Our Nuclear Future - Financial Risk and Externalities II

Hanford Facility, Washington

In my last article on the nuclear issue, "Our Nuclear Future, Financial Risk and Externalities",

I discussed Rating Agency Capital Models in the context of nuclear risks such as those posed at Fukushima, Chernobyl and Three Mile Island.

The issue of managing the risks associated with both military and commercial nuclear applications is a vital one, that should interest all of us and speaks to the very concept of externalities and how to manage them in a global world.  In this article I focus on commercial applications.

The Fukushima disaster was impacted by inadequate safeguards.  The tsunami risk was not adequately taken into account in planning where to place the back up generators which could restore power in the event of an interruption of power.  The back up generators were placed at point too near the sea wall protection that left them exposed to the tidal wave action of the large tsunami that hit off Fukushima on March 11, 2011, when an 8.9 magnitude earthquake was experienced.

How do we deal with the risk management issues concerning the financing, construction and operation of nuclear plants, and with the issue of managing nuclear waste from both military and civilian applications?  These issues concern low probability, high risk events, issues that fall outside of the scope of normal everyday events.

The federal government offers nuclear power plants some degree of protection from liability.  These limits on liability, which exist in order to encourage the construction and operation of nuclear plants for power generation purposes, do not do as thorough a job of mitigating risk as they should.  This is because an external party, the federal government, is responsible for the oversight.  In the case of Fukushima, where plants are constructed and operated across national boundaries, the issues become more complex.

The Fukushima Daiichi nuclear power plant was constructed and operated in Japan, by Fukushima General Electric (GE), Boise, and Tokyo Electric Power Company (TEPCO).  The components of the nuclear plant were provided by contractors such as GE,which provided six GE nuclear reactors. Other contractors were also involved. Multi-national resources were employed.  Liability issues are very difficult to ascertain.  It is very probable that the loss of the ability of the generators to provide power after interruption in service due to the tsunami materially impacted the fate of the nuclear material in those reactors and magnified the effect of the event.

Management of these issues across national boundaries presents a serious issue.  How do you price for risk when governments put caps on liabilities?  It is easier for companies to price for risk when the risk is limited!  The incentive for commercial entities to manage risk is reduced when they do not have to absorb the risk of extreme events in either pricing of their products, mitigation of that risk, or the application of design elements to manage that risk. The risk is shifted to the governments.

When all else fails, due to the failure to put in place elements that will mitigate extreme risk, governments have to step in.  At this point, governments must ascertain their own issues of financial accountability and debate among themselves.  This issue is currently unfolding as nuclear radiation emerges from the Fukushima disaster and manifests itself in the ocean, carried by currents, and in the air, as was the case with the Chernobyl event.

Clearly, there must be a better match between potential liabilities and mitigation of risk.  The problem occurs when it becomes financially unfeasible for companies to price for the risk of very low probability, high risk externalities.  The government(s) must retain the capability to regulate.  History has shown that government regulation is difficult in the face of corporate profits.  This was shown in the history of seeking to regulate the ASARCO smelter.

Nuclear power plants do not arise ex nihilo. They must be financed, built, insured.  How do you finance nuclear power plants?  They can be built with government financing and the government can assume all the risk.  In a commercial enterprise, across national boundaries, private parties can finance nuclear power plants if they have sufficient funds and can insure the risk of loss, either by commercial carriers, government support or by self insuring.

There are many financial instruments that may be available to finance nuclear power plants.  In addition, nuclear power plants require real estate.   A component of a nuclear power plant can conceivably be moved from one site to another, yet the ground below stays, and is subject to the risk of contamination.

It is instructive to look back at the history of Nuclear Power Plant generation in the Northwest.  The situation with Washington Public Power Supply System Bonds is instructive (WPPSS).  An article from HistoryLink.org discusses this history of one of the largest bond defaults in history.  Five WPPSS power plants were envisioned, and WPPSS power plant 2, the Columbia Generating Station, survives.  The facility is now called Energy Northwest, and produces 12% of the power generated by the Bonneville Power Administration.

