Andrew G Haldane: Rethinking the financial network
Speech by Mr Andrew G Haldane, Executive Director, Financial Stability, Bank of England, at
at the Financial Student Association, Amsterdam, 28 April 2009.
I would like to thank Ian Bond, Sebastiano Daros, Kemal Ercevik, David Gregory, Sujit Kapadia, Iman van
Leyveld, Sarah Parkinson, Filipa Sa, Nick Vause, Lewis Webber, Matthew Willison and Peter Zimmerman for
comments and contributions. I would also like to thank Lord Robert May for conversations on the topic.
* * *
On 16 November 2002, the first official case of Severe Acute Respiratory Syndrome (SARS)
was recorded in Guangdong Province, China. Panic ensued. Uncertainty about its causes
and contagious consequences brought many neighbouring economies across Asia to a
standstill. Hotel occupancy rates in Hong Kong fell from over 80% to less than 15%, while
among Beijing's 5-star hotels occupancy rates fell below 2%.
Media and modern communications fed this frenzy and transmitted it across borders. In
North America, parents kept their children from school in Toronto, longshoreman refused to
unload a ship in Tacoma due to concerns about its crew and there was a boycott of large
numbers of Chinese restaurants across the United States. Dr David Baltimore, Nobel prize
winner in medicine, commented: "People clearly have reacted to it with a level of fear that is
incommensurate with the size of the problem".
The macroeconomic impact of the SARS outbreak will never be known with any certainty.
But it is estimated to stand at anything up to $100 billion in 2003 prices. Across Asia, growth
rates were reduced by SARS by between 1 and 4 percentage points. Yet in the final
reckoning, morbidity and mortality rates were, by epidemiological standards, modest. Only
around 8000 people were infected and fewer than 1000 died.
On 15 September 2008, Lehman Brothers filed for Chapter 11 bankruptcy in a New York
courtroom in the United States. Panic ensued. Uncertainty about its causes and contagious
consequences brought many financial markets and institutions to a standstill. The market for
Credit Default Swaps (CDS) froze, as Lehman was believed to be counterparty to around $5
trillion of CDS contracts.
Media and modern communications fed this frenzy and transmitted it across markets. Banks
hoarded liquidity for fear of lending to infected banks, causing gridlock in term money
markets, spreads on lower-rated companies' bonds spiked and there was an effective
boycott of the remaining large US investment banks. Professor Paul Krugman, Nobel prize
winner in economics, commented: "Letting Lehman fail basically brought the entire world
capital market down."
The macroeconomic impact of Lehman Brothers' failure will never be known with any
certainty. IMF forecasts of global growth for 2009 have been revised down by over 5
percentage points since Lehman's failure. Yet in the final reckoning, the direct losses from
Lehman's failure seem likely to be relatively modest. Net payouts on Lehman's CDS
contracts amounted to only around $5 billion.
These similarities are striking. An external event strikes. Fear grips the system which, in
consequence, seizes. The resulting collateral damage is wide and deep. Yet the triggering
event is, with hindsight, found to have been rather modest. The flap of a butterfly's wing in
New York or Guangdong generates a hurricane for the world economy. The dynamics
appear chaotic, mathematically and metaphorically.
These similarities are no coincidence. Both events were manifestations of the behaviour
under stress of a complex, adaptive network. Complex because these networks were a
cat'scradle of interconnections, financial and non-financial. Adaptive because behaviour in these
networks was driven by interactions between optimising, but confused, agents. Seizures in
the electricity grid, degradation of eco-systems, the spread of epidemics and the
disintegration of the financial system - each is essentially a different branch of the same
network family tree.
This paper considers the financial system as a complex adaptive system. It applies some of
the lessons from other network disciplines - such as ecology, epidemiology, biology and
engineering - to the financial sphere. Peering through the network lens, it provides a rather
different account of the structural vulnerabilities that built-up in the financial system over the
past decade and suggests ways of improving its robustness in the period ahead.
