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The authors have declared that no competing interests exist.

Conceived and designed the experiments: NB AR. Performed the experiments: NB AR. Analyzed the data: NB AR MG. Contributed reagents/materials/analysis tools: NB AR MG. Wrote the paper: NB AR MG.

People show higher sensitivity to dread risks, rare events that kill many people at once, compared with continuous risks, relatively frequent events that kill many people over a longer period of time. The different reaction to dread risks is often considered a bias: If the continuous risk causes the same number of fatalities, it should not be perceived as less dreadful. We test the hypothesis that a dread risk may have a stronger negative impact on the cumulative population size over time in comparison with a continuous risk causing the same number of fatalities. This difference should be particularly strong when the risky event affects children and young adults who would have produced future offspring if they had survived longer. We conducted a series of simulations, with varying assumptions about population size, population growth, age group affected by risky event, and the underlying demographic model. Results show that dread risks affect the population more severely over time than continuous risks that cause the same number of fatalities, suggesting that fearing a dread risk more than a continuous risk is an ecologically rational strategy.

Imagine two different risky events: One threatens to kill 100 people at once; the other threatens to kill 10 people every year over a period of 10 years. The first event represents a

People’s higher sensitivity to dread risks compared with continuous risks is often considered a bias: If the continuous risk causes the same number of fatalities, it should not be perceived as less dreadful. In this paper we offer an alternative explanation to the assumption of biased minds and argue that a stronger reaction to dread risks is ecologically rational, because dread risks actually cause a larger cumulative reduction in the population size.

Different hypotheses have been proposed to explain why people fear dread risks more than continuous risks. First, the psychometric paradigm

A different perspective reveals that dread risks lead to significantly worse short- and medium-term consequences than continuous risks, even if they do not eliminate a whole group. Thus, we focus not only on the overall number of immediate fatalities, as in previous accounts, but also on (a) the population size over time, and (b) the role of the age group that is affected by the risky event. Note that a fatal event strikes twice: it kills a number of people immediately, and it reduces the number of future offspring by reducing the number of their potential parents. A risk that affects children and young adults will have stronger negative effects on future group growth than a risk that affects group members who are past their reproductive period. Dread risks such as pandemics, terrorist attacks, or nuclear accidents are more likely to strike children and young adults compared to many continuous risks such as diabetes, cancer, heart attack, or household accidents, which affect primarily older people

We hypothesize that dread risks cause larger cumulative losses on the population level than continuous risks. More specifically, we hypothesize that the number of people-years lost because of a dread risk is larger than the number of people-years lost because of a continuous risk, in particular when the event affects the younger age groups. People-years correspond to the number of people who live 1 year in the population. Hence, by killing a large number of children or young adults at once, dread risks not only deprive the society of their contribution in subsequent years, but they also remove the potential contribution of the offspring the victims could have had if they had survived longer.

To illustrate this hypothesis, consider first a very simplified example. Imagine a population of 40 people, uniformly distributed across four age groups:

Further assume that the population growth is constant and that every year each young adult produces exactly one offspring. This implies that the number of children at time point _{i}_{i}_{-1}. Moreover, at every _{i}_{i}_{+1} corresponds to the number of children at _{i}_{i}_{-1} will be dead at _{i}_{total} = 40 (see

Development of the population size when no risky event is present (baseline), and when a continuous risk (1 individual killed from _{1} to _{5}) or a dread risk (5 individuals killed at _{1}) event occurs. A dread risk leads to a more immediate impact on cumulative population size that lasts longer compared with the continuous risk.

What happens if a dread risk occurs at _{1} that kills 50% of the young adults (i.e., 5 young adults)? At _{1}, the total population is reduced to _{total} = 35 (_{children} = 10, _{young adults} = 5, _{older adults} = 10, _{elderly adults} = 10). At _{2} the population is further reduced to _{total} = 30 (_{children} = 5, _{young adults} = 10, _{older adults} = 5, _{elderly adults} = 10), because the number of newborn offspring is smaller due to the fewer young adults. Finally, the population size settles at _{total} = 30, with continuous fluctuation within the respective groups.

What happens if a continuous risk, a disease, occurs at _{1} that kills five young adults over a period of five time steps (one young adult at every _{i}, from _{1} to _{5})? Note that the total number of fatalities directly caused by the risk is the same as in the dread risk scenario (i.e., 5). The total population is reduced to _{total} = 39 at _{1} and continues to decline until _{6}, where it finally corresponds to the size of the population hit by the dread risk (see

In sum, the continuous risk takes five more generations to affect the population as severely as the dread risk. The difference in the cumulative losses caused in the population by the dread versus continuous risk, can be calculated by determining the area between the curves representing the difference in the cumulative population sizes of the two conditions (i.e., the difference in people-years over time). In the example in

This simple illustration shows that people’s tendency to fear dread risks more than continuous risks can be ecologically rational, because dread risks can affect the population more severely in the long run. It is important to note that we do not claim this to be necessarily a universal pattern. We do not exclude there might be situations (i.e., a set of parameters) in which a continuous risk causes stronger cumulative losses than a dread. However, this is the pattern that occurs in all our simulations. In the following, we present results of two sets of more fine-tuned simulations.

