve in such models, these attack rates can attain equilibrium values within this range. These results suggest that this kind of “prudent predation” [3] represents an evolutionary stable strategy (ESS) at the macro ecological level. However, the detailed underlying mechanisms and processes involved have so far remained opaque. Our study aims to identify relevant mechanisms and evolutionary constraints on species interactions that make prudent predation an ESS for attack rates in food webs. Our model describes a single patch where species are added as mutants of the residents. The evolution of the attack rate was studied within the conceptual framework of adaptive dynamics. We determined the fitness landscape for types with different attack rates, where fitness is computed from the balance between the “birth rate” of types (in our case variant species) and their “death rate” (extinction rate). By establishing how these rates, and therefore fitness, are functions of the attack rate we have shown that an ESS for the inherited trait is reached. Currently, we are building semi-analytic models to give a detailed analysis for how fitness can be determined mechanistically, by identifying which model parameters are most significant in maintaining ESS, constraining species interactions and therefore providing an explanation for “prudent predation”. Future work will upscale this analysis across multiple patches connected via species dispersal.

1Queen Mary University of London, United Kingdom

References

[1] A. G. Rossberg. Food Webs and Biodiversity: Foundations, Models and Data. In Food Webs and Biodiversity: Foundations, Models and Data, chapter 20, pages 255_269. John Wiley & Sons, Ltd, 2013. doi: http://dx.doi.org/10.1002/9781118502181.ch20.

[2] A. G. Rossberg, R. IShii, T. Amemiya, and K. Itoh. The Top-Down Mechanism For Body- Mass-Abundance Scaling. Ecology, 89(2):567_580, 2008.

[3] L. B. Slobodkin. How to be a predator. American Zoologist, 8(1):43_51, 1968. ISSN 0003- 1569. doi: 10.1093/icb/8.1.43. URL http://www.jstor.org/stable/3881531.

Katherine Heath, Mathematical Ecology Research Group, Department of Zoology, University of Oxford, UK

Types of competition in mosquito larvae influence adult population dynamics

(joint work with Michael Bonsall1)

Abstract

Increased larval development times and increased larval mortality have been observed in mosquito larvae at high densities. However, neither the functional form of these associations with density or the competitive process by which they arise are well understood. Aedes aegypti mosquitoes are vectors of major arboviruses including dengue. Therefore comprehensive understanding of the ecology of these vectors is paramount.

We developed a mathematical framework to compare scramble (all individuals are equally detrimentally affected by increased density) and contest competition (with increasing density, a subgroup of individuals monopolise resources to gain a fitness advantage) in Aedes aegypti. We used a system of delay-differential equations with stage-dependent delays allowing larval development time and mortality to depend upon larval abundance.

We observed that environmental factors that influence larval development can have either beneficial or detrimental effects depending on the competitive mechanism assumed. One way that this was demonstrated was using a hypothetical larval source management intervention where high larval mortality was imposed for a limited time period. Following the intervention, scramble competition saw increased adult mosquito population sizes compared to the model trajectory without intervention: temporary increased mortality decreases larval abundance; lower densities result in less competition and faster development; fast development times lead to population increase. The opposite was observed for contest competition. This occurs because when mortality rates are high then individuals with a competitive advantage are not pressured to develop more quickly; therefore, larval development remains slower on average.

The effects of perturbations in larval populations – either environmental or human – upon adult mosquito population dynamics depend upon the type of larval competition occurring. These effects can be either desirable or undesirable from the point of view of vector and disease control. Therefore, proper empirical evaluation of these mechanisms is paramount in order to accurately predict the effects of environmental change or human intervention upon mosquito population dynamics.

1Department of Zoology, University of Oxford, UK

Aviad Heifetz, Open University of Israel, Israel

Feeding at the nest in polygamous groups as a public-good game with intra-sex competition

(joint work with Roni Ostreiher)

Abstract In Arabian babbler (Turdoides squamiceps) groups, breeders constitute either a monogamous pair, a polyandry, a polygyny, or a sub-group of male and female breeders. In simple, monogamous groups, the male and the female share equally the task of feeding nestlings at the nest. In polyandrous groups the breeding males feed nestlings at a higher rate than the breeding female. Conversely, in polygynous groups the breeding females feed nestlings at a higher rate than the breeding male. The following graph demonstrates this phenomenon in a preliminary dataset:

To explain this phenomenon, we model the interaction among breeders as a public-good game, where the overall feeding rate to the nest yields the breeders increasing fitness benefits with decreasing marginal returns; each breeder incurs a convex fitness cost of its own feeding rate; and same-sex breeders (when there are any) enjoy additional fitness benefits which are increasing in their share of the feeding rate of all breeders of the same sex (this share serves as a credible signal to the opposite sex breeder(s) about their relative quality). For example, in a polyandrous group with two male breeders (i=1,2) and one female breeder (i=3), with corresponding feeding rates x1,, x 2 x 3 the aggregate feeding rate is x1, x 2 x 3 , with   consequential fitness benefits x1, x 2 x 3  where  1 , breeder i incurs cost xi for some x   1 , and for each of the two males i=1,2 their share of the male breeders' feeding rate is i . xx12 The resulting fitness functions are therefore (monotonically increasing in):

x1 f1(,,)() x 1 x 2 x 3 x 1  x 2  x 3   x 1 xx12

x2 f1(,,)() x 1 x 2 x 3 x 1  x 2  x 3   x 2 xx12  f1(,,)() x 1 x 2 x 3 x 1  x 2  x 3  x 3 We show that the numerically-computed ESS feeding rates in this game between breeders are indeed compatible with the above empirical findings. This suggests that a public-good game augmented by intra-sex competition may indeed be the driving force behind the empirically observed patterns of feeding rates.

Francisco Herrerías-Azcué, Theoretical Physics, School of Physics and Astronomy, University of Manchester United Kingdom

Stirring does not make the populations well mixed: the effect of motion on fixation probability

(joint work with Vicente Pérez-Muñuzuri1 , Tobias Gala2 )

Abstract

In evolutionary dynamics, the notion of a “well-mixed” population is usually associated with all- to-all interactions at all times. This assumption simplifies the mathematics of evolutionary processes, and makes analytical solutions possible. At the same time the term “well-mixed” suggests that this situation can be achieved by physically stirring the population. Using simulations of populations in chaotic flows, we show that in most cases this is not true: conventional well- mixed theories do not predict fixation probabilities correctly, regardless of how fast or thorough the stirring is. We propose a new analytical description in the fast-flow limit. This approach is valid for processes with global and local selection, and accurately predicts the suppression of selection as competition becomes more local. It provides a modelling tool for biological or social systems with individuals in motion.

1 Theoretical Physics, School of Physics and Astronomy, The University of Manchester, UK

2 Group of Nonlinear Physics, Faculty of Physics, University of Santiago de Compostela, Spain

Hofbauer Josef, University of Vienna, Austria

Permanence via the invasion graph

(joint work with S. Schreiber1)

Abstract

For an ecological system we introduce a graph which describes possible transitions between subcommunities using invasion growth rates. If this invasion graph is acyclic and every subcommunity is invadable then the system is permanent.

1University of California at Davis, USA

Andrew Hoyle, Computing Science and Mathematics, University of Stirling, UK

Optimising antibiotic dosage regimens to treat bacterial infections

Abstract

For too long have antibiotic dosage regimes followed the traditional approach of a giving a fixed dose X per day for N days. With the rise of antibiotic resistance, the need to find better, more efficient strategies is essential. Here we combine mathematical modelling of a bacterial infection (including resistance) with computational optimisation techniques, to find optimal dosage regimes. These regimes improve the treatment success while also giving the option to minimise total antibiotic usage.

John Bryden, Royal Holloway University of London, UK

Groups, words and how humans transmit language: insights in language dynamics from Twitter

(joint work with Vincent Jansen1)

Abstract

Within a community, individuals tend to group together with those with which they share characteristics. At the same time, much of our characteristics and preferences are influenced by those that we interact with. These two processes create dynamics which give rise to clusters of individuals which share certain characteristics [1]. In human networks we have found evidence of such processes in the language that we use [2,3]. We have shown that on Twitter tribes of users tend to form, and the network emerging from user communication can be structured into a hierarchy of communities, and that the members of such tribes have similar word usage, and use specific words [2]. Consequently, communities can be characterised by their words. We can also show that word usage is passed on from speaker to speaker, demonstrating that language use spreads among those engaged in conversation [4] This suggests a mechanism for transmission whereby for each word someone encounters there is a chance they will use it more often. This mechanism for transmission can be used to study language patterns and evolution within populations.

1Royal Holloway University of London, UK

References [1] Bryden, J., Funk, S., Geard, N., Bullock, S. and Jansen, V.A.A., 2011. Stability in flux: community structure in dynamic networks. Journal of The Royal Society Interface, 8, 1031-1040. http://doi.org/10.1098/rsif.2010.0524

[2] Bryden, J., Funk, S. and Jansen, V.A.A., 2013. Word usage mirrors community structure in the online social network Twitter. EPJ Data Science, 2(1), 3. http://doi.org/10.1140/epjds15

[3] Tamburrini, N., Cinnirella, M., Jansen, V.A.A. and Bryden, J., 2015. Twitter users change word usage according to conversation-partner social identity. Social Networks, 40, pp.84-89. http://doi.org/10.1016/j.socnet.2014.07.004

[4] Bryden, J, Wright, S, and Jansen V.A.A. (2018) How humans transmit language: Horizontal transmission matches word frequencies amongst peers on Twitter. J. R. Soc. Interface. 15: 20170738. https://doi.org/10.1098/rsif.2017.0738

Merlin C. Köhnke, Institute of Environmental Systems Research, Osnabrück University, Germany

Wave pinning in a variable environment

Abstract

The spatio-temporal intra- and interspecific competition of two diffusing similar populations is considered. The growth of both populations is either logistic or shows an Allee effect. Local steady state solutions are identified. Conditions of spatial segregation without mixing are investigated. Furthermore, the impact of density-dependent environmental noise on the occurring stationary fronts is studied. The obtained results are associated with a biological case study related to the competition of two invasive weeds.

Oleg Kuzenkov, Lobachevsky State University, Nizhni Novgorod, Russia

Towards constructing a mathematically rigorous framework for modelling evolutionary fitness

(joint work with Andrew Morozov1)

Abstract

Modelling selection in self-replicating systems uses the concept of evolutionary fitness which is related to the original Darwin's idea of the survival of the fittest. However, so far the concept of the evolutionary fitness in modelling is still somewhat vague, intuitive and is often subjective. As a result, using different definitions of fitness one can predict conflicting evolutionary outcomes, which is unfortunate. Here we formalise the definition of the evolutionary fitness to describe selection of strategies in self-replicating systems for generic modelling settings which involve an arbitrary function space of inherited strategies. Our mathematically rigorous definition of fitness is closely related to the underlying equations of population dynamics which govern the selection process. More precisely, fitness is defined using the concept of ranking of competing strategies which compares the long term dynamics of measures of sets of inherited units in the space of strategies. Further, we formulate the variational principle of modelling selection in systems with inheritance which states that in a self-replicating system with inheritance the result of selection will maximise the evolutionary fitness. We demonstrate how the defined evolutionary fitness can be derived for a class of models with age structuring including systems with delay, which was previously considered in the literature as a challenge.

