Mathematical Ecology: A Century of Progress, and Challenges for the Next Century
Presenter
September 21, 2016
Abstract
Mathematical ecology is one of the oldest and most successful branches of mathematical biology, and one that has profited both ecology and mathematics. The great mathematician Volterra was a pioneer a century ago, and the subject has built on the dynamical systems approaches he introduced. As attention has turned to the ecological challenges of the present- climate change, biodiversity loss, critical transitions and the management of the global commons, new methods have entered from stochastic processes to game theory, from statistical physics to topological data analysis, and with a heavy emphasis on high-speed computation. In this talk, I will trace out some of the historic successes, and introduce modern challenges.
Supplementary Materials
Timecodes
- 02:26
- Mathematical Ecology: A Century of Progress and Challenges for the Next Century
- 02:26
- Mathematical Ecology: A Century of Progress and Challenges for the Next Century
- 02:29
- With thanks to
- 02:29
- With thanks to
- 03:01
- Mathematics has been used to address ecological problems for centuries
- 03:01
- Mathematics has been used to address ecological problems for centuries
- 03:47
- Population Sizes from Fibonacci Sequence
- 03:47
- Population Sizes from Fibonacci Sequence
- 04:23
- This is a Trivial Example of a Deep Result
- 04:23
- This is a Trivial Example of a Deep Result
- 05:21
- The (stable) age distribution carries much information about births and deaths
- 05:21
- The (stable) age distribution carries much information about births and deaths
- 05:51
- Later theory extended these considerations to continuous age/time
- 05:51
- Later theory extended these considerations to continuous age/time
- 06:34
- Mathematics has been used to address ecological problems for centuries
- 06:34
- Mathematics has been used to address ecological problems for centuries
- 07:03
- Mathematics has been used to address ecological problems for centuries (cont.)
- 07:03
- Mathematics has been used to address ecological problems for centuries (cont.)
- 07:23
- Theoretical Ecology Has A Long and Rich History
- 07:23
- Theoretical Ecology Has A Long and Rich History
- 07:51
- Volterra's Contributions to Ecology
- 07:51
- Volterra's Contributions to Ecology
- 08:06
- Volterra's Contributions to Ecology (cont.)
- 08:06
- Volterra's Contributions to Ecology (cont.)
- 08:24
- Volterra brilliantly examined the properties of multi-species communities and their statistics
- 08:24
- Volterra brilliantly examined the properties of multi-species communities and their statistics
- 08:37
- But this spawned an increasingly sterile mathematical tradition, ignoring ecological reality
- 08:37
- But this spawned an increasingly sterile mathematical tradition, ignoring ecological reality
- 09:05
- Nonetheless, the challenges remain unabated
- 09:05
- Nonetheless, the challenges remain unabated
- 09:19
- Mathematics has been used to address ecological problems for centuries
- 09:44
- EPIDEMICS - Classical Theory (Kermack - McKendrick)
- 10:16
- Kermack - McKendrick Model - 2 Competing Strains
- 10:49
- Models of the dynamics of iinfectious disease have played a fundamental role in their management, for example in vaccination strategies
- 11:10
- Mathematics has been used to address ecological problems for centuries
- 11:22
- All of these examples lead to some grand challenges, to which I will return
- 11:29
- Mathematics stimulated by ecological problems
- 11:55
- History of Statistics & Probability
- 11:59
- Other Areas of Math Stimulated by Biology
- 12:45
- Other Areas of Math Stimulated by Biology (cont.)
- 14:04
- Other Areas of Math Stimulated by Biology (cont.)
- 15:02
- Mathematical and systems thinking is increasing in influence
- 15:34
- Ecology for Bankers
- 16:26
- Ecology for Bankers (cont.)
- 17:09
- Financial Regulation
- 17:33
- World Politics
- 18:09
- Grand Challenges of Mathematical Systems Theory
- 20:21
- Ecosystems and the Biosphere are Complex Adaptive Systems
- 22:02
- So too are the socio-economic systems with which they are interlinked
- 22:18
- Stock markets crash... as collective consequence of individual actions
- 22:26
- There may be Critical Biosphere Thresholds
- 22:42
- Many... but not all... such transitions have characteristic early warning signals
- 23:48
- When do these work? Avoid excessive claims
- 24:07
- Caution is needed... Mechanisms need to be identified
- 25:13
- Getting Mechanisms right crucial
- 25:30
- Challenges of Systems Theory
- 25:46
- Sustainability must focus on macroscopic features, while recognizing that control of those rests at lower levels of organization
- 26:31
- Forest growth models can scale from individual to ecosystem
- 27:40
- Vegetation models have been sucessful in explaining global patterns, though not individual species abundances
- 28:21
- And similar approaches can examine collective decision-making
- 28:33
- Agent-Based Models Help
- 29:20
- But reduced dimensional descriptions will be essential for robustness of conclusions
- 29:50
- Time out for questions?
- 34:04
- Systems models can inform the potential for critical transitions
- 35:59
- Staver et al. 2011 (Ecology) and Staver & Levin (Amer. Natur.)
- 37:56
- Such phenomena are widespread
- 38:16
- Individual-based models relate the small-scale to the large scale
- 38:51
- Diffusion models inadequate: Organisms don't move randomly, but follow gradients or actively aggregate
- 39:19
- Lagrangian-Eulerian Connections
- 40:37
- But real aggregations are heterogeneous assemblages of individuals
- 40:45
- The dynamics of collective phenomena and collective decision-making
- 41:02
- Role of leadership and collective decision-making
- 41:26
- Two-Target Model
- 42:55
- 1 Informed Individuals in Group of 100
- 43:34
- 10 Informed Individuals in Group of 100
- 44:02
- Cometitioin and Consensus
- 44:42
- Theoretically and empirically, unopinionated individuals are crucial to nature of consensus.
- 45:26
- Challenges of Systems Theory
- 45:42
- Public goods problems are widespread in socio-economic and ecological contexs
- 47:00
- The Tragedy of the Commons
- 47:12
- The Commons solution (Hardin, Ostrom)
- 47:41
- Social norms can sustain and enhance prosocial behavior
- 49:02
- Fairness norms can provide "Mutual coercion, mutually agreed upon"
- 49:24
- Equity-Driven Ostracism: Nash Equilibria
- 50:36
- Equity-Driven Ostracism
- 51:06
- Tavoni, Schluter, Levin: Coordination Game
- 51:45
- Lessons Learned
- 52:38
- Avinash Dixit-Simon Levin: Prosociality and Multiple Groups
- 52:57
- Ostrom: Climate Change
- 53:12
- Climate Clubs: Overcoming Free-riding in International Climate Policy
- 53:20
- Incomplete Cooperation and Co-benefits: Deepening Climate Cooperation with a Proliferation of Small Agreements
- 53:36
- Club Approach
- 53:47
- Summary so far
- 54:42
- Voting Theory and Models of Collective Action
- 54:55
- Modeling of Collective Decision-Making Represents a New Frontier
- 55:20
- Attitudinal shifts affect action on issues like climate change
- 56:17
- Conclusion: Ecological systems and socio-economic systems alike are complex adaptive systems
- 56:30
- Systems Challenges
- 57:31
- These are challenges old, yet new
- 57:48
- Galileo said that
- 58:25
- Thus, we have reason to continue to anticipate and enjoy what Wigner call
- 59:12
- Question: You were talking about anticipating critical transitions on a global socio-economic scale. Do you think there is already sufficient data out there to determine whether or not we are close to such a transition, or is more data needed?