This study developed a model (Fig. 1) using three inputs: (1) the probability of a 10 % agricultural shortfall per year; (2) the lives lost due to this 10 % agricultural shortfall without alternative foods; and (3) the statistical value of a life. These three inputs were used in quantitative analysis software to determine the cost-effectiveness of planning, research, development, and training. To determine each model parameter, the available literature was surveyed to estimate the model parameters. In many cases this is straightforward and there is a high degree of confidence in those inputs. However, in cases where no literature values were available or the confidence was low in those values, logic is employed with large error bounds to recognize the uncertainty. Based on the confidence of a parameter an appropriate probability distribution was chosen for the parameter.

Modeling Environment

The modeling was implemented in Analytica 4.5. Combining the uncertainties in all the inputs was performed with a Median Latin HypercubeFootnote 1 analysis with the maximum uncertainty sample of 32,000 (run time on a personal computer was seconds). The assumption is that all the uncertainties are independent except where noted.

In addition to identifying the input variables whose uncertainties most affect the outputs, an importance analysis was performed using Analytica. This analysis uses the absolute rank-order correlation between each input and the output as an indication of the strength of monotonic relations between each uncertain input and a selected output, both linear and otherwise (Morgan and Henrion 1990; Chrisman et al. 2007).

Explanation of Credible Intervals

A confidence interval is typically used when there are data for the likelihood of events. However, since most of the events considered here have not occurred, the Bayesian credible interval is used (Bolstad 2013). Table 2 summarizes the credible intervals for all the input variables. The upper and lower bounds for the probabilities of success of the alternative food interventions should not be viewed as hard limits, but rather as a logical progression towards greater credible intervals of the probabilities of success with aggregate of no preparation < planning < planning + research < planning + research + development < planning + research + development + training.

Table 2 Credible intervals for all the input variables Full size table

Catastrophe Probability Distributions

There are three types of probability distributions used in this study: (1) log-normal; (2) beta; and (3) gamma. Log-normal distributions are used for a continuous probability distribution of a random variable whose logarithm is distributed according to the normal distribution. The beta distribution is a continuous probability distribution defined on the interval [0, 1] (though this can be modified), which is parameterized by two positive shape parameters that appear as exponents of the random variable and control the shape of the distribution to model the behavior of random variables limited to intervals of finite length. The gamma distribution is a two-parameter family of continuous probability distributions used for cases with a large range of values as it is a maximum entropy probability distribution for a random variable. The types of distributions used for the variables in this analysis are summarized in Table 2. Most of the distributions are lognormal, but this was inadequate to produce reasonable behavior for two of the variables. The overall conclusions are not very sensitive to the choice of distribution type.

Probabilities

The following sections explain the rationale of the distribution types and parameters for the variables in the model.

Probability of a 10 % Global Agricultural Shortfall

A 95 % confidence interval for the probability of a 10 % global agricultural shortfall is estimated to be log-normally distributed between 0.3 % per year and 3 % per year. The lower limit corresponds to the sum of several fairly well-quantified risks. The probability of a volcano eruption like the one of Mount Tambora, Indonesia in 1815 (volcanic explosivity index = 7), which caused “the year without a summer” and famines in 1816 is about 0.1 % per year (Mason et al. 2004). The probability of accidental full-scale nuclear war is roughly 0.2 % per yearFootnote 2 (Barrett et al. 2013). This would likely cause at least a 10 % global agricultural shortfall, and probably a much higher shortfall (Turco et al. 1990). The probability of natural abrupt regional climate change of roughly 10 °C decrease in one decade is 0.01 % per year, and an order of magnitude increase in this probability due to anthropogenic emissions has been estimated (Denkenberger and Pearce 2014). One estimate of the probability of extreme weather causing a 10 % agricultural shortfall is now about 1 % per year (Bailey et al. 2015). The Bailey et al. study found that this risk is increasing, and if the other nonquantified risks are significant, the actual risk could be 3 % per year or more.