1Department of Mathematics, University of Leicester, UK

Louise Lassalle, Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, The Netherlands

Evolution of life history variations in a physiologically structured population

(joint work with Tom van Dooren1, André De Roos2)

Abstract

Changes in feeding strategy throughout the life history are widespread in ecology. It can be a niche shift due to growth in size or a more drastic change like metamorphosis. Moreover, feeding strategies are often subject to phenotypic plasticity. A number of studies have shown the important effect of individual variations onto population dynamics, but it remains unclear which underlying mechanisms drive the evolution of individual life history variations in the first place. To investigate this question, we use a structured population model where growth and reproduction are physiological functions of body size. We show that the population is maturation or reproduction limited. Plasticity has a stronger impact on the population composition if the dynamics are stable and limited by the reproduction. When the population is limited by maturation, complex cohort cycles appear. These two distinct patterns at the ecological level are very likely to be important drivers of the evolutionary outcome. Using an adaptive dynamic approach, we have developed numerical methods to study the evolution of the population feeding strategies in the stable and unstable cases. We aim to understand in which case plasticity will evolve, and if there is a possibility for divergence pattern to emerge.

1 Institute for Biodiversity and Ecosystem Dynamics, University of Amsterdam, The Netherlands

2 Institute of Ecology and Environmental Science , University Pierre and Marie Currie, France

Henri Laurie, Department of Mathematics and Applied Mathematics, University of Cape Town, South Africa

Evolution of life history variations in a physiologically structured population

(joint work with Jannie Hofmeyr1)

Abstract

We consider a population of individuals whose life histories are determined by the DEB standard model. Assuming the population to be at equilibrium in an environment with food supply at constant density, we arrive at the possibility of an equilibrium. Supply/demand analysis determines the elasticity of a given input or output variable when some other variable changes. Typically, it is used to gain insight into the dominant and/or most sensitive actors in a network of processes. Here, we show that when equilibrium is assumed, the techniques of supply/demand analysis illuminate the relative importance of internal metabolic processes of individuals to the state of the population.

1Biochemistry Department, Stellenbosch University, South Africa

Sami Lehtinen, Department of Mathematics and Statistics, University of Helsinki, Finland

Understanding the Venus flytrap through mathematical modelling

Abstract

Among carnivorous plants, the Venus flytrap is of particular interest for the rapid movement of its snap-traps and hypothesised prey selection, where small prey are allowed to escape from the traps. We provide the first mathematical cost-benefit model for the plant. Specifically, we analyse the dynamics of prey capture; the costs and benefits of capturing and digesting its prey; and optimisation of trap size and prey selection. We fit the model to available data, making predictions regarding trap behaviour. We predict that non-prey sources, such as raindrops or wind, cause a large proportion of trap closures; only few trap closures result in a meal; most of the captured prey are allowed to escape; the closure mechanism of a trap is triggered about once every two days; and a trap has to wait more than a month for a meal. We also find that prey capture of traps of the Venus flytrap follows the Beddington-DeAngelis functional response. These predictions indicate that the Venus flytrap is highly selective in its prey capture.

Alexander S. Leonard, Cavendish Laboratory, University of Cambridge, UK

The Evolution of Symmetric and Asymmetric Protein Binding Interfaces

(joint work with Sebastian E. Ahnert1)

Abstract

Although many quantitative studies on protein interface binding strengths have been conducted in recent years, with evolutionary arguments put forth on the greater-than-expected prevalence of symmetric interfaces, the actual evolutionary history is difficult to reconstruct. An abstract protein assembly model can offer strong analytic capabilities while allowing robust and feature ful evolutionary dynamics, and hence allow the evolution of protein interface binding properties like strength and symmetry to be probed in greater detail. Modelling a protein interface to consist of I residues, each with a binary value, the interaction strength between two interfaces can calculated as their Hamming “edit" distance. With mutations and fitness proportional selection providing a framework for evolving a population, the binding interactions can be tracked over time and compared to analytic expectations. While the evolved interfaces are nuanced with respect to certain simulation parameters like the binding threshold “temperature", the general behaviour shows a clear divergence from randomly distributed residues, matching observations in existing literature. Additionally, with complete information on evolutionary history, the increases in structural complexity can be time ordered, offering further insight into the observed distribution of naturally-occurring proteins.

1 Sainsbury Laboratory, University of Cambridge, United Kingdom

Xiang-Yi Li, Department of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland

Evolution of sexual dimorphism by intersexual resource competition (joint work with Hanna Kokko1)

Abstract

Sexes often differ far more clearly in secondary sexual characteristics than in traits that appear naturally selected. Since species coexistence is facilitated by niche differences, the rarity of analogous within-species differences (intersexual niche partitioning) requires an explanation. We show that two spatial factors are crucial in the evolution of sex-specific resource use. First, mating competition often occurs over local spatial scales. If mating groups are moderately or very large, males are not selected to save resources for females who they are unlikely to mate with (the opposite, “gentlemanly” solution is possible under monogamy). Second, multiple resource types can promote the evolution of dimorphism, but concomitant spatial variation can cancel this effect if only one sex can thrive in some sites. Spatial variation can, however, lead to sexually dimorphic trait polymorphism: assuming stronger reproductive competition in males than in females, we predict males to be more often polymorphic in resource use.

1 Department of Evolutionary Biology and Environmental Studies, University of Zurich, Switzerland

Kevin Liautaud, Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, France

Uniting individualistic and organismic visions of nature with competition theory

(joint work with Egbert van Nes2, Marten Scheffer2, Michel Loreau1)

Abstract

A question that has long puzzled ecologists is the degree to which communities are super- organisms rather than loose collection of species. H. Gleason, and F. Clements were first to debated plant community nature, the former arguing for an individualistic vision of communities, whereas Clements considered them as super-organisms. Along environmental gradients, in space or in time, the organismic vision of communities implies abrupt and collective changes in the community composition, functioning and stability. On the opposite side, an individualistic vision implies slow, gradual changes in the community features. To date, empirical evidences are still lacking to identify what are the conditions leading to organismic or individualistic responses of communities when the environment gradually changes, and a rigorous theory is missing to reconcile these two opposite visions of nature. In this study, we focus on how competition theory can bridge the gap between individualistic and organismic views of communities. We used a multi-species competition Lotka-Volterra model to understand the influence of competition in the emergence of different community patterns along a spatial gradient. We showed that under certain competitive conditions, even without mutualistic interactions, unexpected collective behaviours can emerge, leading to organismic community patterns along the gradient. In these cases, we observe discrete communities along space, separated by narrow zones of high species turnover. We demonstrate that these major shifts, from one community to another, are explained by the presence of alternative stable states. We thereby highlight the importance of considering inter-specific interactions when dealing with species responses to environmental changes. Taking into account these interactions could improve reliability in predictions of species distributions in a global change context.

1 Centre for Biodiversity Theory and Modelling, Theoretical and Experimental Ecology Station, CNRS and Paul Sabatier University, France 2 Environmental Science Department, Wageningen University, The Netherlands

Max Lindmark, Department of Aquatic Resources, Institute of Coastal Research, Swedish University of Agricultural Sciences, Sweden

Species interactions determine effects of warming on stability in a stage- structured food chain (joint work with Jan Ohlberger2, Magnus Huss1, Anna Gårdmark1)

Abstract Predicting the impacts of climate change on animal populations and communities requires taking both physiological responses and ecological interactions into account. The combination of food dependent body growth and intra-specific variation in body size has major effects on the structure and dynamics of populations and communities. Yet, this is rarely considered in dynamical models used to infer effects of warming on animal communities – despite the large body of empirical evidence suggesting a link between temperature and population size-structure. Here, we used a dynamic stage-structured biomass model that explicitly accounts for size- and temperature dependence of vital rates to assess how warming shapes coexistence, stability and size-structure in a tri-trophic food chain. When predators selectively feed on juvenile consumers, warming induces bistability (alternative stable states), which occurs due to predation-induced overcompensation in the consumer at high temperatures. This gives rise to a warming-induced Allee effect, as predator population growth is limited by lack of prey at low densities. By contrast, with generalist predators feeding with equal intensity on both consumer life stages, the system goes from limit cycles to stable fixed point dynamics as temperature increases. In all temperature-scaling scenarios, warming leads to a decrease in the mean body size of the community. Moreover, when warming causes a steeper increase in metabolic costs with size (such that energy needs increase more with warming for large than for small individuals) relative to that of ingestion predator extinction occurs at lower temperatures and the parameter space with bistability decreases. These findings suggest reduced likelihood for persistence of higher trophic levels in warmer climates relative to scenarios ignoring the potential for warming-induced Allee effects and size-temperature interactions. We therefore argue that it is necessary to account for variation in body size within species, size-dependent interactions among individuals and size-temperature interactions in biological rates to predict the effects of climate warming on food chains.

1 Department of Aquatic Resources, Institute of Coastal Research, Swedish University of Agricultural Sciences, Sweden 2 School of Aquatic and Fishery Sciences (SAFS), University of Washington, USA

Sébastien Lion, Centre d’Écologie Fonctionnelle et Évolutive (CEFE), CNRS, Montpellier, France

Spatial evolutionary ecology: short- and long-term theory

Abstract

A fundamental question in evolutionary ecology is to understand how dispersal shapes the genetic and epidemiological structure of populations, and how, in turn, population structure may affect the evolution of life-history traits. Using a model of host-parasite interactions, I contrast two approaches for studying this feedback in spatially structured populations. First, I present a novel approach to jointly model epidemiological and evolutionary dynamics, using a combination of spatial moment equations and quantitative genetics. A key insight of this approach is that, even in the absence of long-term evolutionary consequences, spatial structure can affect the short-term evolution of pathogens because of the build-up of spatial differentiation in mean virulence. This analysis can be used to understand and predict the transient evolutionary dynamics of pathogens and the emergence of spatial patterns of phenotypic variation. Second, assuming that ecological and evolutionary time scales are decoupled, I recover previous results based on adaptive dynamics theory. The selective pressures on parasite virulence can then be summed up by a simple balance between genetic and epidemiological effects. Finally, I discuss the connections with kin selection theory, particularly highlighting that the relevant genetic structure can be captured by relatedness coefficients in both the short- and long-term theories. Horst Malchow, Institute of Environmental Systems Research, School of Mathematics/Computer Science, Osnabrück University, Germany

Spatial coexistence of competitors in a variable environment

Abstract

Stochastic reaction-diffusion equations are a popular modelling approach for studying interacting populations in a heterogeneous environment under the influence of environmental fluctuations. Although the theoretical basis of alternative models such as Fokker-Planck diffusion is not less convincing, movement of populations is most commonly modelled using the diffusion law due to Fick. An interesting feature of Fokker-Planck diffusion is the fact that for spatially varying diffusion coefficients the stationary solution is not a homogeneous distribution - in contrast to Fick's law of diffusion. Instead, concentration accumulates in regions of low diffusivity and tends to lower levels for areas of high diffusivity. Thus, the stationary distribution of the Fokker-Planck diffusion can be interpreted as a reflection of different levels of habitat quality. Moreover, the most common model for environmental fluctuations, linear multiplicative noise, is based on the assumption that individuals respond independently to stochastic environmental fluctuations. For large population densities the assumption of independence is debatable and the model further implies that noise intensities can increase to arbitrarily high levels. Therefore, instead of the commonly used linear multiplicative noise model, the environmental variability is implemented by an alternative nonlinear noise term which never exceeds a certain maximum noise intensity. With Fokker-Planck diffusion and the nonlinear noise model replacing the classical approaches, a simple invasive system is investigated based on the Lotka-Volterra competition model. It is found that the heterogeneous stationary distribution generated by Fokker-Planck diffusion generally facilitates the formation of segregated habitats of resident and invader. However, this segregation can be broken by nonlinear noise leading to coexistence of resident and invader across the whole spatial domain, an effect that would not be possible in the non-spatial version of the competition model for the parameters considered here [1-3].

