Cassandra has moved. Ugo Bardi publishes now on a new site called "The Seneca Effect."

Monday, December 15, 2014

Seneca cliffs of the third kind: how technological progress can generate a faster collapse

The image above (from Wikipedia) shows the collapse of the North Atlantic cod stocks. The fishery disaster of the early 1990s was the result of a combination of greed, incompetence, and government support for both. Unfortunately, it is just one of the many examples of how human beings tend to worsen the problems they try to solve. The philosopher Lucius Anneus Seneca had understood this problem already some 2000 years ago, when he said, "It would be some consolation for the feebleness of our selves and our works if all things should perish as slowly as they come into being; but as it is, increases are of sluggish growth, but the way to ruin is rapid."

The collapse of the North Atlantic cod fishery industry gives us a good example of the abrupt collapse in the production of resources - even resources which are theoretically renewable. The shape of the production curve landings shows some similarity with the "Seneca curve", a general term that I proposed to apply to all cases in which we observe a rapid decline of the production of a non renewable, or slowly renewable, resource. Here is the typical shape of the Seneca Curve:

The similarity with the cod landings curve is only approximate, but clearly, in both cases we have a very rapid decline after a slow growth that, for the cod fishery, had lasted for more than a century. What caused this behavior?

The Seneca curve is a special case of the "Hubbert Curve" which describes the exploitation of a non renewable (or slowly renewable) resource in a free market environment. The Hubbert curve is "bell shaped" and symmetric (and it is the origin of the well known concept of "peak oil). The Seneca curve is similar, but it is skewed forward. In general, the forward skewness can be explained in terms of the attempt of producers to keep producing at all costs a disappearing resource.

There are several mechanisms which can affect the curve. In my first note on this subject, I noted how the Seneca behavior could be generated by growing pollution and, later on, how it could be the result of the application of more capital resources to production as a consequence of increasing market prices. However, in the case of the cod fishery, neither factor seems to be fundamental. Pollution in the form of climate change may have played a role, but it doesn't explain the upward spike of the 1960s in fish landings. Also, we have no evidence of cod prices increasing sharply during this phase of the production cycle. Instead, there is clear evidence that the spike and the subsequent collapse was generated by technological improvements.

The effect of new and better fishing technologies is clearly described by Hamilton et al. (2003)

Fishing changed as new technology for catching cod and shrimp developed, and boats became larger. A handful of fishermen shifted to trawling or “dragger” gear. The federal government played a decisive role introducing new technology and providing financial resources to fishermen who were willing to take the risk of investing in new gear and larger boats.

Fishermen in open boats and some long-liners continued to fish cod, lobster and seal inshore. Meanwhile draggers  and other long-liners moved onto the open ocean, pursuing cod and shrimp nearly year round. At the height of the boom, dragger captains made $350,000–600,000 a year from cod alone. ... The federal government helped finance boat improvements, providing grants covering 30–40% of their cost.
By the late 1980s, some fishermen recognized signs of decline. Open boats and long-liners could rarely reach their quotas. To find the remaining cod, fishermen traveled farther north, deployed more gear and intensified their efforts. A few began shifting to alternative species such as crab. Cheating fisheries regulation—by selling unreported catches at night, lining nets with small mesh and dumping bycatch at sea—was said to be commonplace. Large illegal catches on top of too-high legal quotas drew down the resource. Some say they saw trouble coming, but felt powerless to halt it.

So, we don't really need complicated models (but see below) to understand how human greed and incompetence - and help from the government - generated the cod disaster. Cods were killed faster than they could reproduce and the result was their destruction. Note also that in the case of whaling in the 19th century, the collapse of the fishery was not so abrupt as it was for cods, most likely because, in the 19th century, fishing technology could not "progress" could not be so radical as it was in the 20th century.

The Seneca collapse of the Atlantic cod fishery is just one of the many cases in which humans "push the levers in the wrong directions", directly generating the problem they try to avoid. If there is some hope that, someday, the cod fishery may recover, the situation is even clearer with fully non-renewable resources, such as oil and most minerals. Also here, technological progress is touted as the way to solve the depletion problems. Nobody seems to worry about the fact that the faster you extract it, the faster you deplete it: that's the whole concept of the Seneca curve.

So take care: there is a Seneca cliff ahead also for oil!


A simple dynamic model to describe how technological progress can generate the collapse of the production of a slowly renewable resource; such as in the case of fisheries. 

by Ugo Bardi

Note: this is not a formal academic paper, just a short note to sketch how a dynamic model describing overfishing can be built. See also a similar model describing the effect of prices on the production of a non renewable resource

The basics of a system dynamics model describing the exploitation of a non renewable resource in a free market are described in detail in a 2009 paper by Bardi and Lavacchi. According to the model developed in that paper, it is assumed that the non renewable resource (R) exists in the form of an initial stock of fixed extent. The resource stock is gradually transformed into a stock of capital (C) which in turn gradually declines. The behavior of the two stocks as a function of time is described by two coupled differential equations.
R' = - k1*C*R C' = k2*C*R - k3*C,
where R' and C' indicate the flow of the stocks as a function of time (R' is what we call "production"), while the "ks" are constants. This is a "bare bones" model which nevertheless can reproduce the "bell shaped" Hubbert curve and fit some historical cases. Adding a third stock (pollution) to the system, generates the "Seneca Curve", that is a skewed forward production curve, with decline faster than growth.  

