




































Ecology, Economy and Society–the INSEE Journal 4 (1): 5–12, January 2021 

 
COMMENTARY 
 

Mathematical Ecology, Evolution, and the Social 
Sciences  
 

Simon A. Levin   
 
Abstract: The last few decades have seen an enhanced partnership between 
ecologists and social scientists, especially economists, in addressing the 
environmental challenges facing societies.  Not only do ecology and economics, in 
particular, need each other; but also the challenges they face are similar and can 
benefit from cross-fertilization. At the core are scaling from the micro- to the 
macro, the development of appropriate statistical mechanics to facilitate scaling, 
features underlying the resilience and robustness of systems, the anticipation of 
critical transitions and regime shifts, and addressing the conflicts of interest 
between individual agents and the common good through exploration of 
cooperation, prosociality and collective decision-making. Confronting these issues 
will be crucial in the coming years for all nations, especially those in South Asia that 
will suffer in major ways from the consequences of overpopulation, climate change 
and other environmental threats. 

Keywords: Mathematical Ecology and Evolution; Economics; Public Goods; 
Scaling; Complex Adaptive Systems. 

 

1. INTRODUCTION 

Though my academic training was as an applied mathematician, I was 
drawn even as a graduate student to problems in biology, especially in 
ecology. I received my Ph.D. in 1964, two years after the appearance of 
Rachel Carson‘s monumental Silent Spring and just a few years before the 
influential Population Bomb of Paul and Anne Ehrlich (Carson 1962; Ehrlich 
1968). In this context of increasing societal attention to environmental 

                                                        
 James S. McDonnell Distinguished University Professor, Department of Ecology and 
Evolution, Princeton University, Princeton, New Jersey 08544-1003; slevin@princeton.edu. 

Copyright © Levin 2021. Released under Creative Commons Attribution-NonCommercial 
4.0 International licence (CC BY-NC 4.0) by the author.  

Published by Indian Society for Ecological Economics (INSEE), c/o Institute of Economic 
Growth, University Enclave, North Campus, Delhi 110007.  

ISSN: 2581-6152 (print); 2581-6101 (web). 

DOI: https://doi.org/10.37773/ees.v4i1.401  

https://doi.org/10.37773/ees.v4i1.401


Ecology, Economy and Society–the INSEE Journal [6] 

degradation, I was increasingly drawn to studying the environment, and, by 
1970, I was fully committed to the field of ecology, and in particular the 
development of theoretical foundations. 

Theoretical ecology is a subject that is at least a century old. Its earlier roots, 
going back several centuries, were in demography and the biology of 
populations, spurred on by the need for more quantitative approaches to 
these subjects. The first fundamental mathematical advances were made by 
the great mathematician Vito Volterra and the physical chemist and 
mathematician Alfred Lotka, who independently derived sets of differential 
equations to describe the dynamics of species in competition and 
exploitation (Lotka 1925; Volterra 1926). Volterra, in particular, was 
interested in the fluctuations of the Adriatic fisheries, a problem brought to 
him by Umberto d‘Ancona, a formidable fisheries biologist, and his simple 
equations were able to explain those fluctuations. The equations of Lotka 
and Volterra still are at the core of much work in theoretical ecology today 
and have found application in economics and other social sciences 
(Samuelson 1971, 1974). 

I enjoyed pure theoretical ecology and still do; but I soon realized that to 
address environmental issues substantively, I needed to turn more 
effectively towards economics and other social sciences. The key issues that 
needed to be addressed included how to value biodiversity and convince 
others of that value; matters of discounting the future, equity, and the 
interests of others; and the role of cooperation and social norms in the 
development of management strategies in local and global commons. Thirty 
years ago, I was invited to join the nascent Beijer Institute at the Swedish 
Academy of Sciences, and that interdisciplinary paradise changed my 
research trajectory, and those of countless others, forever. I learned how 
much ecology needed economics and how much economics needed 
ecology, and the collaborations that followed have been invaluable. 