A great portion of the Northwest's power supply is generated by hydroelectric sources such as those operating along the Columbia River.

The discussion of financing nuclear power plants rests with a projection of bond default experience over time (default matrices), and how bond ratings emerge through Rating Agency models such as Standard and Poor's, Moody's and A.M. Best.

Clearly, the issue of using bonds to finance nuclear power plants is a critical one, in more than one way.  WPPSS financing has provided an example of the risk of building nuclear plants, financing them, and having companies such as insurers and banks assume the risk of financing them.

Financial institutions take risks when they purchase company bonds.  The construction and operational risks (there are separate bonds for construction and operation) are borne by those that purchase the bonds.  Riskier enterprises are assigned a risk premium that is reflected in the interest rate offered on the bond.  The riskier the enterprise, the higher the interest rate, and the longer it takes the enterprise to retire the bond.  This is basic economics.

Given the history of WPPSS, it is difficult to construct a model for financing nuclear power plant construction.  History has shown that even rating bonds for more ordinary applications, is fraught with risk.  The financial events of 2008 have demonstrated to us how the domino effects of  certain companies being taken down can bring a financial system to the brink.  It is clear that certain financial institutions were allowed fail, while others were bailed out by the government.  Insurer AIG, for example, was bailed out, while Washington Mutual was allowed to fail.  This is a very interesting aspect to investigate, since Chase was left purchasing and holding the assets that Washington Mutual had accumulated over time.

The 2008 financial collapse is another blog article, however it is instructional in how bond defaults can bring down a financial system. Suffice it to say that mortgage backed securities, collateralized mortgage obligations, credit default swaps (CDS's) and collateralized debt obligations (CDO's) played a large role in this collapse. These issues reflected the financial arbitrage reflected in Rating Agency and regulatory agency capital analysis of financial institutions.  The actions that the government took, in deciding which institutions to rescue and which institutions to allow to fail, helped determine the path that would be taken.

Rating Agencies played a large role in the events that unfolded.  I have discussed Rating Agencies in previous articles.

Clearly, nuclear financing issues present complexities beyond those presented by other issues financed by our market system.  There are limits to liability that impact the nuclear arena.  We are left, then, with a cooperative issue impacting the ways in which governmental regulatory agencies can interject themselves into the system and regulate in a manner to mitigate low probability high impact risk.

This takes us again back to the past, and the issues attendant in regulating ASARCO Smelter Emissions and the problems that this issue presented.

These are the issues we face in these times of global warming and climate change, as we consider the risks and benefits of financing nuclear power plants.  Alternative energy sources are discussed in my article "Global Warming and Climate Change - Polar Pioneer" .

We must consider the issues of regulatory government as it is juxtaposed with issues concerning market operations, in dealing with situations that involve low probability, high risk events.  It is clear that unfettered market operations may bring about market collapse through the interrelationships that exist within the structure of markets. It is also clear that government regulation that is not strong enough may not be able to counter the impact of market forces that overrun it, especially considering the profits that can be developed in certain markets.  Furthermore, it is clear that government forces may act in a manner contradictory to public interest by choosing winners and loser, perhaps steered by an array of  predefined values of certain groups.

Can we trust government?  We must have checks and balances.  Do we want government to only have one option, or to offer choices?  I'm in favor of choices, as choices facilitate change, which is needed. Market research has shown that people can tolerate only so many choices; this has been in areas such as bottled peaches, cereal, etc.  Would we ever want our choices in cereals and bottled peaches to govern our choices in power generation and other key areas?  No, however the analogy is instructive.

We need a government strong enough to regulate; the problem in regulation, however, has shown that it is difficult for regulatory agencies to keep up with the profits that can be made from activities under investigation.  This is certainly true in the financial arena where new instruments, especially those employing financial arbitrage, arise in order to present profit opportunities that defy regulation.