The two stock system (i.e. without taking pollution into account) can also produce a Seneca curve if the equations above are slightly modified. In particular, we can write: 
R' = - k1*k3*C*R C' = ko*k2*C*R - (k3+k4)*C.
Here, "k3" explicitly indicates the fraction of capital reinvested in production, while k4 which is proportional to capital depreciation (or any other non productive use). Then, we assume that production is proportional to the amount of capital invested, that is to k3*C. Note how the ratio of R' to the flow of capital into resource creation describes the net energy production (EROI), which turns out to be equal to k1*R. Note also that "ko" is a factor that defines the efficiency of the transformation of resources into capital; it can be seen as related to technological efficiency.
The model described above is valid for a completely non-renewable resource. Dealing with a fishery, which is theoretically renewable, we should add a growth factor to R', in the form of k5*R. Here is the model as implemented using the Vensim (TM) software for system dynamics. The "ks" have been given explicit names. I am also using the convention of "mind sized models" with higher free energy stocks appearing above lower free energy stocks

If the constants remain constant during the run, the model is the same as the well known "Lotka-Volterra" one. If the reproduction rate is set at zero, the model generates the symmetric Hubbert curve. 

In order to simulate technological progress, the "production efficiency" constant is supposed to double stepwise around mid-cycle. A possible result is the following, which qualitatively reproduces the behavior of the North Atlantic cod fishery.

Among other things, this result confirms the conclusions of an early paper of mine (2003) on this subject, based on a different method of modeling.

Let me stress again that this is not an academic paper. I am just showing the results of tests performed with simple assumptions for the constants. Nevertheless, these calculations show that the Seneca cliff is a general behavior that occurs when producers stretch out their system allocating increasing fractions of capital to production. Should someone volunteer to give me a hand to make better models, I'd be happy to collaborate!


  1. The collapse of Newfoundland's cod fishery isn't just a textbook case of resource over-exploitation and collapse. It also has some important lessons for scientists, in particular, the misuse and politicization of scientific findings by public agencies. This cautionary example, and another similar case, were discussed in an excellent 1997 paper by three Canadian fisheries researchers:

  2. It is also a case of study of the failure of the “Maximum sustainable yield” model.

  3. Despite quite a few years of the cod fisheries being virtually closed, cod stocks have not recovered anywhere near as quickly as expected. It appears that we so fundamentally disrupted the overall ecosystem by overfishing them, that that ecosystem itself may have permanently shifted to one which does not support large numbers of cod. So much for a "renewable resource".

    1. And were the trawlers also destroying the sea bottom ecosystems ?
      About halieutic resource depletion, below conference from Daniel Pauly is quite impressive :

  4. "the situation is even clearer with fully non-renewable resources, such as oil and most minerals. "
    How do you know this is a fact?
    Oil is being found way below any "fossil" layers and is said to be produced from the "core" and is percolating upwards. The World is actually getting heavier from the constant bombardment of the Sun.
    The reason oil is becoming difficult to obtain is because "use" has outstripped it's natural production.

    1. Hey I like this reply:
      this is really gerat news, oil is somehow generated in the core (probably meant is the iron and nickel core of earth at elevated temperature) and then percolates through the mantle upwards. The added mass needed for generating this oil is somehow delivered by the sun through its bombardement.
      Some of us know, that oil is made of hydrogen and carbon, not of iron, nickel or whatever other stuff is down in the core, so sun transports this directly down into the core - probably through a channel not known to science.
      Then we have a natural process that generates the new oil and afterwards it just goes up into our wells. And if we know how much is made down there we have a natural renewable source of the best energy.
      This is great news! start telling this to the news agencies!

      You might have heard of Thomas Golds: The deep hot biosphere. Springer, New York: 1999. That book introduces a somehow not totally absurd theory of how hydrocarbons might be formed in lower layers of the continental crust. Sadly he does not provide any estimate of the production rate of new hydrocarbons, but as pressure and temperature at the core are so much higher there must be a much faster generation deep down...

      I am so excited!

    2. Then you will wet your pants when you watch this.

  5. The Seneca cliff for oil is worse than you have depicted because it shows production of oil by volume. The Net energy content available to society declines even faster than this because ERoEI and energy density of the oil resources for a given volume also declines over time.


  6. Very nice, thank you. Experience (history) shows that the Seneca curve is the correct one most of the time. Specifically, thinking of Tulip, NASDAQ, Housing, and other manias.

  7. reblogged it here with a added psych dimension and link to a book of the past 20 years of climate politics in

  8. As YvesT points out, this example is maybe not truly instructive of the good doctor's theory, since the ecosystems of the oceans are all so connected and others have reported on the 90% or more decline in fish stocks and numerous deadzones worldwide. This as a result of overfishing, increased acidity, and habitat destruction, significantly by fishing method known as dragging. Dragging has turned the majority of the ocean beds into dead zones. This has been well established through scientific research and reported on. Now we have Fukushima contributing to this already totally disastrous situation.

  9. The Seneca curve is a special case of the "Hubbert Curve" which describes the exploitation of a non renewable (or slowly renewable) resource in a free market environment. The Hubbert curve is "bell shaped" and symmetric (and it is the origin of the well known concept of "peak oil). The Seneca curve is similar, but it is skewed forward. In general, the forward skewness can be explained in terms of the attempt of producers to keep producing at all costs a disappearing resource.




Ugo Bardi is a member of the Club of Rome, faculty member of the University of Florence, and the author of "Extracted" (Chelsea Green 2014), "The Seneca Effect" (Springer 2017), and Before the Collapse (Springer 2019)