However, I also learned something else. The problems of ecology and 
economics are two sides of the same coin; this is no accident, because both 
disciplines address the self-organization and evolution of communities of 
individual agents competing, exploiting, and cooperating with emergent 
dynamics at higher levels of organization that produce systems that cycle 
various kinds of capital, natural and created, and provide a context in which 
individual behaviours change. Kenneth Arrow, one of the key members of 
the Beijer community, pointed out to us that the fact that both disciplines 
begin with ―eco-,‖ meaning household, was not coincidence; they both face 
similar issues—both confront complex adaptive systems (CAS) and the 
challenges of understanding and managing them (Arrow, Ehrlich, and Levin 
2014). 



[7] Simon A. Levin 

2. SOME COMMON PROBLEMS IN ECOLOGY AND 
ECONOMICS 

Because similar problems have been addressed in both disciplines, there are 
reciprocal benefits from revisiting the different approaches that have been 
developed in the two. Such mutualisms are increasing in number, and I will 
touch on only a few of them in this section. These include but are not 
limited to the matter of scaling across levels and across space and time 
(Chave and Levin 2003); foraging theory and search theory (Pyke, Pulliam, 
and Charnov 1977); the potential for critical transitions (Steele 1998; 
Scheffer 2009); and identifying the structural features that make systems 
robust and resilient (Holling 1973; Levin et al. 1998; Levin and Lubchenco 
2008). 

Evolutionary ecology to a large extent addresses how genomes have been 
adapted to deal with uncertain environments. The vertebrate immune 
system is a wonderful example of evolution‘s hierarchical response to the 
certainty of uncertain events and is a model for how societies might deal 
with everything from pandemics to terrorist attacks to financial collapse 
(Levin and Lo 2015). More generally, life history theory in evolution deals 
in large part with the allocation of resources over an evolutionary lineage 
(Stearns 1992) and has strong parallels with models of the theory of interest 
(Haberler and Fisher 1931) and of resource allocation and dynasty theory in 
economics (Becker 1965; Heckman 2015). Kenneth Arrow and I merged 
these by examining through dynamic programming how uncertainty of 
various kinds would affect consumption patterns and deferral of resources 
to one‘s offspring, a fundamental problem in evolution and economics alike 
(Arrow and Levin 2009). 

More generally, evolution deals with fitnesses and the processes that select 
more fit genotypes over less fit ones, while economics does the same, with 
the word ―fitnesses‖ replaced by ―utilities‖. Both ecology and economics 
therefore utilize techniques from optimization and game theory to 
understand what strategies can be expected to prevail; indeed, cross-
fertilization between the two perspectives on such problems is rapidly 
gaining traction. 

 

3. COMPLEX ADAPTIVE SYSTEMS 

Ecological systems, the socio-economic systems with which they interact, 
and the interconnected global socio-ecological system that emerge, are all 
examples of CAS (Holland 1995; Levin 1998, 1999; Arrow, Ehrlich, and 
Levin 2014). Such systems are composed of individual agents that interact 



Ecology, Economy and Society–the INSEE Journal [8] 

with one another at local scales, leading to the emergence of higher order 
patterns and processes that feed back to modify individual behaviours. The 
agents—be they genomes, organisms, institutions, or nations—adapt their 
behaviours, in some cases over evolutionary time, generally in response to 
differential payoffs, utilities, or fitnesses; hence, the term ―adaptive‖ in the 
name. The term, however, can be misleading, since the myopic benefits to 
individuals may not advance the collective good; the adaptation is at levels 
below the whole system. 

Whatever the natures of the CAS, similar questions arise: What factors 
underlie the robustness and resilience of these systems to change, 
exogenous or endogenous? Are there early warning indicators of impending 
transitions? How do patterns vary across scales, and how can we use 
coarse-grained models to understand the emergent properties as statistical 
consequences of behaviours and interactions among large numbers of 
agents? And perhaps most challenging, how do conflicts between the 
interests of individual agents and the collective good play out, and to what 
extent do they undermine equity or system resilience?  