Part 1 provides the diagnosis. Using network theory and evidence, it explains the emergence
of two characteristics of the financial network over the past decade - complexity and
homogeneity. Together, these resulted in a financial network:
•
Which was at the same time both robust and fragile - a property exhibited by other
complex adaptive networks, such as tropical rainforests;
•
Whose feedback effects under stress (hoarding of liabilities and fire-sales of assets)
added to these fragilities - as has been found to be the case in the spread of certain
diseases;
•
Whose dimensionality and hence complexity amplified materially Knightian
uncertainties in the pricing of assets - causing seizures in certain financial markets;
•
Where financial innovation, in the form of structured products, increased further
network dimensionality, complexity and uncertainty; and
•
Whose diversity was gradually eroded by institutions' business and risk
management strategies, making the whole system less resistant to disturbance -
mirroring the fortunes of marine eco-systems whose diversity has been steadily
eroded and whose susceptibility to collapse has thereby increased.
This evolution in the topology of the network meant that sharp discontinuities in the financial
system were an accident waiting to happen. The present crisis is the materialisation of that
accident.
Given that diagnosis, Part 2 of the paper provides some tentative policy prescriptions. The
experience of other network disciplines suggests a rather different approach to managing the
financial network than has been the case in the past, if future systemic dislocations are to be
averted. Three areas in particular are discussed:
•
Data and Communications: to allow a better understanding of network dynamics
following a shock and thereby inform public communications. For example, learning
from epidemiological experience in dealing with SARs, or from macroeconomic
experience after the Great Depression, putting in place a system to map the global
financial network and communicate to the public about its dynamics;
•
Regulation: to ensure appropriate control of the damaging network consequences of
the failure of large, interconnected institutions. For example learning from
experience in epidemiology by seeking actively to vaccinate the "super-spreaders"
to avert financial contagion; and
•
Restructuring: to ensure the financial network is structured so as to reduce the
chances of future systemic collapse. For example, learning from experience with
engineering networks through more widespread implementation of central
counterparties and intra-system netting arrangements, which reduce the financial
network's dimensionality and complexity.
Networks and finance are not complete strangers. There has been growing interest among
network theorists in applying their techniques to financial phenomena over the past few
years. For example, network techniques have already been applied extensively to the
dynamics of payment systems and inter-bank networks. But the financial crisis of the past
two years provides both a greater body of evidence, and a stronger incentive, to apply the
lessons from other network disciplines to the pressing problems facing financial policymakers
today.
Part 1: Topology of the financial network
In many important respects, the current financial crisis is cut from familiar cloth. Its genesis
was the over-extension of credit, over-inflation of asset prices and over-exuberance of
participants. From the South Sea bubble to the sub-prime crisis, this roll-call of excesses is
familiar. Gerald Corrigan, ex-President of the New York Fed, said ahead of the crisis:
"In recent years the pace of change and innovation in financial markets
and institutions here and around the world has increased enormously as
have the speed, volume and value of financial transactions. The period
has also seen a greatly heightened degree of aggressive competition in
the financial sector. All of this is taking place in the context of a legal and a
regulatory framework which is increasingly outdated and ill-equipped to
meet the challenges of the day. This has led to...concern that the fragility
of the system has increased, in part because the degree of operational,
liquidity and credit interdependency has risen sharply".2
Corrigan was speaking in January 1987. The crisis foretold was the October 1987 stock
market crash. Plus ça change.
Yet in some more fundamental respects this time's crisis feels different - larger probably,
more discontinuous, complex and interconnected certainly. There are already numerous
accounts of why that might be. Here, I argue that these knife-edge dynamics can essentially
be explained by two structural features of the financial network. These have developed over
many years but at particular pace over the past decade. They are complexity on the one
homogeneity
hand, and on the other.
In essence, the financial network has over time become progressively more complex and
less diverse. Why? And what have been the consequences?
Wall
In the 1987 film Street, the financial sector mantra was "greed is good". The stock
market crash of the same year put paid to that doctrine, at least temporarily. By the early part
of this century, both the circumstances and the individuals had changed. So too had the
mantra. It had become the rather gentler "diversification is desirable". Risk-taking became
less Gordon Gekko and more Merton Miller.
Diversification came care of two complementary business strategies. The first was "originate
and distribute". Risk became a commodity. As such it could be bundled, sliced, diced and
then re-bundled for onward sale. Credit became, in the jargon, structured. Securitisation was
one vehicle for achieving this. Derivatives, such as CDS, were another. As these marketable
instruments passed between participants, the network chain lengthened.
In principle, these instruments delivered a Pareto-improving reallocation of risk. Risk would
flow to those best able to bear it. They had deep pockets which they sought to line with
higher yield. For the system as a whole, this sounded like the land of milk and honey. For a
risk shared was a risk halved - perhaps more than halved, given the magic of diversification.