References

[1] Bengfort, M., Malchow, H., Hilker, F.M. (2016). The Fokker-Planck law of diffusion and pattern formation in heterogeneous media. Journal of Mathematical Biology 73(3), 683-704.

[2] Siekmann, I., Malchow, H. (2016). Fighting enemies and noise: Competition of residents and invaders in a stochastically fluctuating environment. Mathematical Modelling of Natural Phenomena 11(5), 120-140. [3] Siekmann, I., Bengfort, M., Malchow, H. (2017). Coexistence of competitors mediated by nonlinear noise. European Physical Journal Special Topics 226(9), 2157-2170. Robert Manning Smith, Rothamsted Research, Harpenden, UK

Modelling lifestyle change in Arsenophonus phytopathogenicus, from mutualistic insect-endosymbiont to plant pathogen.

Abstract

Relationships between host and symbiont can vary over time. This can be a result of evolutionary or ecological changes. The breakdown of a mutualistic relationship can result in the emergence of novel disease, an example of this is the sugar beet disease ‘syndrome basses richesses’. The bacterial causal organism, Arsenophonus phytopathogenicus, has an evolutionary past as a mutualistic endosymbiont of the insect host Pentastiridius leporinus, but now exists as an insect vectored plant-pathogen. Using adaptive dynamics, we begin to answer the question, why did this evolutionary change occur?

Angela Martiradonna, Institute for Applied Mathematics M. Picone, CNR, Italy

Optimal spatiotemporal control of Ailanthus altissima (Mill.) Swingle in the Alta Murgia National Park

(joint work with Baker CM2,3, Blonda P4, Casella F5, Diele F1, Marangi C1, Ragni S6, Tarantino C4)

Abstract

The threat, impact and management problems associated with alien plant invasions are increasingly becoming a major issue in environmental conservation. Invasive species cause significant damages, and high associated costs. Controlling them cost-effectively is an ongoing challenge, and mathematical models and optimizations are becoming increasingly popular as a tool to assist managers. The aim of this study is to develop a modelling approach for the optimal spatiotemporal control of invasive species in natural protected areas of high conservation value. Typically, control programs are either distributed uniformly across an area, or applied with a given fixed intensity, although there is no guarantee that such a strategy would be cost-effective at the conservation asset. The proposed approach, based on diffusion equations, is spatially explicit, and includes a functional response (Holling type II) which models the control rate as a function of the invasive species density. We apply a budget constraint to the control program and search for the optimal effort allocation for the minimisation of the invasive species density. Remote sensing derived input layers and expert knowledge have been assimilated in the model to estimate the initial species distribution and its habitat suitability, empirically extracted by a land cover map of the study area. Both the initial density map and the land cover map have been generated by using very high resolution satellite images and validated by means of ground truth data. The approach has been applied to the Alta Murgia National Park, where the EU LIFE Alta Murgia Project is underway with the aim to eradicate Ailanthus altissima, one of the most invasive alien plant species in Europe. The Alta Murgia National Park is one of the study site of the on-going H2020 project ECOPOTENTIAL which aims at the integration of modelling tools and Earth Observations for a sustainable management of protected areas. The H2020 project ‘ECOPOTENTIAL: Improving Future Ecosystem Benefits Through Earth Observations’ (http://www.ecopotential-project.eu) has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No 641762. All ground data regarding Ailanthus altissima (Mill.) Swingle presence and distribution are from the EU LIFE Alta Murgia Project (LIFE12 BIO/IT/000213 titled “Eradication of the invasive exotic plant species Ailanthus altissima from the Alta Murgia National Park” funded by the LIFE+ financial instrument of the European Commission).

1Institute for Applied Mathematics M. Picone, CNR, Bari, Via Amendola 122/D, Italy 2School of Biological Sciences, The University of Queensland, QLD 4072, Australia 3CSIRO Ecosystem Sciences, Ecosciences Precinct, Dutton Park, Brisbane, QLD 4102, Australia 4Institute of Atmospheric Pollution Research, CNR, Bari, Via Amendola 173, Italy 5Institute of Sciences of Food Production, CNR, Bari, Via Amendola 122/O, Italy 6Department of Economics and Management, University of Ferrara, Via Voltapaletto 11, Ferrara, Italy Leonardo Miele, Department of Mathematical Biology and Medicine, University of Leeds, UK

Eco-Evolutionary dynamics and the emergence of life cycles in microbial populations

(joint work with Silvia De Monte1)

Abstract

The emergence of multicellular lives is considered one of the major transitions in evolution [SS97]. It led to a burst of complexity among living systems, and to new forms of organization such as life cycles, that from the physicist perspective can be studied as examples of complex collective behaviour. The achievement of the transition to multicellularity relies on the resolution of a "social conflict" among unicellular entities endowed with different interests and survival strategies. In the framework of Evolutionary Game Theory, such conflict is tipically cast in terms of cooperators versus cheaters playing a Public Good Game [Tar17]. However, if social interactions among players are random, cheaters will always outperform cooperators, leading to the so called Tragedy of the Commons. In order to avoid this tragedy several solutions have been proposed. but rarely the ecological context and the demography of the problem have been taken into account [Wei+16; Hau+02]. Starting from an example of social conflict inspired by the microbial world, I will introduce a novel approach based on the coupling between evolution and ecology, with explicit ecological and demographic dynamics. I will show how our model is able to resolve the Tragedy of the Commons, and how it leads to the emergence of an oscillating collective behaviour that can be interpreted as life cycles. Finally, I will discuss the relation of these theoretical life cycles with those observed in microbial populations such as the social amoeba Dictyostelium discoideum, and how our theoretical study can help to shed light on the emergence of cooperation in the microbial world [RR03].

1IBENS ENS Paris

References

[Hau+02] Christoph Hauert et al. “Replicator dynamics for optional public good games”. In: Journal of Theoretical Biology 218.2 (2002), pp. 187–194 (cit. on p. 1).

[RR03] Paul B Rainey and Katrina Rainey. “Evolution of cooperation and conflict in experimental bacterial populations”. In: Nature 425.6953 (2003), p. 72 (cit. on p. 1).

[SS97] John Maynard Smith and Eors Szathmary. The major transitions in evolution. Oxford University Press, 1997 (cit. on p. 1).

[Tar17] Corina E Tarnita. “The ecology and evolution of social behavior in microbes”. In: Journal of Experimental Biology 220.1 (2017), pp. 18–24 (cit. on p. 1).

[Wei+16] Joshua S Weitz et al. “An oscillating tragedy of the commons in replicator dynamics with game-environment feedback”. In: Proceedings of the National Academy of Sciences 113.47 (2016), E7518–E7525 (cit. on p. 1).

Géza Meszéna, Department of Biological Physics, Eötvös University, Budapest, Hungary

Sympatric, or allopatric? Adaptive emergence of reproductive isolation in different ecological situations

(joint work with Benjamin Márkus1, Kristóf Törkenczy1)

Abstract

While the classical allopatric theory of speciation mandated the allopatric route, the recently favored ecological/adaptive speciation is agnostic in this respect. Is it still true that spatial segregation is advantageous for speciation? Our goal is to compare the allopatric and the sympatric modes of speciation within the adaptive speciation framework by modelling habitat-based and resource-based niche segregation in a comparable way. Specifically, we consider an environment with two habitats with two resources in each. Individuals migrate between the habitats with a fixed migration rate; their ecology is controlled by a single biallelic locus. We study the adaptive dynamics of assortativity in this ecology.

This setting allows comparison between three different ways of niche segregation: (1) pure resource segregation with no difference between the habitats; (2) pure habitat segregation (e.g. with temperature difference between them) with no difference between the resources; (3) mixed segregation, when the (otherwise identical) habitats differ in their resource content. By and large, reduced fitness of the ecological heterozygote promotes emergence of reproductive isolation, independent of the way of segregation. Decreased migration makes the onset of the speciation process easier in Case (2) but not in Case (3); low migration rate makes the completion of reproductive isolation difficult both in Cases (2) and (3).

1Department of Biological Physics, Eötvös University, Budapest, Hungary

Vuk Milisic, CNRS, Laboratoire Analyse, Géométrie & Applications, Université Paris 13, France

Mathematical Modelling of cell adhesion forces: from global to local existence, from delay to friction.

Abstract

In this talk we present the starting mechanical model of the lamellipodial actin-cytoske- leton meshwork. The model is derived from the microscopic description of mechanical properties of filaments and cross-links and also of the life-cycle of cross-linker molecules [1, 6, 5]. We introduce a simplified system of equations that accounts for adhesions created by a single point on which we apply a force. An adimensionalisation leads to a singular limit in ε, motivating our mathematical study. Then we give results for the fully coupled system with unbounded non-linear off-rates [3]. This leads to two possible regimes: under certain hypotheses on the data there is global existence, out of this range we are able to prove blow-up in finite time. In the last part of the talk, we present introduce the space dependency we give the mathematical framework allowing to extend the previous results. We show in particular a new energy estimates and the extension of a stability result established formerly in [2] that together show again the asymptotics when ε goes to zero [4].

References

[1] V. Milisic and D. Oelz. On the asymptotic regime of a model for friction mediated by transient elastic linkages. J. Math. Pures Appl. (9), 96(5):484–501, 2011.