Uncertainty in the Number of Fatalities Due to a 10 % Agricultural Shortfall

The uncertainty in the number of fatalities due to a 10 % agricultural shortfall is very large. On the optimistic extreme, there could be aggressive government support or charity such that the vast majority of the global poor could generally afford sufficient food. If the crisis were only a year or two, loans could be feasible, either to poor individuals or poor countries. The necessary conservation (less waste, less food to animals, and so on) in the developed countries could be achieved by higher prices or rationing. However, even if mass starvation is averted, generally there would be more malnutrition and increasing susceptibility to disease. The poor would be less able to afford other lifesaving measures, and a pandemic would be more likely. Even if food aid is available, it may not be possible to get the food to the people who need it. Therefore, near zero mortality is unlikely. At the same time, even with no catastrophe, 6.5 million people die of hunger-related diseases per year (UNICEF 2006). On the other extreme, there could be food export restrictions or bans, as implemented by India, Vietnam, Egypt, and China in 2008 (Helfand 2013) when the situation was much less serious. This hoarding on a country level could also be coupled with hoarding on an individual level. This could dramatically reduce the food supply available to poor people.

Armed conflict could be in some countries’ best interest, which could also aggravate famine (Keller 1992; Waldman 2001; Goodhand 2003). These wars could even evolve into nuclear conflict, which would further impact food supplies. One estimate of the number of people at risk of starvation due to regional nuclear conflict is 2 billion (Helfand 2013). To capture this very large variation in behavior, a gamma function was used with a 95 % credible interval of about 20 million to 2 billion fatalities, with a median of 400 million.Footnote 3 Figure 2 shows cumulative probability, so the vertical axis values of 0.025 and 0.975 bound the range. There are currently 870 million people who are chronically malnourished (Helfand 2013). These people could quickly starve if there were a significant price increase (urban) or a significant reduction in farm output (rural). However, once 400 million people have starved to death (6 % of the current global total population), this would free up significant food for the remaining people. Therefore, 400 million people starving to death is used as the median (vertical axis value of 0.5 in Fig. 2). This distribution also includes the uncertainty in the duration of the shortfall which would run from 1 year for extreme weather to more than 10 years for nuclear war (Özdoğan et al. 2013). The uncertainty also captures the variation in the scope of the shortfall—it could be fairly uniform globally or concentrated in either developed or developing countries. If there are large regional imbalances, shipping would be adequate technically (Denkenberger and Pearce 2014), but there would be economic and political difficulties.

Fig. 2 Cumulative probability of lives lost given a 10 % agricultural shortfall and no alternate food (G is billion) Full size image

Lives Saved and the Statistical Value of a Life

To calculate the lives saved, the expected lives saved in the first year are multiplied by the time horizon. This is because future lives saved are typically not discounted, and the number of lives saved per year would likely increase because of population growth. With an expected total lives saved and cost of plan, the cost per life saved is calculated.

Most of the people who would die in an agricultural catastrophe would currently be living in global poverty. The most effective interventions can save these people’s lives now for only about USD 3000 per life (GiveWell 2015b). This is the cost to save a life, not necessarily the value of a statistical life. However, many people believe all people should be valued equally, and closer to the developed country valuation of USD 1–10 million per statistical life (Robinson 2007). This is questionable operationally because the global poor may prefer money to be spent on their own consumerism (for example, for food now), rather than reducing risks to lower levels.

However, there will likely be some fatalities even in developed countries. Because of the higher price of food, people would be more willing to eat spoiled food and in food scarcity-aggravated conflict scenarios, many rich people could die. Therefore, an attempt was made to bridge these perspectives with a lognormal distribution with a 95 % credible interval ranging from about USD 3000–USD 3 million per life. This has a median value of approximately USD 100,000 per life. One global compilation of values of statistical lives (VSLs) indicated that the VSL was roughly 100 to 200 times the gross domestic product (GDP) per capita (Miller 2000). This study found a global average VSL of USD 650,000. If the people were in dollar-a-day poverty, this would imply roughly USD 50,000 for the VSL. Since not all of the people who die in a catastrophe would be in dollar-a-day poverty, the USD 100,000 median VSL considered here is roughly consistent with Miller (2000). Thus, for those who view lives as being worth more, this analysis is conservative.

