Superstition is a belief or practice resulting from ignorance, fear of the unknown, trust in magic or chance or a false conception of causation. In an ecological sense, superstitious behaviour is the incorrect assignment of cause and effect.

Superstition does not just exist in humans. All animals capable of displaying associative learning can express superstitious like behaviour, in that an action or behaviour is incorrectly assigned to an effect. Superstition is thus a consequence of an organism’s ability to learn from observations of coincidences. Because of the incorrect associations which occur when displaying superstitious behaviour, there are no clear benefits to such behaviour.

The difference between superstition observed in humans and animals is that; humans apply a psychological aspect to the belief. A superstitious human may (incorrectly) believe that an action directly results in a consequence. A superstitious animal on the other hand will respond to a stimulus as though it is responsible for a given consequence, they do not think – merely respond to the stimulus.

Cause & Effect

Superstitious behaviour is essentially a potential waste of time, energy and resources and may also expose an individual to increased risk (such as predation in animals). Why is it that superstitious behaviour could therefore evolve?

Superstition is all about relating costs to benefits:

• If a superstition has a high cost and the benefit of performing that superstitious act is low, then it is unlikely that the superstitious behaviour will be performed
  • For example – Associating a certain food type with sickness following food poisoning after its consumption. If food variety is low and the sickness was only mild, an individual avoiding consuming that food again might risk starvation – it would therefore not be beneficial to avoid that food type without further reassurance
• If the cost of the superstitious behaviour is low and the benefit is great, then there is essentially little reason not to perform the superstitious behaviour
  • Following the above example; If food variety is high and the sickness was severe, then with a cost of risking severe food poisoning again it seems beneficial to the individual to avoid that food type in future

The Risks of Superstitious Behaviour

Superstitious beings run two primary risks:

1. They believe an untrue cause and effect i.e. superstition
2. They fail to believe the truth i.e. ignorance

These risks are a result of learning from observation, i.e. concluding a pattern exists when in reality it doesn’t (superstition) or failing to detect a pattern which actually exists (ignorance).

Similar occurrences are observed in statistics in the form of type I and type II errors:

• Type I errors are the equivalent of superstition – A test is believed to be significant, when the significant results occur solely by chance
• Type II errors are the equivalent of ignorance – The null hypothesis of a statistical test is not rejected (i.e. no statistically significant results) even though there is a cause and effect

In statistics, the probability of making a type I error = α. The value of α is typically set before analysis and usually the null hypothesis is rejected if p≤α.

If the threshold for α is set too high (i.e. a low α value such as 0.01 meaning low probability of a type I error) then the analysis is likely to suffer from ignorance i.e. no statistically significant results even though in reality there is a cause and effect.

If the threshold is set too low (e.g. 0.1) the analysis is more likely to suffer from the disadvantages of superstition i.e. the test is believed to be significant, when the significant results occur solely by chance.

It is impossible to diminish one risk without increasing the other

Modelling Superstition

Simplistic Model

A simple model was created by K. R. Foster & H. Kokko (2008), which can be used to determine whether an animal should react to an event in a superstitious manner. It requires that an initial event (such as the production of a noise) is associated with a later, second event (such as the arrival of a predator) and an action arises as a result.

The model uses:

• p – The probability that the second event is associated to the first event
• b – The benefit of performing an action should the second event occur
• c – The cost of performing the action, regardless of whether the second event occurs

For example:

A prey animal hears a noise and later a predator arrives, the response of the prey animal is to hide. The prey animal may now have associated the first event (noise) with the second event (predator) by associative learning. In future occurrences of the same noise, whether the animal responds depends on if pb>c. That is, if the probability of the predator’s appearance being related to the noise multiplied by the benefit of avoiding the predator is greater than the cost of running and hiding.

• If p = 0 i.e. the events are not related at all, then the prey animal should never respond to the noise
• If c = 0 i.e. there is no cost of hiding, then as long as hiding provides some benefit and there is a probability that the events are related (p and b are at least slightly greater than 0) the prey animal should always respond to the initial event
• If b is much greater than c i.e. benefits greatly outweigh the costs, then the prey animal should also always respond to the initial event (even if p is low)

However, this model is highly simplified and there are a number of factors which need to be considered. For instance, there are many ‘initial events’ which an animal could relate to later events and how is it that an animal can determine the probability of an initial event being related to a secondary event?

Extended Model

Building on the simplicities of the basic model, K. R. Foster & H. Kokko (2008) began to determine a more robust model. Whereas before, it was required that an animal must be able to associate an initial event with a later event, the extended model allows for more ‘normal’ situations.

The extended model considers the possibility of two initial factors being associated with the arrival of a predator. The example used is the rustling of grass and the rustling of a tree both being associated with the arrival of a predator.

The prey animal has a choice; respond to either one of the initial events, respond to both or respond to neither. As the probability of the latter event following the initial event increases, responding to only one initial event or none at all impacts survivability more. As a result, it is most beneficial for the prey animal to respond to both initial events unless p <0.2.

The extended model is by no means a definitive model from which superstition can be calculated, but it shows that there are many more factors to be considered.

Conclusion

In certain circumstances, it is beneficial to accept superstitions. For example, natural selection can favour strategies which lead to frequent errors in assessment (beliefs in superstition) as long as the occasional correct response carriers a large enough benefit. Therefore animals should accept superstitions when the cost of rejecting true, low frequency association, is high

However, superstitious behaviour should carry low costs. It is likely that superstitious behaviour will be more common when the cost of not acting is very high (such as predation). Frequent events provide the potential for increased amount of false associations (i.e. superstitions) but they also give more opportunities for the elimination of superstitions by associative learning.