[2] V. Milisic and D. Oelz. On a structured model for load-dependent reaction kinetics of transient elastic linkages mediating nonlinear friction. SIAM J. Math. Anal., 47(3):2104–2121, 2015.

[3] V. Milisic and D. Oelz. Tear-off versus global existence for a structured model of adhesion mediated by transient elastic linkages. Communications in Mathematical Sciences, 14 5: 1353- 1372, 2016.

[4] V. Milisic and D. Oelz. From memory to friction: convergence of regular solutions towards the heat equation with a non-constant coefficient preprint, submitted.

[5] D. Oelz and C. Schmeiser. Derivation of a model for symmetric lamellipodia with instantaneous cross- link turnover. Arch. Ration. Mech. Anal., 198(3):963–980, 2010.

[6] D. Oelz, C. Schmeiser, and V. Small. Modelling of the actin-cytoskeleton in symmetric lamellipodial fragments. Cell Adhesion and Migration, 2:117–126, 2008

Christopher Overton, Department of Mathematical Sciences, University of Liverpool, UK

Deterministic approximations of stochastic dynamics in evolutionary graph theory

(joint work with Mark Broom1, Christoforos Hadjichrysanthou2, Kieran J. Sharkey3)

Abstract

Evolutionary graph theory aims to investigate the dynamics of evolution in a context where there is spatial population structure which is represented by a graph. Previous studies in this area have mainly focused on the outcome of evolutionary processes on highly idealised graphs. On such structures, quantities of interest, such as the fixation probability of an invading mutant, can be calculated analytically.

Investigations of the evolution of populations represented by complex heterogeneous graphs require computationally intensive methods. In this presentation we discuss methods of obtaining approximate descriptions of the underlying stochastic dynamics within a deterministic framework. In particular, we derive approximations directly from the master equation. Although these approximations are commonly used in the modelling of epidemics on networks, their application in evolutionary dynamics is particularly challenging. The purpose of this work is to develop deterministic approximation methods with low computational complexity to describe stochastic evolutionary dynamics on arbitrary graphs.

1Department of Mathematics, City University of London, UK

2Department of Mathematics in Imperial College London, UK

3Department of Mathematical Sciences, University of Liverpool, UK

Kalle Parvinen, Department of Mathematics and Statistics, University of Turku, Finland

Evolution of Dispersal in Metapopulation Models

Abstract

Invasion fitness is the long-term exponential growth rate of a rare mutant in the environment set by the resident. It is a key concept in adaptive dynamics, which is a general framework for studying evolution by natural selection in realistic population models. A mutant may invade if it has positive invasion fitness. Adaptive dynamics investigates long-term consequences of such invasions. Metapopulation models describe population dynamics in fragmented landscapes. A metapopulation is thus a collection of local populations connected with dispersal. In metapopulation models the invasion fitness is often difficult to calculate. The metapopulation reproduction ratio introduced by Gyllenberg and Metz (2001) and Metz and Gyllenberg (2001) is often easier to calculate. Consider a single mutant disperser arriving in a patch. This mutant may reproduce and thus gain descendants in this patch, but this will not necessarily happen because of demographic stochasticity. As long as this mutant or at least one of its descendants is present in the local population, we call it a mutant colony. Again, because of demographic stochasticity or catastrophes, the mutant colony will eventually go extinct. During its lifetime, some mutants will emigrate from this mutant colony to the disperser pool. Their average number is the metapopulation reproduction ratio Rm of the mutant. In other words, it is the expected number of successful dispersers produced by a typical mutant colony initiated by a single mutant disperser.

In this talk I will present general results about the evolution of dispersal in metapopulation models, and discuss general mechanisms selecting for/against dispersal, including temporal heterogeneity vs. constant environments, spatial heterogeneity, kin competition and direct cost of dispersal.

Alberto Pascual-García, ETH-Zurich, Department of Environmental Systems Science, Institute of Integrative Biology, Zürich, Switzerland

Structural stability of complex ecosystems: effective competition theory and the role of mutualistic interactions in biodiversity maintenance

Abstract

Understanding the role of species interactions in biodiversity maintenance originated the stability- complexity controversy which is still a matter of intense research. Much of our current theoretical understanding is based on the analysis of dynamical stability pionereed by Robert May. Dynamical stability focuses on the effect of perturbations in population abundances, and has led to counterintuitive results like the reportedly negative effects of mutualistic interactions on biodiversity. Recent advances in the collection of species information or in the estimation of parameters from theory following allometric principles, prompted new efforts for the appropriated incorporation of data into theoretical models. Evolution has strongly constrained the space of parameters we should deal with, thus leading, in many cases, to highly uneven distributions. This fact has led theoreticians to emphasize the importance of i) building feasible systems, which are those whose parametrization is compatible with positive biomasses and ii) shifting from the analysis of dynamical stability to structural stability, i.e. the analysis of stability after perturbations in the model parameters. In this talk I will first present introductory concepts and the state-of-the-art of structural stability analysis and how it may help in the crosstalk between ecological and evolutionary modelling. To continue with, I will present some results showing how structural stability analysis helps to root out some misconceptions about the role of mutualistic interactions on biodiversity [1]. To finish, I will introduce a new formalism that we call Effective Competition Theory [2], a formalism that allowed us to develop analytic results to predict structural stability of complex ecosystems. It has helped us to rationalize previous controversies of the complexity- stability debate [3] and we believe that its further development will be helpful for eco-evo analysis.

References

[1] Bastolla, U., Fortuna, M. A., Pascual-García, A., Ferrera, A., Luque, B. and Bascompte, J (2009). The architecture of mutualistic networks minimizes competition and increases biodiversity. Nature, 458(7241), 1018- 1020.

[2] Ferrera, A., Pascual-García, A., & Bastolla, U. (2017). Eective competition determines the global stability of model ecosystems. Theoretical Ecology, 10(2), 195-205.

[3] Pascual-García, A., & Bastolla, U. (2017). Mutualism supports biodiversity when the direct competition is weak. Nature Communications, 8, 14326. Karan Pattni, Department of Mathematical Sciences, University of Liverpool, UK

Evolutionary dynamics and the evolution of multiplayer cooperation in a subdivided population

Abstract

The classical models of evolution have been developed to incorporate structured populations using evolutionary graph theory and, more recently, a new framework has been developed to allow for more flexible population structures which potentially change through time and can accommodate multiplayer games with variable group sizes. In this paper we extend this work in three key ways. Firstly by developing a complete set of evolutionary dynamics so that the range of dynamic processes used in classical evolutionary graph theory can be applied. Secondly, by building upon previous models to allow for a general subpopulation structure, where all subpopulation members have a common movement distribution. Sub- populations can have varying levels of stability, represented by the proportion of interactions occurring between subpopulation members; in our representation of the population all subpopulation members are represented by a single vertex. In conjunction with this we extend the important concept of temperature (the temperature of a vertex is the sum of all the weights coming into that vertex; generally, the higher the temperature, the higher the rate of turnover of individuals at a vertex). Finally, we have used these new developments to consider the evolution of cooperation in a class of populations which possess this subpopulation structure using a multiplayer public goods game. We show that cooperation can evolve providing that subpopulations are sufficiently stable, with the smaller the subpopulations the easier it is for cooperation to evolve. We introduce a new concept of temperature, namely “subgroup temperature”, which can be used to explain our results.

Natalia Petrovskaya, Department of Mathematics, University of Birmingham, UK

Detection and classification of spatial patterns arising during invasive spread: is seeing believing?

Abstract

Biological invasion of alien species is regarded as one of the major threats to ecosystems all around the world and understanding of spatio-temporal patterns arising in invasive species spread is necessary for successful management and control of harmful species. Various growth-dispersal-type models of population dynamics predict that invasive species spread can follow two qualitatively different scenarios such as the propagation of a continuous population front and the `no-front' patchy invasion. Correct identification of those two patterns of spread is important, in particular because the patchy invasion poses a much greater challenge for monitoring and control. In my talk I will suggest some criteria that can be used to distinguish between the patchy invasion and the continuous front propagation. I will also discuss sensitivity of the spatial pattern topology to the parameters of monitoring protocol.

Yuriy Pichugin, Max Planck Institute for Evolutionary Biology, Plön, Germany

Evolution of simple multicellular life cycles in a dynamic environment

Abstract

We investigate evolution of reproduction in undifferentiated multicellular species. For new groups to emerge, existing groups must fragment. The fragmentation mode, the group size at the fragmentation and the distribution of fragments’ sizes, directly affect fitness. Therefore, it is subjected to natural selection. If the environment is static, the optimal life cycle always involves fragmentation into exactly two parts. We developed a matrix population model to investigate the evolution of fragmentation modes in dynamic environment, where different seasons favour different modes. The model shows that in dynamic environment, the range of possible optimal reproduction modes is much wider than in the static environment. However, at the same time, binary fragmentation modes remain locally stable under a wide range of selective conditions. Jean-Christophe Poggiale, Aix-Marseille University – MIO (Mediterranean Institute of Oceanography), France

Geometric tools for multiple time scales problems: applications in ecological modelling

Abstract

In systems with several time scales, an intuitive approach consists in considering the fast processes at equilibrium and in focusing on the slow processes by replacing the fast variables by their equilibrium values. This approach is commonly called the quasi-steady state assumption. In this talk, we present a predator – prey model and a virus – bacteria model with several time scales, in which the quasi-steady state assumption fails. We present in details a geometrical approach (blow up) to analyze the previous models. The method is general and can be extended to other situations. We show how it can help us to detect phenomenon like canards explosion, which may be useful in systems with tipping points, as we’ll discuss briefly.

Jonathan Potts, Department of Mathematics and Statistics, University of Sheffield, UK

How movement responses can shape demographic dynamics in strongly competing populations

(joint work with Sergei Petrovskii1)

Abstract

Animal movement is a key mechanism for shaping population dynamics. However, the processes by which movement can affect the survival and co-existence of interacting populations are not well understood. Here, we examine the effect of movement responses to foreign populations on demographic dynamics. We look at a simple model of two competing populations, where inter- specific competition is greater than intra-specific competition. Without space, this is a bistable system. When space is incorporated as diffusive movement, a travelling wave moves from the stronger population to the weaker. However, by incorporating behaviourally-induced directed movement towards the stronger population, the weaker one can slow the travelling wave down, even reversing its direction. Hence movement responses can switch the predictions of traditional mechanistic models. Finally, incorporating dynamic movement responses can also enable stable co- existence in a homogeneous environment, overturning long-held assumptions about the Competitive Exclusion Principle.