The network chain, meanwhile, just kept on growing.
The second strategy was diversification of business lines. Firms migrated activity to where
returns looked largest. As each new day dawned - leveraged loans yesterday, CDOs today,
proprietary trading tomorrow - the whole sector was drawn to the new source of sunlight.
Through competitive forces, finance engaged in a frantic game of follow-the-leader, played
for real money.
From an individual firm perspective, these strategies indeed looked like sensible attempts to
purge risk through diversification: more eggs were being placed in the basket. Viewed across
the system as a whole, however, it is clear now that these strategies generated the opposite
result: the greater the number of eggs, the greater the fragility of the basket - and the greater
the probability of bad eggs.
Securitisation increased the dimensionality, and thus complexity, of the financial network.
Nodes grew in size and interconnections between them multiplied. The financial cat's-cradle
became dense and opaque. As a result, the precise source and location of underlying claims
became anyone's guess. Follow-the-leader became blind-man's buff. In short, diversification
strategies by individual firms generated heightened uncertainty across the system as a
whole.
Meanwhile, a strategy of changing the way they had looked in the past led to many firms
looking the same as each other in the present. Banks' balance sheets, like Tolstoy's happy
families, grew all alike. So too did their risk management strategies. Financial firms looked
alike and responded alike. In short, diversification strategies by individual firms generated a
lack of diversity across the system as a whole.
So what emerged during this century was a financial system exhibiting both greater
complexity and less diversity. Up until 2007, many participants in financial markets would
have viewed that network evolution as the inevitable by-product of technical progress in
finance. Until then, complexity plus homogeneity equalled stability.
But in just about every non-financial discipline - from ecologists to engineers, from
geneticists to geologists - this evolution would have set alarm bells ringing. Based on their
experience, complexity plus homogeneity did not spell stability; it spelt fragility. In
understanding why, it is useful to explore some of the wider lessons from those disciplines,
taking in turn the effects of complexity and diversity on stability.
Complexity and stability
Tropical rainforests are a complex adaptive system. In the immediate post-war period, these
eco-systems were often used as a case-study when demonstrating why complex systems
tended to exhibit greater stability.3 In Elton's (1958) words, this was because there are
"always enough enemies and parasites available to turn on any species that starts being
unusually numerous". Complexity strengthened self-regulatory forces in systems, so
improving robustness. This was the prevailing ecological wisdom up until the early 1970s.
That conventional wisdom has since been turned on its head. From the 1970s onwards,
orthodoxy was altered by a combination of enriched mathematical models and practical
experience.4 Counter-examples emerged, with some simple eco-systems - savannas and
grasslands - found to exhibit high robustness and some complex eco-systems proving
vulnerable to attack. Perhaps tellingly, large-scale clearance of tropical rainforests
highlighted their inherent fragility. Not for nothing did rainforests become known as a
"nonrenewable" resource from the early 1970s.
Finance appears to be following in ecologists' footsteps, albeit with a generational lag. Until
recently, mathematical models of finance pointed to the stabilising effects of financial network
completeness.5 Connectivity meant risk dispersion. Real-world experience appeared to
confirm that logic. Between 1997 and 2007, buffeted by oil prices shocks, wars and dotcom
mania, the financial system stood tall; it appeared self-regulating and self-repairing. Echoes
of 1950s ecology were loud and long.
The past 18 months have revealed a system which has shown itself to be neither
selfregulating nor self-repairing. Like the rainforests, when faced with a big shock, the financial
system has at times risked becoming non-renewable. Many of the reasons for this have a
parallel in other disciplines. In particular, in making sense of recent financial network
dynamics, four mechanisms appear to have been important: connectivity; feedback;
uncertainty; and innovation.
(a) Connectivity and stability
Over the past 30 years, a great deal has been established about the links between network
connectivity and robustness. These lessons span a range of disciplines including physics,
biology, engineering and epidemiology. There are perhaps three key robustness results from
this literature which are relevant to the financial system.
6
Perhaps the key one concerns the "robust-yet-fragile" property of connected networks. The
intuition behind this result is beguilingly simple, but its implications profound. In a nutshell,
interconnected networks exhibit a knife-edge, or tipping point, property. Within a certain
range, connections serve as a shock-absorber. The system acts as a mutual insurance
device with disturbances dispersed and dissipated. Connectivity engenders robustness.