Constitutional issues such as due process and informed consent are bell weather issues in our financial and social system.  The Justice Department has a long storied history in regulating monopoly.  These are all important issues as we consider regulation of markets, intrusion of regulators/law enforcement into markets, and imposition of systems which defy Constitutional rights.

These issues all reflect ongoing issues of climate change and global warming and the effect of the environment on certain populations.

Our Constitutional rights are now under attack and must be defended, especially as regards issues of due process and informed consent.  I have made a thorough examination of the social processes existing in our society today and find material flaws in social systems.

Social systems and the justice system as they currently exist need serious reforms to enforce the Constitutional rights that we hold so dear to us, as do imposed belief systems.

marilyndunstan.blogspot.com

Our Nuclear Future - Financial Risk and Externalities
Our Nuclear Future - Hanford and Spent Nuclear Fuel
Global Warming and Climate Change - "Polar Pioneer" and Arctic Drilling

Externalities

Chernobyl 25th anniversary 
Energy Choices and Risk
Global Warming and Climate Change-Polar Pioneer
Processing Risk and Uncertainty
Log in the Surf - 8.9 Japan Earthquake (9.0 updated)

History Link.org
Washington Public Power Supply System

The Odd Couple: The Mitochondria and the Cell Nucleus

Mitochondrion (Creative Image)

Mitochondria are key to understanding many life processes, in the body, in nature,
and in our environment.

Years ago, the Eukaryotic cell   developed as a symbiotic relationship between a prokaryotic cell and a proteobacteria.  The prokaryotic cell may have been an archaea. The proteobacteria was was incorporated into the cell as an endosymbiont.  As gene transfer took place between mitochondrial DNA  and the cell's nuclear DNA, the extent of the  mitochondrial DNA (mtDNA) decreased and the nuclear DNA incorporated more of the functions performed previously by mitochondrial DNA.  As this occured, the relationship changed from being symbiotic to the development of the mitochondrion as an organelle within the cell.

Much of the work developing the theory of symbiogenesis was done by Lynn Margulis in a 1967 paper..  The theory behind symbiogenesis is a very important topic with wide ranging implications due to the complexities involved in the interoperablity of nuclear DNA and mitochondrial DNA.  These issues are ongoing and represent a major challenge in understanding a wide range of scientific issues confronting our society today.

Mitochondria are present in most living cells that include DNA.  Mitochondria are responsible for  a large portion of the energy generated by the cell.  Mitochondria are responsible for the generation of adenosine triphosphate (ATP) from adenosine diphosphate (ADP)  through aerobic processes using its electron transport chain (ETC).  The energy generated as ATP is many times greater than the energy generated through anaerboic glycolysis, which is an energy generation process that does not use oxygen.

The use by the cell of anaerobic  vs aerobic respiration has significance in studying various physiological processes which occur throughout the body.  These issues have implications in wide ranging areas from cancer to the relationship between sleep and wakefulness.

As energy is generated throughout the body, principles of conservation of energy must be satisfied.  Whether energy is generated through aerobic respiration and Oxidative Phosphoylation (OXPHOS)  using the mitochondrial electron transport chain (ETC), energy generation requires inputs and outputs that must be balanced.  This is a principle called "conservation of energy".  OXPHOS generates ATP,  the "energy equivalent of currency" in the body, energy in the form of heat, and outputs such as oxygen radicals (Reactive Oxygen Species (ROS))  as a byproduct of the process.

Oxygen Canisters

Oxygen reactive species such as superoxide (O-), hydrogen peroxide (H202) and the hydroxyl radical (OH-) can be generated depending upon a number of factors.   This includes natural process in the body involving signaling and homeostasis and also exposure to a number of environmental factors which may increase their generation.  Antioxidants may help the cell counter some of the impacts of reactive species.

Exposure to pollution, chemicals, toxins and radiation may increase oxygen reactive species exposure.  Radiation exposure may include ionizing radiation or non-ionizing radiation  such as cosmic rays  (e.g. gamma rays ).  Geomagnetic storms  and reduced ozone layer  protection at polar regions as Antarctica and the Arctic may increase such exposure, with greater historical ozone depletion  over the Antarctic.