1Department of Mathematics, University of Leicester, UK Thomas Rawson, Mathematical Ecology Research Group, Department of Zoology, University of Oxford, UK

Optimal control approaches for combining medicines and mosquito control in tackling dengue

(joint work with Michael Bonsall1, 2)

Abstract

Over half the world's population live at risk of dengue (and other flavivirus) infections. This work builds on an integrated epidemiological and vector ecology framework to investigate cost-effective approaches for tackling dengue. Our aim was to determine whether vector control and/or vaccination strategies work best for dengue disease control. Using optimal control approaches, it was found that both vaccination programmes and the release of genetically modified self-limiting mosquitoes (comparable to sterile insect approaches) could be combined to reduce the number of infected individuals. However, coupled with the impact of human movement on the disease dynamics, it was found that the optimal way to combat the spread of disease was to focus prevention efforts on large population centres.

Keywords: Dengue; Optimal Control; Vaccine; Sterile Insect Technique; Migration; Network

1Mathematical Ecology Research Group, Department of Zoology, University of Oxford, New Radcliffe House, Radcliffe Observatory Quarter, Woodstock Road, Oxford, OX2 6GG, UK 2St. Peters College, New Inn Hall Street, Oxford, OX1 2DL, UK

Cordula Reisch, Technische Universität Braunschweig, Institute Computational Mathematics, Germany

Impact of geometry variations on solutions of reaction-diffusion models for hepatitis C infections

(joint work with Dirk Langemann1)

Abstract

Among liver infections, hepatitis C is one of the most spread virus and tends to chronify very often. Mathematical models provide insight in underlying mechanisms and allow to formulate hypotheses. We start with a reaction-diffusion model for two species, virus and immune reaction. Based on this model, we vary the geometry in different manners. The variations represent different features of the liver. The liver consists of large hepatic lobes and again of small hepatic lobules on a small scale. Regarding the lobes leads to a ramified structure with changed neighbourhood relations in unchanged dimensions. We study the effect of this ramified structure on the chronification tendency by adding cuts and obstacles in the domain describing the liver. Consequently, the mean distance between two points in the domain increases. We show that this results in a higher chronification tendency according to an analytic theorem based on J. Smoller (Shock waves and Reaction- Diffusion Systems, 1994, Springer).

Secondly, we model veins crossing the observed domain. The veins transport T cells directed and faster than the general slow blood flow through the liver. As a result, T cells get to areas faster, where veins are leading to. The veins change the topologic structure of the liver and the domain is part of a higher-dimensional manifold, now. For modelling veins, we couple a transport equation for the T cells on the vein with a reaction diffusion equation. We compare the results of the hybrid system of partial differential equations with the results of a cellular automaton. Finally, we generalize the geometry variations in a problem formulation on manifolds.

1Technische Universität Braunschweig, Institute Computational Mathematics, Germany

Andy Reynolds, Rothamsted Research, Harpenden, UK

Langevin dynamics encapsulate the microscopic and emergent macroscopic properties of midge swarms

Abstract

In contrast with bird flocks, fish schools and animal herds, midge swarms maintain cohesion but do not process global order. Nonetheless, high-speed imaging techniques have revealed that these swarms have surprisingly macroscopic properties, including a finite Young’s modulus and yield strength, and that they consist of a dense inner core and a more diffuse outer region that is reminiscent of a liquid/vapour phase equilibrium. Here I show that simple models found on the Langevin equation are consistent with this wealth of recent observations. The models also provide new insights into the influence of environmental conditions on swarm dynamics. They predict that correlations between midges increase the strength of the effective force binding the swarm together. This may explain why such correlations are absent in laboratory swarms but present in natural swarms which contend with the wind and other disturbances.

Tanya Rogers, Northeastern University Marine Science Center, USA

Hidden similarities in the asynchronous dynamics of Atlantic blue crab populations

(joint work with Stephan B. Munch1,2)

Abstract

Although theoretical and experimental work has explored the conditions that produce metapopulation synchrony or asynchrony, the reasons for asynchrony in wild populations have received much less attention. A variety of factors including nonlinear (chaotic) dynamics and/or spatial variation in these dynamics might lead to asynchrony, but quantifying spatially variable nonlinear dynamics in field data has been challenging. In this study, we present a hierarchical time- delay embedding framework based on Gaussian process (GP) regression that not only estimates nonlinear responses to predictors, but also produces a “dynamic correlation” metric that quantifies similarity in the response of populations to predictor variables (as opposed to similarity in observed abundances across time). In the first application of this method to empirical data, we examined the dynamics of blue crabs (Callinectes sapidus) from 16 populations across the U.S. Atlantic coast using fishery-independent time series data. Dynamic correlations across populations were strong and showed spatial patterning, particularly when environmental drivers were included in the model. Responses to predictors were broadly similar across populations, with some local variability. However, observed crab abundances did not show strong Pearson correlations or spatial synchrony across populations, even though the environmental predictors did. Moreover, the time series for all populations had positive Lyapunov exponents, suggesting chaotic dynamics. These results suggest that nearby populations, which appeared superficially independent, may have hidden dynamical similarities, and that the observed asynchrony potentially results from chaos. This is the first study to document these results in wild populations.

2 Southwest Fisheries Science Center, National Marine Fisheries Service, National Oceanic and Atmospheric Administration, 110 McAllister Way, Santa Cruz, CA 95060, United States

Axel Rossberg, Queen Mary University of London, UK

On the irrelevance of ecological theory and modelling

Abstract

Advanced ecological modelling is the logical response to today’s big challenges to humanity. We have entered the anthropocene, where every habitat on earth is affected by societal decisions: climate change is accelerating; climate change mitigation measures, biodiversity conservation, population and economic growth put competing pressures on land use; and diffuse environmental pollution now noticeably impact ecosystems. Much could be gained by anticipating and managing the responses of the world’s ecosystems to these pressures. Yet, there is more than anecdotal evidence that ecological modelling and the underlying theory have in practice remained largely irrelevant. This problem has long been recognised, but here it is argue that past analyses of the underlying reasons and proposals for solutions have fallen short of the magnitude and multifaceted nature of the challenge.

Some of the barriers to the advancement of ecological theory and modelling are extrinsic (e.g. the fascinations of ecological fieldwork, the perceived dominance of socio-economic issues in conservation, the inertia of science), some arise at the interfaces of the field (e.g. the small number of theorists in ecology, the constant flux of laypeople into the field, barriers to communication at the science-policy interface), and some are intrinsic to ecological theory and modelling (e.g. the complex, complicated, and variable nature of ecosystems, the fragmentation of the research community, the high costs of quantitatively predictive models).

To overcome these barriers, it is not enough to do what we do just more and better. Radical changes in attitudes and approaches might be required. The presenter proposes changes under keywords unity, pride, and visibility. To strengthen unity of the field, we need better understanding of how our models relate to and derive from each other; clearer canonification of concepts and terminology, and documentation of this knowledge in advanced textbooks. To avoid the costs of re-inventing wheels, more efforts should go into developing open-source, modular, reusable ecological modelling software with state-of-the art fitting facilities. Ensemble modelling should become commonplace. To build pride, recognition by us and others of the marginalised status of theory in ecology is the first step. Rising to the scientific challenges we face requires special skills and knowledge. There is also scope for a clearer differentiation from pseudo-science and pseudo theory in ecology. To improve our visibility, we must not only identify and name the big scientific and applied challenges we face, but also become more effective in celebrating their solutions.

Tim Russell, Royal Holloway, University of London, UK

Fluctuating dynamics in breakage-dependent selection and recombination systems

(joint work with Matthew Russell1, Francisco Úbeda2, Vincent A. A. Jansen3)

Abstract

Genetic systems with multiple loci can have complex dynamics. Particularly if fitness is non- epistatic, the population mean fitness need not increase continuously. Fisher's fundamental theorem does not hold in that case and the dynamics need not settle on equilibrium but can show sustained fluctuations. Here, we study the dynamics of a set of deterministic genetic systems in continuous and discrete time, inspired by the biology of breakage-dependent recombination, fertility selection, crossover and recombination. This results in the possibility of strong epistasis and strong selection. Importantly, the dynamics can give rise to heteroclinic cycles with repeated invasion of a modifier gene that then eliminates its own target sequence. This can result in dynamics dominated by recurrent selective sweeps. We study the dynamics and show that they can be understood in terms of a codimension 2 bifurcation, in which a heteroclinic orbit appears in a structurally stable manner. To analyse and characterise the dynamics we extract a closed form expression for the quasi-linkage equilibrium manifold using a quasi-steady state arguement and describe the dynamics in terms of stability of the equilibria and the heteroclinic orbit. We show that the dynamics differ between discrete and continuous time formualtions of the model.

1School of Mathematics at Nottingham University

2Department of Mathematics and Statistics, University of Sheffield, UK

3School of Biological Sciences, Royal Holloway University of London, UK

Alexey Ryabov, University of Oldenburg, ICBM, Germany

Imperfect prey selectivity of predators promotes biodiversity and irregularity in food webs

Abstract

(joint work with Bernd Blasius1 and Andrew Morozov2)

Ecological communities are often characterised by many species occupying the same trophic level and competing over a small number of vital resources. The mechanisms maintaining high biodiversity in such systems are still poorly understood. Here, we revisit the role of prey selectivity by generalist predators in promoting biodiversity. We consider a generic tri-trophic food web, consisting of a single limiting resource, a large number of primary producers and a generalist predator. We suggest a framework to describe the predator functional response, combining food selectivity for distinctly different functional prey groups with proportion-based consumption of similar prey species. Our simulations reveal that intermediate levels of prey selectivity can explain a high species richness, functional biodiversity, and variability among prey species. In contrast, perfect food selectivity or purely proportion-based food consumption leads to a collapse of prey functional biodiversity. Our results are in agreement with empirical phytoplankton rank-abundance curves in lakes.

1University of Oldenburg, ICBM, Germany 2Department of Mathematics, University of Leicester, UK

Simran Sandhu, Department of Mathematics, University of Leicester, UK

Revealing Evolutionary Optimal Strategies in Self-Reproducing Systems via a New Computational Approach

(joint work with Andrew Morozov1 and Oleg Kuzenkov2)

Abstract

Modelling evolution of complex life traits and behavioural patterns observed in the natural world is a challenging task, particularly when the behavioural pattern is described by a continuous function. We introduce a new computational method of obtaining the evolutionarily stable strategy in a generic population model with a strong inheritance based on reconstruction of a fitness function. This novel method can be applied to reveal optimal strategies in arbitrary self-reproducing systems for which such a generalised fitness exists. As a meaningful ecological case study, we explored the phenomenon of Diel Vertical Migration (DVM) of zooplankton in the vertical water column which is generally considered to be the largest synchronized movement of biomass on Earth. We are interested in revealing the optimal trajectory of DVM of zooplankton depending on the presence of food and predators. Unlike previous studies, we modelled the realistic case of DVM by including developmental stages of zooplankton and their predators as a dynamical variable. Implementing our method, we found that the optimal pattern of DVM drastically changed in the presence of dynamical predation and in the case where the strengths of intraspecific competition for adult and juvenile stages are different.