Risk-sharing - diversification - prevails.
But beyond a certain range, the system can flip the wrong side of the knife-edge.
Interconnections serve as shock-amplifiers, not dampeners, as losses cascade. The system
acts not as a mutual insurance device but as a mutual incendiary device. Risk-spreading -
fragility - prevails. The extent of the systemic dislocation is often disproportionate to the size
of the initial shock. Even a modest piece of news might be sufficient to take the system
beyond its tipping point. This same basic logic has latterly been applied to financial systems,
using mathematical models and simulated data.7
These knife-edge dynamics match closely the behaviour of the financial system in the recent
past. A lengthy period of seeming robustness (the Golden Decade from 1997 to 2007) was
punctuated by an acute period of financial fragility (the period since). The shock causing this
tipping point to be reached - the sub-prime crisis - was by global financial standards rather
modest. The robust-yet-fragile property of networks helps make sense of these non-linear
financial dynamics. Though they looked and felt like chaos, these dynamics were in fact
manifestations of a new network order.
The second key robustness result concerns the "long-tailed distribution" of connected
networks. The degree of a node measures the number of links to other nodes. So the degree
distribution
could be thought of as a histogram of the number of links for each node. For a
network whose links are randomly configured, this degree distribution would be symmetric
and bell-shaped; it would have a fat middle and thin tails.
But many real-world networks do not exhibit these properties, including the internet,
biological food webs and epidemiology networks.8 Instead these networks have been found
to have a thin middle and long, fat tails. There is a larger than expected number of nodes
with both a smaller and a larger number of links than average. Some financial networks, such
as payment systems, have also been found to exhibit long tails.9
Long tails have been shown to have important implications for network robustness. In
particular, long-tailed distributions have been shown to be more robust to random
disturbances, but more susceptible to targeted attacks.10 Why? Because a targeted attack on
a hub risks bringing the heart of the system to a standstill, whereas random attacks are most
likely to fall on the periphery.
This result carries important policy implications. Long periods of apparent robustness, where
peripheral nodes are subject to random shocks, should offer little comfort or assurance of
network health. It is only when the hub - a large or connected financial institution - is subject
to stress that network dynamics will be properly unearthed. When large financial institutions
came under stress during this crisis, these adverse system-wide network dynamics revealed
themselves.
The third result is the well-known "small world" property of connected networks.11 The origin
of this was a chain letter experiment by Stanley Milgram in 1967. This showed that the
average path length (number of links) between any two individuals was around six - hence
"six degrees of separation". Although networks tend to exhibit local clustering or
neighbourhoods, certain key nodes can introduce short-cuts connecting otherwise detached
local communities.
This small world property has again been found across a range of physical networks,
including the World Wide Web and forest fires.12 Its implications for network robustness are
subtle. In general, however, it will tend to increase the likelihood of local disturbances having
global effects - so-called "long hops". That could occur between different institutions or
between different nation states. Either way, a small world is more likely to turn a local
problem into a global one.
So what evidence do we have on these three characteristics in real financial networks?
Charts 1-3 look at the evolution in the international financial network. In particular, they look
at cross-border stocks of external assets and liabilities in 18 countries at three dates: 1985,
1995 and 2005. These data can be used to gauge the scale and evolution of interconnectivity
within the global financial network.
In Charts 1-3, the nodes are scaled in proportion to total external financial stocks, while the
thickness of the links between nodes is proportional to bilateral external financial stocks
relative to GDP.13 Table 1, meanwhile, provides some summary statistics for the international
financial network, in particular measures of the skew and fat-tailedness in the degree
distribution and its average path length.
Three key points emerge. First, it is clear that the scale and interconnectivity of the
international financial network has increased significantly over the past two decades. Nodes
have ballooned, increasing roughly 14-fold. And links have become both fatter and more
frequent, increasing roughly 6-fold. The network has become markedly more dense and
complex. And what is true between countries is also likely to have been true between
institutions within countries.
Second, the international financial network exhibits a long-tail. Measures of skew and
kurtosis suggest significant asymmetry in the network's degree distribution. Global finance
appears to comprise a relatively small number of financial hubs with multiple spokes.
Third, the average path length of the international financial network has also shrunk over the
past twenty years. Between the largest nation states, there are fewer than 1.4 degrees of
separation. Were the network extended beyond the 18 countries in the sample, the evolution
of this "small world" property would be clearer still.
