Answer by Rory Young:
There are many external physical signs of fear. These may or may not be detectable depending on the species manifesting them and the species observing.
The eyes are the strongest indicator and easiest for us to pick up, although different animals rely on different dominant senses.
Many animals show the sclera or the whites of their eyes to display surprise or fear. We do the same, our eyes widen in fear or surprise as do many animals.
Here are pictures of a dog and then a human showing fear. Look at the eyes:
Here are two images of an elephant eyes. The first shows a relaxed animal and the second is showing fear..
There are many other signs of fear. These are all known as fight or flight responses.
Breathing and heart rate speed up. This is directly related to the fight or flight response. The animal is gearing up to run or fight. It needs oxygen and increased heart rate to be able to use its physical abilities to the max. We are the same of course. Think about the last time you got a big fright.
Relaxation of the sphincter muscles means that they can defecate fear. I have seen this often with both baboons and vervet monkeys treed by leopards. This also happens with people in cases of extreme fear.
The tear and saliva glands shut down which means a dry mouth and eyes. This is of course difficult to see but if an animal is dripping saliva from its mouth it could indicate a lack of fear.
The pupils dilate. Add this to the sclera showing and together they transform the eye. The reason for the pupil dilating is so that the animal can see better.
Animals and people can urinate in fear. This is very common among apes.
Shaking is very common especially once the adrenaline really starts flowing.. Muscle tension is also common and this is obvious in cats. Lions' tails twitch, domestic cats' backs arch and the hair on their back rises. People raise their shoulders.
Lastly there is smell. When animals and people experience fear a part of the brain called the amygdala can allow the release of homones including epinephrine and norepinephrine and cortisol. We may not smell a difference but a dog, elephant, bee or other animal with an exceptional sense of smell or the ability to sense pheremones may well pick up a change caused by these.
Sensing fear in the animal world is a fact. My own personal experience is that in tense situations with elephants or lions showing fear is not a good idea. The best way to handle it is not to pretend but to train yourself to be calm or even better to transform fear to controlled aggression. In this regard fear and aggression are closely related.
My own experience dealing with wild African animals on foot has taught me that knowledge, experience and confidence can reduce fear when dealing with animals and the best way of not having them pick it up is to not be afraid. It is easy to start using my rifle as a safety blanket (that doesn't sound right!) but the best is to avoid encounters which could cause fear in the animals or ourselves. But should it happen then the fear has to be controlled.