This allows the model to find a benefit to cost ratio; the model conservatively ignores benefits other than lives saved, such as lower food prices for people who would have survived anyway. The total benefit minus the cost yields the net present value (NPV). The payback time is the number of years after the project has been completed for the expected benefit to pay back the cost. Since the payback times are short, a good approximation of the internal rate of return (IRR) is the reciprocal of the payback time (Pearce et al. 2009).

Cost-Effectiveness

Figure 3 shows the functionality within the research cost-effectiveness module. The other cost-effective modules are organized similarly. Though alternate foods may not prevent all the fatalities in a given scenario, the probability of alternate foods solving the problem could be thought of as a larger probability only partially solving the problem.

Planning

With global cooperation (for example, sharing information and trading food), it was estimated that these alternate food solutions could feed everyone even without preparation (Denkenberger and Pearce 2014). There is evidence in the literature that humans are capable of such noble behavior in a local crisis (for example, the famine in Ethiopia in 1984–1985) (Von Braun et al. 1999). However, this assumption may be overly optimistic given counter examples such as the Bengal, India famine in 1943 that was much worse than the food supply shortfall (Lazzaro 2013). Knowledge that everyone could be saved would facilitate global cooperation, but still relatively few people know about the solutions.

The equivalent probability that alternate foods would prevent everyone from starving with current preparation is quite uncertain. At least 700,000 people have heard about the concept based on impression counters for the roughly 10 articles, podcasts, and presentations for which there were data including Science (Rosen 2016) (out of more than 100 media instances). It is also possible that, if there is some warning before a catastrophe, people knowledgeable about alternate foods could use the intense media interest to inform the general public (including policymakers). It is possible that given a catastrophe, people will independently invent these solutions. Because of this, a lognormal probability distribution is assumed with a 95 % credible interval of 0.1–1 % chance of alternate foods working as planned with current preparation.

If there were an international plan for how efforts could be coordinated to ramp up alternate foods given a catastrophe, the probability of success is expected to increase significantly. This is especially true because a plan could start to be implemented if there is warning before a catastrophe. A lognormal distribution is assumed with a 95 % credible interval of 1 to 10 % chance of feeding everyone with alternate foods in this case. There is overlap between this distribution and the probability distribution of alternate foods working with current preparation. It is not reasonable that the addition of the plan would increase the probability of success less than 1 %, so it is truncated at 1 %.

The cost of the plan is assumed to be lognormally distributed and have a 95 % credible interval of USD 1 million–USD 30 million. The lower values correspond to a few person years of planning plus briefing the relevant individuals. The higher values would involve more continuous briefing and updating and allow for cost overruns. The time horizon of the effectiveness of the plan is assumed to be lognormally distributed and have a 95 % credible interval of 3–30 years. Lower values are similar to a presidential term, while higher values indicate more maintenance. The probability of success, cost, and time horizon of the plan are assumed to be independent, which produces larger variances than reality, which is conservative with respect to the unfavorable bound of cost-effectiveness.

Research

If targeted experiments and modeling of alternate foods were performed, the probability of success would increase significantly as this is the primary uncertainty in alternative food proposals. A lognormal distribution with a 95 % credible interval of 3–30 % chance of feeding everyone with alternate foods is assumed with both a plan and experiments. The improvement is truncated at 1 %.