I photographed in Antarctica in November/December 2004, and in October 2006 and photographed in the Arctic in July 2005.  The year 2006 saw the worst levels of depletion (2004 Image-Halley Bay Station, Antarctica) in recorded history.

Cellular processes guide apoptosis, or programmed cell death under a number of circumstances, generating  an intrinsic pathway or extrinsic pathway for cell death.  Reactive species play key roles in this process, as signaling mechanisms, and also in promoting cell death, as free radicals generated by a variety of situations trigger apoptosis.

Mitochondria play a large role in enforcing 'group identity' in a cell. The mitochondria helps to sustain certain energy needs within the body and when certain system parameters (group identity system requirements) are not fulfilled, the process of apoptosis or programmed cell death is intended to kill off certain cells that do not meet those system parameters.

Mitochondria can be loosely or tightly coupled; this means that they can "leak" protons so that more heat is produced (uncoupled) relative to amount of ATP produced;  there are certain uncoupling proteins  that aid in this process, which decreases  the generation of potentially damaging oxygen radicals.  A highly coupled system will thus be more efficient in the generation of energy, less efficient in generating heat, and will generate more oxygen radicals, which can cause damage to the system.  A more loosely coupled system will produce more heat, will generate less oxygen radicals, and will be less efficient in generating energy.  A loosely coupled system will be more valuable in colder climates due to the greater heat protection.  A tightly coupled one will result in more conditions, such as diabetes, which are impacted by the generation of oxygen reactive species.

The generation of reactive oxygen species is a significant issue in DNA damage  and mutations involving mutagenesis.  Mitochondrial DNA (mtDNA) are much less protected from the generation of reactive species than nuclear DNA.  In the proverbial sense, they sit at the edge of the  oxidative phosphorylation 'fiery furnace' and absorb more damage than nuclear DNA.  Nuclear DNA has greater protection from reactive species, being protected by histones   and telomeres.

Mitochondria can be damaged by reactive species, however, there is a certain amount of punishment that mitochondria can take before a process called heteroplasmy  takes place. Heteroplasmy in the mitochondria is a process where, due to mutation, mitochondrial damage or other process, more than one mitochondrial genome can exist.  This process may be associated with mitochondrial disease and be more extensive the greater the degree of heteroplasmy.  However some individuals may live to long ages with some degree of heteroplasmy.

There is a basic problem with mitochondrial damage and mutation in so far as the mtDNA and the nuclear DNA interoperate in the OXPHOS process.  This is because, as mentioned earlier in the article, some mitochondrial functions ages ago were shifted into the nuclear DNA through the process of gene transfer.  Cytochrome C belongs to the cytochrome c family of proteins and is an integral part of the ETC.  Cytochrome C has a long history, which goes back to time periods when the Earth was subject to heavy amounts of radiation.  Illnesses associated with Cytochrome C may involve both nuclear DNA and mitochondrial DNA.

Since Nuclear DNA has greater protection than mitochondrial DNA (mtDNA) from the insult of reactive species, the degree of damage in each case will differ, or in the case of nuclear DNA, there may be minimal or no damage.  This will lead to interoperability issues as mutations and damage occurs. Interoperability is the ability of systems to work together.  As oxidative stress occurs at different rates and to different but  inter-operating parts of the cell (mtDNA and nuclear DNA), illness and damage occurs, and potentially mutations.  This occurs in systems requiring heavier use of energy, including muscles.  Respiratory muscles bear the burden of oxidative stress, as these muscles are those subject to the greatest use during sleep.  Sleep apnea may be associated with higher levels of exposure to oxidative stress.

As we are subject to greater and greater levels of substances that create oxygen reactive species, we can see that problems can add up.  There are greater and greater chances of damage and mutations, the probability of heteroplasmy increases, the levels of heteroplasmy in the cell may come closer to the levels of heteroplasmy that may be tolerated in the cell without incurring mitochondrial disease.