These are, of course, all familiar challenges to economists, who are used to 
dealing with the interplay between microeconomics and macroeconomics 
and with the challenges of public goods and common-pool resources. It 
might be surprising, however, for economists to learn that such questions, 
especially of cooperation in the face of public goods, are at the centre of 
much evolutionary theory. Bacteria produce extracellular polymers that 
provide collective benefits as well as antibiotics that poison susceptible 
neighbours; plants fix nitrogen, transforming it into a form more widely 
available to free-riders; and species from cellular slime moulds to birds, fish, 
and humans engage in collective behaviours that improve access to 
resources or mutual defence. All involve costs and all are susceptible to 
free-riding. Understanding how and under what conditions such behaviours 
are maintained, and when they break down (as in tumour growth), are 
among the deepest problems in evolutionary theory—puzzles that worried 
Charles Darwin enough to delay publication of The Origin of Species for many 
years.  

 

4. PUBLIC GOODS, COMMON-POOL RESOURCES, AND THE 
TRAGEDY OF THE COMMONS 

Our planet is threatened by a litany of interlocking problems—climate 
change, biodiversity loss, overpopulation, and increasing inequity—that 
must be solved if we are to achieve a sustainable future. William Forster 
Lloyd first spoke of the commons nearly two centuries ago (Lloyd 1833), 



[9] Simon A. Levin 

and Garrett Hardin famously introduced the notion of the ―tragedy of the 
commons, arguing that the solution was in ―mutual coercion, mutually 
agreed upon‖ (Hardin 1968). Views about managing the commons were 
changed, however, by the landmark work of another core Beijer participant, 
Elinor Ostrom, who showed, through empirical and theoretical arguments, 
that societies could self-regulate through the development of social norms 
and other institutions that limited overexploitation (Ostrom 1990). Dealing 
with the commons is at the centre of the partnership that must grow 
between biology and the social sciences in the coming decades. Economists 
have with great success developed frameworks for dealing with public 
goods by addressing questions such as: What is the social optimum? 
Without top-down regulation, can the social optimum be approximated and 
sustained as a Nash equilibrium or does discounting of the future 
undermine it? Where it cannot be sustained, are there second-best solutions 
that can be? In cooperative games, can co-operators develop social norms, 
for example, the punishment of defectors, that can flip the system to more 
favourable equilibria? What is the role of prosociality and how can it be 
achieved (Gintis 2003; Akcay et al. 2009; Dixit, Levin, and Rubenstein 2013; 
Dixit and Levin 2017)? Evolutionary biologists have had to tackle the same 
problems from different perspectives, focusing attention on the evolution 
of altruism and cooperation and the importance of genetic relatedness 
(Hamilton and Axelrod 1981; Nowak, Tarnita, and Wilson 2010; Levin, 
2014). We now need to bring these separate approaches together to develop 
a theory of governance for the global commons. (Polasky et al. 2019). 
Ostrom‘s ideas of polycentric governance (Ostrom 2009) are likely to play a 
central role in what must be at the top of the agenda for ecological and 
environmental ecologists for many years to come. 

 

5. CONCLUDING THOUGHTS  

The problems discussed in this paper are, of course, of general relevance to 
all nations, but they pose special challenges for India and other parts of 
South Asia. Overpopulation, biodiversity loss, and the growing inequity in 
well-being are especially acute in these parts of the world, as documented in 
the Dasgupta report for the British government on the economics of 
biodiversity (H M Treasury 2020). Infectious diseases, like the current 
COVID-19 pandemic, threaten devasting consequences. Climate change 
will impact India, China, Pakistan, and Bangladesh especially hard, and 
expanding populations and their resource needs will exacerbate the climate 
crisis, unless steps towards promoting alternative energy are successful. It is 
no surprise then that there has been increasing attention on implementing 
decarbonization as rapidly as possible, especially in India and China, and in 



Ecology, Economy and Society–the INSEE Journal [10] 

addressing the social norms issues that will be crucial to people‘s willingness 
to accept it. Thus, the marriage of ecology, economics, and other social 
sciences is especially crucial in South Asia and stands to benefit enormously 
from the efforts of the readers of this journal. I hope this call to action will 
find enthusiastic acceptance. 

 

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