So based on evidence from a sampled international financial network, the past twenty years
have resulted in a financial system with high and rising degrees of interconnection, a
longtailed degree distribution and small world properties. That is an unholy trinity. From a stability
perspective, it translates into a robust-yet-fragile system, susceptible to a loss of confidence
in the key financial hubs and with rapid international transmission of disturbances. That is not
the worst description of financial events over the past decade - and in particular over the
past 18 months.
(b) Feedback and stability
In epidemiology, the impact of a disease depends crucially on such structural parameters as
the mortality rate once infected and the transmission rate across agents.14 The first is largely
fixed and biological. But the second is likely to be variable and sociological. In other words,
agents' responses to infection, or indeed the fear of infection, are often crucial in determining
its rate of transmission.
In practice, these behavioural responses typically take one of two forms: "hide" or "flight". For
example, the response to the SARS epidemic in the 21st century was a "hide" response, with
people self-quarantining by staying at home and with flight, in this case literally, prohibited.
But the response to yellow fever in North America in the 19th century was "flight", with half
the population of Memphis fleeing in 1878.15
Either response is rational from an individual perspective. Both responses have the aim of
removing that individual from circulation with other, potentially infectious, agents. But the
implications of these responses for infection rates across the system are potentially very
different. Hide responses tend to contain infection locally, thus protecting the system globally.
This was the SARS experience. Flight, by contrast, tends to propagate infection globally.
This was the yellow fever experience, as incidence of the disease followed the railroad line
out of Memphis.16
During this financial crisis, faced with fears about infection, similar sets of behavioural
responses by financial institutions have occurred. Only the names are different. The "hiding"
has taken the form of hoarding, typically of liquidity. And the "flight" from infected cities has
taken the form of flight from infected assets, as institutions have sold toxic assets. Unlike in
an epidemiological context, however, both behavioural responses have aggravated stresses
in the financial system. How so?
Banks entered the crisis with a large portfolio of risky assets. As risk materialised, banks
rationally sought to protect themselves from infection from other banks by hoarding liquidity
rather than on-lending it. The result has been enduring stress in money markets. Banks'
mutual interdependence in inter-bank networks meant that individually-rational actions
generated a collectively worse funding position for all.
That, in turn, contributed to the second behavioural response. Unable easily to fund their
asset portfolio, some financial firms instead opted for flight through sales of assets. These
acted like the railroad out of Memphis, placing downward pressure on asset prices and
thereby spreading the infection to other institutions. Others' immunity to infection was
simultaneously being lowered by widespread marking of assets to market. In escaping the
plague, asset flight served to propagate it.
These behavioural dynamics - panic hoarding of liabilities, distress sales of assets - have
been defining features of this crisis. Placing these responses in a network framework clarifies
the individual rationalities, but collective externalities, that drove these actions. These rational
responses by banks to fear of infection added to the fragility of an already robust-yet-fragile
financial network.
(c) Uncertainty and stability
A related, but separate, behavioural response to fear of infection is felt in the pricing of
financial instruments. Networks generate chains of claims. At times of stress, these chains
can amplify uncertainties about true counterparty exposures. Who is really at the end of the
chain - Warren Buffett or Bernard Madoff? Through their impact on counterparty uncertainty,
networks have important consequences for dynamics and pricing in financial markets.
To illustrate, consider the case of pricing in the CDS market - an inherently complex, high
dimension market. In particular, consider Bank A seeking insurance from Bank B against the
failure of Entity C. Bank A faces counterparty risk on Bank B. If that were the end of the
story, network uncertainty would not much matter. Bank A could monitor Bank B's
creditworthiness, if necessary directly, and price the insurance accordingly.
But what if Bank B itself has n counterparties? And what if each of these n counterparties
n
itself has counterparties? Knowing your ultimate counterparty's risk then becomes like
solving a high-dimension Sudoku puzzle. Links in the chain, like cells in the puzzle, are
unknown - and determining your true risk position is thereby problematic.
For Bank A, not knowing the links in the chain means that judging the default prospects of
Bank B becomes a lottery. Indeed, in some ways it is worse than a lottery, whose odds are at
least known. In this example, Bank A faces uncertainty in the Knightian sense, as distinct
from risk, about the true network structure. Counterparty risk is not just unknown; it is almost
unknowable. And the higher the dimensionality of the network, the greater that uncertainty.