We can see, therefore, that exposure to reactive species such as environmental toxins and radiation may provide for mutations in both nuclear and mitochondrial DNA, that these processes may occur at different rates, and that past a certain point, mitochondrial disorders may develop as the result of such exposure. At the same time, mutations that are beneficial may sometimes occur, and mutations and damage that are harmful may indeed result.  The ability for mutations that are adaptive to occur may reflect the ability of the mitochondrial DNA and the nuclear DNA to inter-operate, which is statistically difficult, considering the conditions under which each of these processes work.

Thus any process which seeks to advance a species by introducing mutagenic factors via the use of the creation of oxygen radicals must take into consideration that mutations and damage may result in the process and that individuals may be harmed in such process.  Due consideration must exist for who is subject to such exposure, and when the risk of subjecting certain individuals to such exposure constitutes a material risk that makes such experimentation untenable in  a civilized society.

 The risks of exposure to reactive species increases with the degree and length of the exposure, impacting the risk of early morbidity and mortality. Mutagenesis is more effective when it occurs in germ line cells which can pass mutations, either favorable, or unfavorable on to the next generation

Where such experiments are conducted, they must be conducted in an ethical fashion, they must be done with full informed consent of those involved, they must adhere to the law of civilized nations, and the ongoing experience of such studies must be monitored and measured so that those involved are not unduly harmed and the patient population put at excessive risk.

It must be made abundantly clear that if our society depends upon mutations to adapt the species to future environmental (or other) challenges, that those who have been subject to environmental (or other) assaults for such purpose be treated with due respect, that their contributions be valued, and their condition be measured, monitored and treated. It is clear that what these individuals are doing on a collective basis is aiding the future development of humanity. They are test subjects in a process that will benefit others, later.

What are our future ecological and planetary challenges and how can we adapt to them?  How do these challenges impact our exposure to environment risks and how we deal with them?  These are all important issues.

The mitochondria, as a vital cog in the production of energy has a very important part of the story that must be told as we seek to deal with the environment, climate change and other planetary challenges that we face.

Nuclear Balance-of-Risks

Trojan Nuclear Power Plant Cooling Tower, Rainier Oregon (before being dismantled) - image on Alamy

Nuclear reactor technology has allowed the world-wide use of nuclear reactors for energy production. With the world faced with mounting carbon dioxide levels and global warming a concern, nuclear energy provides a low carbon emission alternative to traditional energy sources (World Nuclear Association and MIT study). This aspect of nuclear energy makes it a very attractive energy alternative. With President Obama wishing to expand the United States nuclear power plant program, the question becomes an issue of balance-of-risks.

Accelerating nuclear reactor development provides a low carbon emission energy source; however there is risk associated with the use of nuclear materials. If we do not take advantage of nuclear’s low carbon footprint and instead pursue other, higher carbon footprint strategies, we risk exacerbating global warming issues. There are other options, as well, such as cleaner technologies, emerging energy technologies and reducing fertility rates to decrease population size.

We seek to understand the low probability, high impact, long-tail risks associated with the use of nuclear materials. Since the dawning of the nuclear age, mankind has worked to harness the power of the atom. There have been many benefits from the use of radionuclides. However, there are risks as well.

Risk areas to consider in looking at nuclear energy include:

• Economic, including Externalities
• Design and Construction
• Natural Disasters
• Operations and Management
• Political and Regulatory
• Terrorism, War and Sabotage
• Radioactive Waste Treatment and Storage

We have had experience with nuclear accidents that display some of that high impact, long-tail risk. Previous blog articles have discussed Chernobyl, Three Mile Island and Fukushima (3/12/11, 3/25/11 and 3/28/11).

We have seen historical flooding on the Missouri River which threatened Fort Calhoun Nuclear Plant and Cooper Nuclear Plant in Nebraska. Recently we have seen the large Las Conchas Wildfire threaten the Los Alamos Energy Department facility in New Mexico.