In the first set of simulations, we assumed a small population size, similar to groups in which people lived throughout most of evolutionary history

We set the total population to 160 people. The individuals were distributed equally across 80 years (i.e., there were 2 individuals for each age at _{0}) and across four age groups, as in the illustrative example above. Between conditions, we manipulated (a) whether a dread or a continuous risk occurred, (b) the population growth rate, and (c) which age group was hit by the risk. The risk simulated was either a dread risk that immediately killed 50% of the population of the age group hit, or a continuous risk that killed the same total number of people in the same age group over a period of 10 years. The population growth rate was manipulated by setting the birth rate to either 0.05 (constant population), 0.075 (increasing population), or 0.025 (decreasing population). All individuals would die naturally after their 79^{th} year. The risk hit only children, only young adults, only older adults, or only elderly adults.

In total there were 24 scenarios. Each scenario was simulated 500 times, and we calculated for every time point the average population size within the simulations. We analyzed each scenario by comparing the log difference in cumulative people-years between the dread risk condition and the continuous risk condition after 25, 50, 75 and 100 years.

Log difference in people-years lost because of continuous and dread risk, by age group hit by the risk, separately for A. constant, B. increasing and C. decreasing populations. The dread risk killed 50% of a specific age group at once; the continuous risk the same total number of people over a period of ten years. A negative value of the difference indicates that the loss in people-years is larger for the dread risk; a positive value that the loss is larger for the continuous risk. Results show that dread risks lead to larger losses in people-years across time compared with continuous risks, in particular when children and young adults are affected.

When children and young adults were hit by the risks, the effect was stronger and lasted for the entire 100-year-range simulated. When older and elderly adults were hit, the difference between dread and continuous risks was weaker, decreased over time, and sometimes even became positive.

In sum, the results show that the dread risk affected the cumulative population size more strongly for most scenarios, particularly when it hit children or younger adults. The objective of this first set of simulations was to evaluate the impact of a dread and a continuous risk on small samples that would reflect the sample size of social circles. With a second set of simulations we investigated the effects of such risks on a much larger population of the size of the U.S. population in 2010.

We set the population size to the actual U.S. population size in 2010

We again ran 500 simulations for each scenario, calculated the averaged population size of the dread risk and continuous risk and plotted the log integrals after 25, 50, 75, and 100 years.

Using real U.S. data, we found support for the findings of the previous simulations. The differences between the cumulative population hit by dread versus continuous risks occurred across all conditions and lasted over, at least, 100 years. Independent of which age group was affected, the dread risk led to a higher loss in people-years than the continuous risk (

Log difference in people-years lost because of continuous and dread risk, based on the US population. The dread risk killed 20% of a specific age group at once; the continuous risk killed the same total number of people over a period of 10 years. Results show that the dread risk leads to a larger loss in people-years over time across all age groups. The loss was largest when children and young adults were affected.

The third set of simulations wanted to test whether the results obtained from the first two sets of simulations also hold when an alternative model underlies computation. We used ecology models to define population growth and the impact of a dread and continuous risk. Specifically, we used models described in Lande

We used a basic growth model of population, given the current population size _{t}

We specified that a dread risk kills a particular proportion of the population (see also

Immediately after the dread, the remaining population grows as follows:

In the following time steps, the population again grows according to (1). For the continuous risk, the same total amount of people as in the dread was killed, but over a period of

During these

We use these formulas to simulate changes of population size subject to dread and continuous risks. An analytic solution for time to extinction of a population after random catastrophes is given in Lande

In our simulations, we set the growth rate to either _{0} was set to 100 people and the carrying capacity to

In line with the findings of the previous simulations, we found that, over the time period considered, the dread risk resulted in higher losses in cumulative people-years than the continuous risk. The integral for the increasing population was −906, for the constant population −355, and for the decreasing population −137. Hence, even when using another model to test the impact of dread and continuous risks and even when not differentiating between different age groups, the results of the first two sets of simulations still hold.

People’s stronger reaction to dread risks compared with continuous risks is often perceived as a bias. This result proposes a new perspective against which the current hypotheses accounting for people’s perception and reaction to dread risks might be reconsidered.

We showed through three different sets of simulations that this is in fact an ecologically rational strategy. The effect of dread risks compared with continuous risks is amplified twice: First by killing more people at a specific point in time, and second by reducing the number of children and young adults who would have potentially produced offspring. Hence, this effect is particularly strong when children and young adults are hit which is often the case for dread risks (e.g., earthquakes, terrorist attacks, pandemics). This result is also in line with findings suggesting that people are more concerned about risks killing younger, and hence more fertile, groups

Where does the fear of dread risk come from? Although our study was not designed to provide this answer, we can speculate about some possible answers to this question. According to the preparedness hypothesis mentioned at the beginning, people may be prone to fear risks that threaten their whole group. This trait may be a product of either individual or group selection. Because individual fitness depends and improves with group living

There are important practical implications of this finding. For instance, from a public policy perspective, an appropriate reaction to dread risks would be to stimulate increase in birth rates and/or immigration to counterbalance the stronger loss in population size.

In sum, people’s fear and stronger risk perception of dread risk, compared to continuous risks, should not be considered an irrational bias, an emotional overreaction to a dramatic event. In fact, people’s intuition seems to capture the objective severity of the two different risks.

We thank Henrik Olsson for his helpful comments and Anita Todd for editing the paper.