It is assumed that the cost of the research is lognormally distributed and has a 95 % credible interval of USD 10 million–USD 100 million. 445 tree species made up 76 % of the growing stock in 88 countries (FAO 2005).Footnote 4 It was found that 100 tree species for half the global growing stock is a reasonable order of magnitude estimate. However, even simply testing on one hardwood and one softwood could have significant explanatory value because of the significant differences in constituent compounds. For solutions involving nonwoody biomass (for example, leaf tea and enzyme-produced food), fewer species would likely be required for a given fraction of biomass coverage. This is because of the large fraction of nonwoody biomass that are crops, and the domination of rice, maize, and wheat among crops.Footnote 5 For the fishing solution, relatively few feedstock organisms (for example, algae) may need to be investigated. For methane-digesting bacteria, only a few different natural gas compositions may need to be tested. There is also the issue of how many food organisms would need to be tested. In the case of currently domesticated animals like chicken and cattle, it would be relatively few. However, it could be significantly more for other categories like mushrooms. Other experiments include growing photosynthetic crops in the crisis conditions of the tropics (cold and high ultraviolet radiation), biomass supply experiments, and human nutrition experiments. It would be valuable to synthesize existing experiments for relevant insights. Further modeling of other issues such as energy and water would be important.

The order of magnitude cost of a graduate student year in the United States with some experimental facilities and overhead is USD 100,000. A scientific paper can be produced in roughly 3 years when running a targeted experiment like one organism consuming one feedstock type. Therefore, the lower bound roughly corresponds to 30 such studies. This would involve significant extrapolation to other species. However, the upper bound would allow about 300 studies, producing higher confidence. The brute force method of testing hundreds of feedstock species with many food species could cost billions of dollars. Using a designed experiment approach the number of experiments could be greatly reduced while yielding the majority of the explanatory value (Myers et al. 2009). Research is generally longer-lived than planning, so the time horizon of the effectiveness of the plan is estimated to be lognormally distributed and have a 95 % credible interval of 6 to 60 years.

Development

If in addition to planning and research, development of alternate foods outside the laboratory were achieved, the probability of success would increase further. A lognormal distribution is assumed with a 95 % credible interval of 7–70 % chance of feeding everyone with alternate foods with a plan, research, and development approach. The improvement is truncated at 1 %.

The cost of the development is assumed to be lognormally distributed and has a 95 % credible interval of USD 10 million–USD 100 million, the same as for research. This is because even though moving to a scale of production outside the laboratory is more expensive for a particular scenario, only the most promising scenarios would be chosen. The lower values correspond to choosing the most promising food and feedstock organisms and extrapolating to other organisms. The higher values would involve more organisms. This development would also facilitate the estimation of costs given mass production. The same time horizon is used as for research.

Training

If in addition to planning, research, and development, catastrophe training were continuously implemented, this would further increase the probability of success. Three low-cost training options are described here. First, audio and video training modules could be distributed by the media after the catastrophe. Second, lower levels of government could be trained how to respond and to train others. Third, public service announcements before the catastrophe would ensure that nearly everyone knows about the alternate food solutions and therefore will be more likely to stay calm if a catastrophe occurs (this could even be done as part of the planning intervention). More expensive approaches would be training engineers and technicians how to retrofit industrial processes for alternate food production. Farmers could be trained on alternate food production (for example, with school curricula).

If training involved 3 % of the global population, and the sum of the cost and opportunity cost of the training were USD 10 per hour, and it were 5 h per year, this is roughly USD 10 billion per year. The lower bound could be training 0.3 % of the global population similarly. The low-cost options could be significantly less expensive than this, but it is assumed that the training package is generally larger than the other interventions. More money than the upper bound could be spent to train the majority of citizens. However, because of food storage, it is not critical that alternate food production begin immediately and it is assumed that the media can be restored quickly (if the catastrophe even disrupts media services in the first place) to disseminate the message. If direct apprenticeship is required, as long as this is of short duration, such as weeks, it could quickly spread exponentially through the population. Therefore, there will be diminishing returns for additional training before the catastrophe. A beta distribution (to avoid truncation) is assumed with a 95 % credible interval of 9–90 % chance of feeding everyone with alternate foods with a plan, research, development, and training.Footnote 6 The improvement is truncated at 1 %. The cost of the training is assumed to be lognormally distributed and has a 95 % credible interval of USD 10 billion–USD 100 billion. In this case, it is assumed that the training is over a specific period of 10 years.