These situations, including those situations where facilities were threatened but not breached, are all reminders that radiation is a serious risk and not simply an abstract probability.

Externalities

Externalities


Refinery Exhaust Stacks, Anacortes, Washington (image on Photoshelter)

Air pollution from a fixed stack is a good example that can be used to explain the concept of an externality. I discussed the externalities previously in a blog article (Risk and Externalities) in the context of the BP oil spill and its widespread impact in the Gulf of Mexico.

On the production side, externalities come into play when the full cost of production is not reflected in the cost of the good.

Air pollution emissions may contain various pollutants, gaseous and particulate matter. The area impacted and the degree of impact will be affected by the pollutants released and the meteorological conditions.

For example, a temperature inversion will keep cold air close to the surface under a layer of warm air so that the air does not mix well vertically. The pollutants will be kept closer to the surface and their impact will be greater.

Sulfur dioxide emissions may impact lakes and fish (as acid rain), and thus ecosystems. Sulfur dioxide is a harmful pollutant for humans as well as fish. Sulfur dioxide can adhere to airborne suspended particulate matter. If the particulate matter is small, this may ease entry into the lung where the sulfur dioxide can do greater harm.

Air pollution is a direct result of the manufacturing process that extends from the stack into the community and beyond. It’s impact results in costs to others. Thus there are costs associated with air pollution that are not included in the production costs. To the extent that this is true, the product produced is under priced, and the public, an external entity, is paying those additional costs.

Costs include medical costs, as well as reduced life expectancy due to the pollution. Air pollution, in addition to being unhealthy, reduces visibility, may add odor, and adds quality of life issues. Pollution impacts maintenance of buildings and other structures.

Determing costs attributable to air pollution is a complex problem. There have been studies done to ascertain such costs. For example, a RAND study looked at health costs in California attributable to air pollution above state standards. That study would reflect air pollution due to a variety of causes, not just the point sources discussed in this blog article. California has a great deal of automobile pollution which contributes to carbon monoxide and ozone pollution problems.

Monitoring and regulation of air pollutants requires resources as well. Air pollution regulation and monitoring exists at the federal, state and local levels.

To reiterate, the producer’s price does not reflect these costs. Thus the price of the good is under priced with respect to other options because it does not include the cost of these “external” costs which others must bear.

When full external costs are brought into the mix, the producer’s price must necessarily increase. As it increases, other competing options may become more attractive and the producer may lose business. Alternatively, the producer may choose to upgrade the method of production to reduce the pollution, a cost they may not be willing to take if full external costs were included.

Air pollution is one example of an externality.

The situation becomes more complicated where the risk matrix considers low probability, high risk events. Such events may be difficult to estimate and to price for. Even assuming these low probability, high risk events could be reasonably priced for, it may be impossible for the producer to compete with prices reflecting such a risk margin. Competitors in the same field may refuse to include such a risk margin, thus driving the producer out of business. Competitors in other fields without such a risk margin will be at an advantage.

Where the risk margin for the low probability, high impact event is not priced for and is not included in the pricing there is the potential for considerable externality impacts should the low probability high impact risk event materialize.

As previous nuclear disasters have shown, the low probability, high risk event presents considerable externality issues in the nuclear arena, considering the serious impacts of radiation. (See my blog articles, Chernobyl 25th Anniversary and Energy Choices and Risk).

Emperor Penguin Energy-Risk Model - Part 2

Emperor Penguin Diving onto Ice Shelf from Sea, Stancomb Wells Ice Edge, Weddell Sea, Antarctica (Image on Alamy.com)

In my last blog post “An Emperor Penguin Energy-Risk Model” on April 14, 2011, l discussed the predator-prey relationship between the leopard seal and emperor penguin in Antarctica. The leopard seal waits at the edge of the ice shelf and opportunistically picks off emperor penguins entering or leaving the sea. For the emperor penguin, feeding at sea is a decision between the need to feed to live and the risk of dying in the mouth of a leopard seal..