It is possible to formalise this intuition with some simple numerical examples.17
Consider two states of the world, pre-crisis and crisis. And consider the impact of network
complexity on CDS pricing. Once we introduce Knightian uncertainty, asset prices are no
longer determinate; they are defined by a range rather than a point. So the range of
equilibrium CDS spreads can be taken as a metric of the uncertainty, and hence distortion,
arising from different network structures.
Chart 4 plots a pre-crisis world where it is assumed that counterparty default probabilities,
and the uncertainty around them, are low. Subject to those assumptions, it illustrates how the
range of CDS spreads is affected by Bank B's number of counterparties. Larger numbers of
counterparties are marginally beneficial. There is a "law of large numbers" benefit.
Broadlyspeaking, however, network dimensionality has no material bearing on CDS pricing.
Chart 5 simulates a crisis world in which the default probability of Bank B has risen and so
too the uncertainty around that probability. The difference is striking. Pricing uncertainty now
increases with the dimensionality of the web. Extra counterparties add to, rather than
subtract from, pricing distortions. There is a "law of large numbers" cost. That uncertainty
cost, or Knightian distortion, is roughly proportional the dimension of the network.
It is difficult not to draw comparisons with Lehman's experience. Lehman had large CDS
counterparty exposures relative to its balance sheet and hundreds of counterparties. AIG
was similarly situated. It is little wonder participants took fright as both institutions came
under stress, fearful not so much of direct counterparty risk, but of indirect counterparty risks
emanating from elsewhere in the network. The network chain was so complex that spotting
the weakest link became impossible. This added yet a further layer of fragility to the financial
system.
(d) Innovation and stability
A fourth dimension to complexity in network chains derives from the effects of financial
innovation. Over the past decade, this often took a particular form - structured credit - with
risk decomposed and then reconstituted like the meat in an increasingly exotic sausage. The
result was a complex interlocking set of claims. With each restructuring of ingredients, the
web branched and the dimensionality of the network multiplied.
Chart 6 shows some of the interlocking networks of structured products that emerged. I will
not attempt to describe this chart; it would take too long and, even if I had the time, I doubt I
would have the ability. These were the self-same constraints - time, complexity - which
faced investors in these products. Due diligence was the casualty. End-investors in these
instruments were no more likely to know the name of the companies in their portfolios than
the name of the cow or pig in their exotic hot dog.
To illustrate, consider an investor conducting due diligence on a set of financial claims:
RMBS, ABS CDOs and CDO2. How many pages of documentation would a diligent investor
need to read to understand these products? Table 2 provides the answer. For simpler
products, this is just about feasible - for example, around 200 pages, on average, for an
RMBS investor. But an investor in a CDO2 would need to read in excess of 1 billion pages to
understand fully the ingredients.
With a PhD in mathematics under one arm and a Diploma in speed-reading under the other,
this task would have tried the patience of even the most diligent investor. With no time to
read the small-print, the instruments were instead devoured whole. Food poisoning and a
lengthy loss of appetite have been the predictable consequences. Though it had aimed to
dampen institutional risk, innovation in financial instruments served to amplify further network
fragility.
Diversity and stability
A final dimension to network robustness concerns the effects of diversity. The oceans
provide a rich and lengthy test-bed of the links between diversity and robustness. Over the
past millennium, studies of coastal eco-systems reveal some dramatic patterns.18 For around
800 years, between the years 1000-1800AD, fish stocks and species numbers were
seemingly stable and robust. Since then, almost 40% of fish species across the world's major
coastal eco-systems have "collapsed", defined here as a fall in population of greater than
90%. That is systemic by any metric.
There appear to be many environmental reasons for this collapse, some natural, others
manmade. But the distribution of this collapse across eco-systems is revealing. For species-rich -
that is, diverse - eco-systems the rate of collapse has been as low as 10%; for species-poor
eco-systems, as high as 60%. Diverse coastal eco-systems have proved to be markedly
more robust, measured over century spans.
Results for large marine eco-systems suggest a similar picture. Over the period 1950-2003,
the incidence of collapsed fisheries declines exponentially with species-diversity.19 Diversity
also appears to increase the resilience of fisheries - that is, their capacity to recover - in the
event of collapse. These results reappear throughout marine eco-systems, "in coral reefs in
Jamaica and on rocky shores in Panama".20
And they do not appear to be unique to marine eco-syst