1Department of Mathematics, University of Leicester, UK 2Lobachevsky State University, Nizhni Novgorod, Russia Belgin Seymenoglu, Department of Mathematics, University College London, UK

Invariant manifolds of the Selection-Recombination model from Population Genetics

Abstract

I have been analysing a continuous-time model in Population Genetics which focuses on two evolutionary forces at play: selection and recombination. After plotting many phase plane diagrams for this system, I (almost) always found a stubborn special surface in my plots, which is called an invariant manifold. Now I have proved the manifold does indeed exist in the model for a certain case.

Nadav Shnerb, Bar-Ilan University, Department of Physics, Israel

Population and community dynamics under environmental stochasticity

Abstract

Biological populations are subject to two types of noise: demographic stochasticity due to fluctuations in the reproductive success of individuals, and environmental variations that affect coherently the relative fitness of entire populations. We have studied the dynamics of a two-species system under the effect of demographic noise with fluctuating selective forces, and calculated the chance of fixation [1,2], the time to fixation and the time to absorption [1,4] for a mutant (or invading) population. A highly diverse community in which all species have the same average fitness (a time-averaged neutral model) was also considered [3], and the resulting species abundance distribution is contrasted with the Fisher log-series distribution that characterizes the neutral model with pure demographic stochasticity.

References

[1] M. Danino and N.M. Shnerb, Fixation and absorption in a fluctuating environment. Journal of theoretical biology, 441 84 (2018).

[2] I. Meyer and N.M. Shnerb, Noise-induced stabilization and fixation in fluctuating environment, arXiv:1801.05970 (2018).

[3] M. Danino and N.M. Shnerb, A time-averaged neutral model with environmental stochasticity, arXiv:1711.11332 (2017).

[4] M. Danino, D.A. Kessler and N.M. Shnerb, Stability of two-species communities: drift, environmental stochasticity, storage effect and selection, Theoretical population biology 119, 57-71 (2018).

Michael Sieber, Max Planck Institute for Evolutionary Biology, Plön, Germany

Prophage-mediated competition between two key members of the Hydra vulgaris microbiota

Abstract

The two commensal bacteria Curvibacter sp. and Duganella sp. protect their host, the fresh-water polyp Hydra vulgaris, from fungal infections, but only if both of them are present. Coexistence of the two bacteria is thus beneficial for Hydra. In vitro, however, Duganella appears to be the superior competitor due to its higher growth rate when both bacteria are grown separately. But, intriguingly, in co-culture their growth rates depend on the relative initial abundances of the two species, with Duganella's growth rate suppressed when there is either a lot of Curvibacter present, or very little, but not at intermediate Curvibacter abundances. Using a mathematical model we show that the interplay between the lysogenic and lytic life cycles of an inducible Curvibacter prophage can explain the observed interaction between the two bacteria. This highlights the importance of taking lysogeny into account for understanding microbe-virus interactions and show the complex role phages can play in the interactions of their bacterial hosts.

References

Li, X.-Y., Lachnit, T., Fraune, S., Bosch, T.C.G., Traulsen, A., and Sieber, M. (2017). Temperate phages as self-replicating weapons in bacterial competition. J. R. Soc. Interface 14:20170563.

Anuraj Singh, ABV-Indian Institute of Information Technology and Management Gwalior, India

Complex dynamics in a fractional-ordered prey-predator model

Abstract

In this work, a fractional ordered prey-predator model is investigated. A sufficient condition for existence and uniqueness of the solution of the discretized system is determined. Jury stability test is applied for the occurrence of stability of equilibrium point of the discretized system. The system undergoes Neimark-Sacker and flip bifurcation under certain conditions. Numerical simulation suggests rich dynamical behavior including limit cycles, quasi-periodicity and chaos. The system exhibits a wide range of dynamical behaviors for key parameter fractional order α.

Jitendra Singh, Innovative Internet University for research, Kanpur, (UP), India.

The effect of density dependent emigration on the spread of infectious diseases: A Modelling study

(joint work with Shikha Singh1)

Abstract

In this paper, an SIS Mathematical model is proposed and analyzed by considering population density depended emigration. It is assumed the disease is transmitted by direct contact of susceptibles and infectives with immigration and emigration dependent contact rate. The equilibrium analysis of the model is conducted by using the stability theory of ordinary differential equation and computer simulation. The model analysis shows that the spread of infectious disease increases as the rate of constant immigration increases but its spread decreases as emigration rate increases. The simulation study also confirms these analytical results.

Kew words: Epidemiology, mathematical modelling, Density dependent migration, Stability.

1Department of Mathematics PPN College, CSJM University, Kanpur (UP), India.

Max Souza, Departamento de Matematica Aplicada, Universidade Federal Fluminense, Brazil

Fixation: The Fingerprint of Evolutionary Processes

Abstract

Starting from the classical Moran and Wright-Fisher processes we will show how a class of discrete processes can be completely determined by prescribing their fixation probability, and also that there are interesting processes for which such determination does not hold. We will also show that, if we assume that the prescribed fixation comes from a smooth function, then, for large populations, the corresponding processes will be in the weak-selection regime. Finally, we will show how fixation in large population of d-player games can produce very complex fixation patterns, and how these games can be recovered from fixation data.

Helena Stage, Department of Applied Mathematics, University of Manchester, UK

Anomalous metapopulation dynamics on scale-free networks

Abstract

We model transport of individuals across a heterogeneous scale-free network where a few weakly connected nodes exhibit heavy-tailed residence times. Using the empirical law Axiom of Cumulative Inertia and fractional analysis we show that `anomalous cumulative inertia' overpowers highly connected nodes in attracting network individuals. This fundamentally challenges the classical result that individuals tend to accumulate in high-order nodes. The derived residence time distribution has a non-trivial U-shape which we encounter empirically across human residence and employment times.

Markus Stark, University of Potsdam, Germany

How spatial networks affect food web structure and persistence

(joint work with Johanna Häussler1, Remo Ryser1, Björn Rall2, Ulrich Brose2, Christian Guill3)

Abstract

Dispersal is an essential strategy for a large number of species that allows them to find for instance mating partners, suitable nesting places, better growing conditions or to escape predation pressure. Species habitats are connected through dispersal in the landscape forming a spatial network. However, environmental and anthropogenic drivers alter the spatial structure causing fragmentation and isolation of natural habitats. Modelling studies addressing the impact of habitat isolation on biodiversity focused so far mainly on meta-populations dynamics and ignored trophic interactions. To gain understanding how ecological communities persist in a heterogeneous landscape, we extended an allometric food web model with spatial networks linking local populations via dispersal between habitat nodes and evaluated its diversity patterns. With an increased isolation of habitats we observed that species persistence (γ-diversity) and the local diversity (α-diversity) decreases whereas β-diversity is rather constant but exhibits a peak for a high isolation. The number of available habitats in contrast has a minor effect on species persistence and shows no clear pattern.

1German Centre for Integrative Biodiversity Research, Theory in Biodiversity Science, Leipzig, Germany

2Institute of Biodiversity, Friedrich-Schiller-Universität Jena, Germany

3Institute of Biochemistry and Biology, Universität Potsdam, Potsdam, Germany

Michael Stich, Aston University, Birmingham, UK

Evolutionary search processes in simple replicator populations

Abstract

RNA molecules, through their dual identity as sequence and structure, are an appropriate experimental and theoretical model to study the genotype-phenotype map and evolutionary processes taking place in simple replicator populations. In this study, we relate properties of the sequence-structure map, in particular the abundance of a given secondary structure in a random pool, with the number of replicative events that an initially random population of sequences needs to find that structure through mutation and selection. For common structures, this search process turns out to be much faster than for rare structures. Furthermore, search and fixation processes are more efficient in a wider range of mutation rates for common structures, confirming that evolvability of RNA populations is not simply determined by abundance. We extend the evolutionary process by considering changing environments and incorporating recombination into the dynamics.

Michiel Stock, Department of Data Analysis and Mathematical Modelling, Ghent University, Ghent, Belgium

Disentangling ecological networks using graph embedding methods

(joint work with Timothée Poisot2 and Bernard De Baets1)

Abstract

Species interaction networks, such as plant-pollinator networks, host-parasite networks and food webs, are principal tools to understand ecosystems from a community perspective. These networks, a collection of species as nodes and their interactions as edges, encode the structure of an ecosystem. Such networks are often analyzed by computing various indices that quantify properties such as connectance, nestedness, modularity and the like, or by using other attributes such as the edge distributions. These indices can subsequently be related to emergent properties or be used to compare networks. Often, computing such indices is hard and it not always clear which index is the most useful for a particular research question. Rather than using such a statistical approach to networks, we suggest a framework based on data mining and machine learning.

In our work, we have studied how to use graph embedding to construct numerical descriptions of the species, describing their role and functionality in the network. Basically, our methods try to find for every species a vector such that the inner product of two vectors can be related to the probability of the two species interacting. We show that these representations can be used to clearly visualize the network structure and predict missing interactions. From a more theoretical point of view, we found that a small number of dimensions are often sufficient to reconstruct the network, confirming the established idea that ecological networks are inherently low dimensional, i.e. a small number of traits can explain the interactions. By generating numerical representations of the species based on how they fit into the network, all established supervised and unsupervised machine learning methods can directly be applied to such data sets. The representations can, for example, be used to predict hard-to-measure traits, or, vice versa, traits can be used to predict the representations. Furthermore, using a suitable aggregation function, the individual species representations can be combined into a holistic network description, allowing to compare or even to predict networks. In short, graph embedding approaches allow to transform a complex network in a standard numerical representation, which can be processed by most machine learning methods. They allow for a more flexible way of analyzing ecological networks compared to using indices.

Keywords Species interaction networks — Graph embedding — Machine learning

1Department of Data Analysis and Mathematical Modelling, Ghent University, Ghent, Belgium 2Département de Sciences Biologiques, Université de Montréal, Montréal, Québec, Canada Christopher D Terry, Department of Zoology, University of Oxford, UK

Identifying significant trophic interaction modifications for population dynamics in ecological communities

(joint work with R.J. Morris1 and M.B. Bonsall1)

Abstract

Historically, efforts to understand the dynamics of ecological communities have focussed almost exclusively on pairwise trophic interactions. However, it has been repeatedly demonstrated that trophic interactions can be strongly influenced by other species in the community. Improvements to our understanding of the impact of these trophic interaction modifications (TIMs) has been slow; this is in part due to the overwhelming complexity that these processes can introduce and the highly multi-dimensional demands on data.

As an initial step to move from demonstrations of the potential impact of TIMs to an understanding of how they lead to consequences in a food web context, we have developed a set of approaches to conceptualise and quantify the strength and topological distribution of TIMs. A feature of these metrics is that they maintain the multi-species nature of TIMs, in contrast to approaches that coerce the effects into pairwise non-trophic interactions. To identify properties of TIMs that are particularly significant we apply the metrics to models of simulated ecological communities. We test which metrics are best able to identify a subset of TIMs that drive the dynamics of the whole community, in terms of directional response to press perturbation and local stability.