In the blog post I state: “From studying the emperor penguin and the leopard seal we know the emperor penguins will continue to feed, but so will the leopard seal. Some emperor penguins, despite their various risk protection strategies, will get eaten. It is important to note that in a probabalistic sense, we know that some penguins will be eaten by the leopard seal, but we don’t know which specific penguins will “bite the dust”.” This is true casually looking at a row of emperor penguins lined up to go into the sea in search of food.

However, upon closer analysis and study, over a period of time, it might be possible to determine which emperor penguins have a bit of catch in their step, have been injured in a narrow escape from a leopard seal, or have slowed down. These emperor penguins might come a belly-flop short of landing on the ice, and end up as prey in the mouth of a leopard seal. However, it is also possible, that a healthy, fit, member of the emperor penguin colony might suffer a particularly ill-fated episode of bad luck. This penguin might be in the wrong place at the wrong time when the leopard seal is rising out of the water with its mouth wide open ready for business. In fact, you could have the emperor penguin equivalent of the 4.0-40 yard dash champion, and end up as leopard seal “dinner”, with some bad luck and timing.

Looking at emperor penguin energy-seeking behavior and risk, it becomes apparent that probabilities have a great deal to do with the outcome but are not deterministic. You may attach a relatively higher probability of being eaten to the more fragile members of the emperor penguin population and a relatively lower probability of being eaten to those fitter members. The larger the colony size, and the more emperor penguins entering the sea at the same time, the lower the risk, the probability of being eaten, for any particular emperor penguin as there are more penguins entering the sea. (“there’s safety in numbers”).

You can run scenarios with differing proportions of fragile and fit emperor penguins, with higher and lower probabilities of being eaten (mortality rates), varying degrees of illness (morbidity rates) or accident, including leopard seal attack. In such scenarios, the leopard seal would most likely pick off different emperor penguins each time the scenario is run, however there would be objective tendencies to pick off more members of the more fragile group versus those of the fitter group.

In performing mathematical modeling of the fate of the emperor penguins by running scenarios with objective data and assumptions, we may set up a stochastic process which helps us to understand the behavior of the system as it evolves under a variety of scenarios.

Mathematical models involve expressing real world problems in mathematical language. This entails defining variables and establishing a formulaic process which will express the model as evolves. Variables are elements in the model which may change during the model. Because they may change, the model needs to calculate how they change over the course of the model and how they interact with other model variables, and are affected by the constants assumed by the model. Constants may arise from established data or may be assumptions plugged in to the model.

Stochastic processes incorporate non-deterministic, random elements into a mathematical model. The result may vary with time and with each model run. In comparison, a deterministic model will always produce the same result given the same assumptions and initial state. Thus, a stochastic process is run using random processes, employing a variety of assumptions and probability distributions informing objective tendencies for various model events to occur..

The random process in stochastic modeling will randomly choose which penguins are attacked, survive, suffer morbidity or injury from accident, and die over a period of time. Each run will be unique, as specific, members of the colony are differently impacted by the random process each time. By running many such models, one can get a picture of the survival data for the colony as a whole under a wide range of assumptions. Depending on the characteristics of the data, model and variables, results may be similar on an overall group basis, while differing by individual members impacted over time.

Under a normal range of assumptions and outcomes, this model may well predict overall group behavior over a period time. However modeling becomes much challenging when very low probability events enter into the model or rear their head in actual life.

For example, a eruption of an Antarctic volcano may be infrequent, however it could certainly impact emperor penguins. If the model assumed a volcanic eruption with a low probability, a robust number of stochastic model runs may randomly select such an event resulting in a BBQ penguin supper for the leopard seals.

The objective of the stochastic processes is to help us inform our decision making process, to help us understand the impact of variables under a wide range of assumptions, conditions, and scenarios. Thus a stochastic process should inform us about the expectations of the model under a wide variety of conditions, including the impacts of low probability / high risk events.