We find that it is possible to identify features of a critical subset of TIMs. Structural properties of key TIMs include low density modifier species, the modification of high flux interactions, and modifications directed ‘down’ the web from top predators. Direct metrics of TIM strength are also valuable metrics, as measured by the influence of the modifier density on either the interactor species growth rates or the underlying direct interaction strength. By contrast, the centrality of the interaction being modified and the distance across the web had comparatively little significance.

This theoretical work demonstrates that analysis of interaction modifications can be tractable at the network scale. It allows us to make suggestions of where experimental emphasis should be placed in practical efforts to understand the effect of interaction modifications in ecological communities.

1Department of Zoology, University of Oxford, UK

References

Terry, J.C.D., Morris, R.J., Bonsall, M.B. (2017) Trophic Interaction Modifications: An empirical and theoretical framework, Ecology Letters, 20:1219-1230

Terry, J.C.D., Morris, R.J., Bonsall, M.B. Identifying Important Interaction Modifications in Ecological Systems (bioRxiv preprint) https://doi.org/10.1101/228874 Martina Testori, Department of Applied Mathematics, University of Southampton, UK

How psychopathic people help us to survive (or not)?

(joint work with R.B.Hoyle1 and H.Eisenbarth2)

Abstract

We investigate how individuals with high levels of psychopathic traits might contribute to community survival in an environment where resources are sometimes scarce. Psychopaths are described as lacking of remorse, heartless, unresponsive in interpersonal relations, rational, egoistic and successful players of economic games [1, 5, 4]. However, they are also depicted as slow learners, callous and indifferent to punishment [3, 2]. We simulate the evolution of populations that include highly psychopathic individuals using evolutionary game theory to see whether the presence of such individuals can have a positive impact on survival. Each generation plays an iterated ultimatum game with nature, through which they gather the necessary resources to survive, and a public goods game with their fellow citizens, which partially redistributes resources across the population. Both the community and the individual require a minimum level of resources to survive and individuals that hold more resources have a greater chance of reproduction. The community is composed of individuals belonging to one of two phenotypes - psychopaths and controls - that have distinct strategies in the ultimatum and public goods games. Preliminary results show that community starting with a higher proportion of psychopaths collect a higher threshold of resources overall, and so are able to survive in harsher environments. Hence, the presence of psychopaths appears to provide a benefit to the community. However, in more favourable environments, communities with a lower proportion of psychopaths amass more resources. We explore the trade-off between the dynamics in the two games that leads to these opposing results and investigate how changes in the environment over time can favour different community compositions.

1Department of Mathematical Sciences, University of Southampton 2Department of Psychology, University of Southampton

References [1] Joanna M. Berg, Scott O. Lilienfeld, and Irwin D. Waldman. Bargaining with the devil: Using economic decision-making tasks to examine the heterogeneity of psychopathic traits. Journal of Research in Personality, 47(5):472-482, 2013.

[2] K. S. Blair, J. Morton, A. Leonard, and R. J R Blair. Impaired decision-making on the basis of both reward and punishment information in individuals with psychopathy. Pers. Individ. Dif., 41(1):155-165, 2006.

[3] Sarah Gregory, R. James Blair, Dominic Ffytche, Andrew Simmons, Veena Kumari, Sheilagh Hodgins, and Nigel Blackwood. Punishment and psychopathy: A case-control functional MRI investigation of reinforcement learning in violent antisocial personality disordered men. The Lancet Psychiatry, 2(2):153-160, 2015.

[4] Robert Mnookin. Bargaining with the devil: When to negotiate, when to fight. Simon and Schuster, 2010.

[5] Takahiro Osumi and Hideki Ohira. The positive side of psychopathy: Emotional detachment in psychopathy and rational decision-making in the ultimatum game. Pers. Individ. Dif., 49(5):451- 456, 2010. Paulo Tilles, University of Leicester (UK) and Universidade Federal de Santa Maria (Brazil)

On Stochastic Animal Movement Across Temporal Scales

(joint work with Sergei Petrovskii1)

Abstract

Over the last two decades there has been an intense discussion as to whether animals move predominantly diffusively or super-diffusively. While many plausible mechanisms for Levy walks have been identified, there's still relative little work done to relate the observed movement pattern to animal's biological traits and to the properties of the environment. In this talk we are going to resent an approach to stochastic animal modeling based on its most fundamental temporal scale, which is able to address the former requirement while also shows that diffusive and super-diffusive types of motion are inherent parts of the same general process. We are going to discuss its implications under the light of the growing amount of high resolution movement data and how it can help understand the typical patterns observed at large temporal scales.

1Department of Mathematics, University of Leicester, UK

Tyutyunov Yuri, Southern Scientific Centre of Russian Academy of Sciences, Rostov-on-Don, Russia

Spatial demogenetic models of population dynamics

(joint work with Lyudmila I. Titova1)

Abstract

The general demogenetic framework was first proposed by V.A. Kostitzin [1] who applied the Lotka – Volterra competition theory [2, 3] to describe interactions of genotypes in a diploid population. Such models couple description of both population demography and natural selection of traits at the level of genotypes. Operating directly with genotype densities, the Kostitzin model generalizes the classical Fisher–Haldane–Wright genetic equations that deal with allele frequencies [4–6]. At the same time domain of applicability of demogenetic models is much wider compared to conventional frequency-based Fisherian models of population genetics. Though originally the Kostitzin model was formulated for a non-spatial case, this approach offers a natural and easy way of accounting for the genetic structure of population in spatially- explicit models containing the diffusion and taxis terms [7, 8]. The demogenetic description of population dynamics can be used either for isolated population or can be built into a model that considers interactions of populations constituting a trophic community. We review our results obtained with spatial demogenetic models constructed for solving particular applied and theoretical problems of biological methods of plant protection and weed control, discussing the advantages and limitations of the approach. In particular, the demogentic approach is extremely helpful in revealing the factors that determine successful application of phytophagous biological agent combating against invading weed species [8]. The work was funded by the research project 0259-2014-0004 of SSC RAS “Development of GIS-based methods of modelling marine and terrestrial ecosystems”, RFBR project 18-01-00453 “Multistable spatial-temporal scenarios for population models”, basic research program of the Presidium of RAS No. 52 “Ensuring of stable development of the South of Russia under climatic, environmental, and man-caused challenges” and by the basic part of the state assignment research, project 1.5169.2017/8.9 of SFedU “Fundamental and applied problems of mathematical modelling”.

1Southern Federal University (SFedU), Rostov-on-Don, Russia

References: 1. Kostitzin, V.A. Biologie Mathématique. Librairie Armand Colin, Paris. 1937. 223 p. 2. Lotka, A.J. Elements of Physical Biology. Williams and Wilkins, Baltimore. 1925. 460 p. 3. Volterra, V. Leçons sur la Théorie Mathématique de la Lutte Pour La Vie. Gauthiers–Villars, Paris. 1931. 214 p. 4. Fisher, R.A. The General Theory of Natural Selection. Clarendon Press, Oxford. 1930. 354 p. 5. Haldane, J.B.S. A mathematical theory of natural and artificial selection. III. Proc. Camb. Phil. Soc., 1926. Vol. 23. P. 363–72. 6. Wright, S. Evolution in Mendelian populations. Genetics, 1930. Vol. 16. P. 97–159. 7. Tyutyunov, Yu., Zhadanovskaya, E., Bourguet, D., Arditi, R. Landscape refuges delay resistance of the European corn borer to Bt-maize: A demogenetic dynamic model. Theoretical Population Biology, 2008. Vol. 74, No. 1. P. 138–146. 8. Tyutyunov, Yu.V., Kovalev, O.V., Titova, L.I. Spatial demogenetic model for studying phenomena observed upon introduction of the ragweed leaf beetle in the South of Russia. Mathematical Modelling of Natural Phenomena, 2013. Vol. 8, No. 6. P. 80–95.

Rik Verdonck1,2

Phase related behaviour in the desert locust: classification versus characterization

(joint work with Jozef Vanden Broeck2, Swidbert R. Ott3)

Abstract

The desert locust, Schistocerca gregaria, exhibits extreme phenotypic plasticity resulting in two very distinct morphs: a solitarious and a gregarious phase. Upon the presentation of certain stimuli, animals of the solitary phase acquire a set of gregarious-like behaviours in a matter of hours. Under natural conditions, this shift in behaviour marks the beginning of phase transition, where increased interaction between animals causes a positive feedback loop resulting in the transition to the gregarious phase. For more than two decades, an arena-based assay has been used in studies where typically models are fitted on the behaviour of long-term gregarious and solitarious animals. These models are then used to assess intermediate phase states of animals during phase transition under a range of experimental regimes. Here, we present our observations of solitarous, gregarious and transitioning animals in this same arena. Using PCA and EFA we show that phase-related behaviour is composed of multiple latent factors that need not necessarily change in a concerted manner. Our findings corroborate a growing body of evidence that transitioning animals are not simply intermediates between extreme phases. By comparing animals that underwent different stimulus regimes, we also demonstrate that cases exist where behaviour shifts outside the multivariate distribution typically seen in animals from either long-term phase. This finding may have implications for the validity of the one-dimensional Pgreg that is commonly seen in literature.

1Theoretical and Experimental Ecology station (SETE), Moulis, France

2Animal Physiology and Neurobiology, Zoological Institute, KU Leuven, Belgium

3Department of Neuroscience, Psychology and Behaviour, University of Leicester, UK

Kai Uwe von Prillwitz, Institute for Chemistry and Biology of the Marine Environment, University of Oldenburg, Germany

Mid-domain effect for food chain length

(joint work with Bernd Blasius1)

Abstract

The classical mid-domain effect (MDE) states that in a spatially bounded habitat maximal species richness is observed in general in the interior of the habitat, even in the absence of any environmental gradient. Here, we extend this effect from species richness to food chain length. We employ a spatially explicit patch-dynamic model, allowing for simple trophic interactions. First, we restrict the model to linear food chains and demonstrate that the average food chain length peaks in the center and declines towards the boundaries, both in one-dimensional and two-dimensional habitats. We are able to provide a simple explanation of the effect based on properties of the underlying spatial structure. Next, we go beyond simple food chains by introducing an omnivore. In addition to the usual MDE, i.e. the monotonous decline towards the boundaries, we find that diversity and food chain length are maximal in a layer at an intermediate distance to the boundary. The maximum is caused by the omnivore that predominantly occupies this intermediate layer. In the mid of the domain, which is dominated by the specialist top predator, diversity is slightly smaller. Finally, we show that the MDE can be extended to more general spatial network topologies, where the average food chain length, or species richness, is related to network centrality measures. Our results can give additional insights into the role of space, or of the specific spatial structure, on food web assembly and persistence.

1University of Oldenburg, ICBM, Germany

Nicola Walker, Centre for Environment, Fisheries and Aquaculture Science (Cefas), United Kingdom

Can individual-based models provide useful insights into the management of recreational and commercial fisheries?

(joint work with Kieran Hyder1)

Abstract

The European seabass is a slow growing and late maturing high value fish that is exploited by both commercial and recreational fisheries, and exhibits very large interannual variability in recruitment driven by environmental factors. In recent years, increased fishing mortality and poor recruitment is thought to have led to decline of the northern stock. As a result, management measures have been introduced to reduce fishing mortality including closed areas and seasons, increased minimum landing sizes, and bag and boat limits. Individual-based models (IBMs) have been shown to be effective management tools in many systems, but have yet to be applied to seabass. Here, an IBM that accounts for temperature, reproduction, growth, mortality, behaviour, and exploitation was developed to model the population dynamics and spatial distribution of seabass. The model was parameterised using existing knowledge from the literature and can reproduce the dynamics observed in scientific assessments of the stock when similar assumptions are made. The model is used to test strategies for the recovery of seabass, including spatial management measures. We discuss the utility of such an approach for the conservation and sustainable management of recreational and commercial seabass fisheries.

1Centre for Environment, Fisheries and Aquaculture Science (Cefas), UK

Marcel Weiss1,2

Studying the Causes of Phenotype Robustness and Evolvability in Genotype- Phenotype Maps

(joint work with Sebastian E. Ahnert1,2)

Abstract

Genotype-phenotype (GP) maps and their properties fundamentally affect evolutionary processes. A particularly striking property found in several GP maps, such as that of RNA secondary structure, is the positive correlation between the robustness and evolvability of phenotypes. It implies the beneficial ability of phenotypes to be strongly robust against mutations and at the same time evolvable to a diverse range of alternative phenotypes. In this talk, we present our modelling approaches to identify the underlying characteristics in GP maps that lead to this property. With the help of two analytically tractable models that build on basic principles of real biological GP maps, we deduce that the emergence of a positive correlation between phenotype robustness and evolvability depends on the possibility that mutations can have non-local effects on sequence constraints, highlighting that these effects are likely to be an important feature of many biological GP maps.

References

Weiss M, Ahnert SE, Phenotypes can be robust and evolvable if mutations have non-local effects on sequence constraints, J. R. Soc. Interface 15: 20170618 (2018)

1Theory of Condensed Matter Group, Cavendish Laboratory, University of Cambridge, UK

2Sainsbury Laboratory, University of Cambridge, UK Haim Weissmann, Bar Ilan University, Department of Physics

Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition.

(joint work with R. Kent2, Y. Michael2 and N.M. Shnerb1)

Abstract

The process of desertification in the semi-arid climatic zone is considered by many as a catastrophic regime shift, since the positive feedback of vegetation density on growth rates yields a system that admits alternative steady states. Some support to this idea comes from the analysis of static patterns, where peaks of the vegetation density histogram were associated with these alternative states [1]. We present a large-scale empirical study of vegetation dynamics, aimed at identifying and quantifying directly the effects of positive feedback. To do that, we have analyzed vegetation density across 2.5 106 km2 of the African Sahel region, with spatial resolution of 30X30 meters, using three consecutive snapshots [2]. The results are mixed. The local vegetation density (measured at a single pixel) moves towards the average of the corresponding rainfall line, indicating a purely negative feedback. On the other hand, the chance of spatial clusters (of many "green" pixels) to expand in the next census is growing with their size, suggesting some positive feedback. We show that these apparently contradicting results emerge naturally in a model with positive feedback and strong demographic stochasticity. Static patterns, like the double peak in the histogram of vegetation density, are shown to vary between censuses, with no apparent correlation with the actual dynamical features. Our work emphasizes the importance of dynamic response patterns as indicators of the state of the system, while the usefulness of static modality features appears to be quite limited.

1Department of Physics, Bar-Ilan University, Israel

2Department of Geography and Environment, Bar Ilan University, Israel.

References

[1] H Weissmann and NM Shnerb, Predicting catastrophic shifts. Journal of theoretical biology 397, 128-134 (2016).

[2] H Weissmann, R Kent, Y Michael, NM Shnerb, Empirical analysis of vegetation dynamics and the possibility of a catastrophic desertification transition. PloS one 12 (12), e0189058 (2017).

Robert West, Applied Mathematics Department, University of Leeds, UK

The influence of external and internal noise on the cyclic Lotka-Volterra Model

(joint work with M. Mobilia1 and A. M. Rucklidge1)

Abstract

We study the influence of external and internal noise on the cyclic Lotka-Volterra model, equivalent to the paradigmatic zero-sum rock-paper-scissors game, a popular method of modelling three species that compete with each other non-transitively. The effect of internal noise is well known, causing extinction of all but one species in finite time with the survival probabilities following the “law of the weakest” when population sizes are large. The influence of external noise is examined in the by defining one of the reproduction-predation rates to be a Dichotomous Markov Process switching between a high and low value with constant rate \nu, corresponding to more or less favourable conditions. We show that under intermediate switching rates, the law of the weakest no longer holds and the new survival probabilities depend on the strength of the noise. If time permits, we will also outline the effect on the fixation probabilities of the coupling of demographic and external noise, which results from the random switching according to a Dichotomous Markov Process of the carrying capacity.

1Department of Applied Mathematics, University of Leeds, UK

References

Ref: e-print arXiv:1711.08966.

Yuval Zelnik, Centre for Biodiversity Theory and Modelling, CNRS, France

The three regimes of spatial recovery

(joint work with Jean-Francois Arnoldi1 and Michel Loreau1)

Abstract

Identifying the drivers of ecosystem and population stability is a fundamental aspect of ecology. In an spatially explicit context, the basic ingredients to consider are the spatial structure of the landscape, the local dynamics of species, and their dispersal behavior which mediates between the two former ingredients. Much work has been done on each of these ingredients as a driver of stability, but little is known on the interplay between them. Missing has been a more integrative approach, able to map and identify the possible dynamical regimes which determine the response to perturbations, i.e. the stability properties of ecosystems and populations. We focus on a simple, yet relatively general, scenario: the recovery of a homogeneous metapopulation from a single, spatially localized pulse disturbance. We find that the response can take one of three forms each representing one of three dynamical regimes: Isolated, Interplay and Mixing. Using dimensional analysis we can predict the transition points between these regimes, and how these change with basic system properties such as its total area and the nonlinearities of local dynamics. We deduce a framework which enables us to address pertinent questions for ecology such as the effect of habitat fragmentation, which effectively pushes systems towards the Isolated regime, or of global change which may slow down local dynamics as conditions deteriorate, pushing systems towards the Mixing regime. Finally, we can also better position other studies that address various questions, from the stabilizing effect of disturbances on populations prone to synchrony-induced extinctions, to the mechanisms underlying biomass productivity in metacommunities.

1Centre for Biodiversity Theory and Modelling, CNRS, France

Anna Zincenko, Department of Mathematics, University of Leicester

An Economic-Demographic Dynamical System.

(joint work with Sergei Petrovskii1 and Vitaly Volpert2)

Abstract

Human population growth has been called the biggest issue the humanity faces in the 21st century, and although this statement is globally true, locally, many Western economies have been experiencing population decline. Europe is in fact homeland for population decline. By 2050 many large European economies are predicted to lose large parts of their population. In this work, we have investigated, as a preliminary step to the spatial model investigation, introduced by (Volpert et. al 2017) the behaviour of the dynamical system. We have found various scenarios of population and wealth evolution which depend on different levels of parameters. These scenarios represent three possibilities: population extinction, population stabilisation with damped oscillation, and undamped oscillation. The considered dynamical system is absolutely stable, so that unlimited growth of population is not possible within this framework. We have found two kinds of local bifurcations: Hopf Bifurcation, and saddle-node bifurcation.

1Department of mathematics, University of Leicester, UK

2Institut Camille Jordan, University Lyon 1, France

Posters

Omar Alzeley (Mathematics, University of Leicester, UK). Modelling Predator-Prey behaviour via quantum random walk.

Nadir Amir (Université de Bejaia, Algeria). Genetic ancestry of a Berber population of Bejaia (Northern Algeria) revealed by STR analysis.

Cecilia Berardo (University of Helsinki Finland). Modelling Prey cooperation and predator learning interaction.

Boris Berkhout (Biology, University of Leicester, UK). Temperature effects on a parasite effect with a complex life-cycle, an integral approach.

Wonhyung Choi (Mathematics, Korea University, South Korea). A SIS epidemic reaction- diffusion model with risk-induced dispersal.

Natasha Ellison (University of Sheffield, UK). Mechanistic Home-Range Pattern Formation of Long-Tailed Tits.

Mitchell Field (Biology, University of York, UK). Biological analysis of a plankton-oxygen dynamics model.

Benjamin Girardot (Mediterranean Institute of Oceanogaphy, France). Analysis of the effects of disturbances on the structure and dynamics of marine food webs: a size-structured modelling approach.

Leanne Massie (Imperial College London, UK). Synthetic Nitrogen Fixing Bacteria: A whole cell modelling approach

Laurent Mémery (LEMAR, CNRS, France). Impact of tidal front dynamics on phytoplankton biodiversity: a modelling approach.

Leonardo Miele (Mathematical Biology and Medicine, University of Leeds, UK). Statistical physics of evolutionary biology.

Suhayl Mulla (Mathematics, Aston University, UK). Life in equation: Computational analysis of lifespan in multiple organisms reveals conserved biphasic dynamics

Sizah Mwalusepo (Dar es Salaam Institute of Technology, Tanzania). Modelling the impact of climate change on the future distribution of honeybees in Indian Ocean Island Nations: Case study of Zanzibar Island

Richard Sheppard (Imperial College London, UK). Plasmid persistence and species diversity in microbial communities.

Anthony Sun (University of Osnabruck, Germany) A social-ecological model of lake pollution dynamics.

Titova Lyudmila (Southern Federal University (SFedU), Rostov-on-Don, Russia). Studying natural selection of animal movement ability with demogenetic model.

Tatiana Tyukina (Mathematics, University of Leicester). Oscillations in physiological adaptation: limit cycles, oscillating death and recovery.

Irina Vortkamp (University of Osnabruck, Germany). Metapopulations with Allee effects and essential extinction in local patches. Jonathan Woodward University of York, UK Dynamics of buoyant plankton in Taylor-Green flow

Suggestions for lunch on Campus

Charles Wilson Building, ground floor: cafeteria Piazza and the student canteen

Charles Wilson Building, first floor: academic staff canteen

Percy Gee Students’ Union, Nineteen Twenty Three restaurant and other cafeterias in the same building

The Library Building: cafeteria

There is also a plenty of café and restaurants on London Road (about ten minute walk from the campus) but having lunch there normally requires at least 1.5 hours.

All talks are here! (Bennett) Main Campus Map Lunch suggestions!!!