On fish jumping and the fallacy of observation

tenurepro

New member
Hi All,

I thought it would be fun to put this out there after some discussions on the leopard wrasse thread. Essentially; some folks claim that a certain group of fish never jump (because of personal experience of keeping a few fish) while others claim that the same group of fish are jumpers and are thus ultimately doomed to certain death in an open top tank. This little writeup shows how both view points can be reconciled with some simple math.

Ok, we hear a lot of general statements about certain fish being jumpers versus others that are not. But obviously, there are some individual specific tendencies (personality), species specific tendencies, genera specific tendencies, and all of this is modified by the tank environment (etc. size of tank, depth, interactions with other fish). I don't really think that fish are either jumpers or not jumpers... way too binary. For the simplicity of the model developed below, lets think of fish have a 'probability' of jumping for any given day; this probability depends on species (some species of fish/wrasse have higher probabilities of jumping than others) and tank environment / scape. We can probably all agree that most fish can in theory jump, so the probability of jumping is almost always a number that is greater than zero.

If the probability of jumping is greater than zero and substantially high. (say 10% a day), then it is inevitable that the fish will jump given enough time, and that a cover is absolutely needed to keep the fish alive in a tank.

Even if the probability of jumping is really low, say, 1 in 100,000 (0.001%) a day... it doesn't mean that the fish will never jump. Given enough time, rare events will occur (think of people winning the lottery, or getting struck by lighting... it happens, but it is rare). When we are dealing with such low probabilities, then it is totally conceivable to see how some reefers can keep the same species in an open top without them ever jumping, while others having them jump a few times... (just like some people win the lottery while most don't; you can't argue that just because you didn't' win the lottery, that nobody wins the lottery; also, you can't argue that if you win the lottery, than every one will win the lottery)...

So i decided to explore some models of fish jumping in an open top tank given a CONSTANT (assumption) daily probability of jumping. The constant assumption and the discrete nature of jumping (and dying) vs. not jumping (and living) make this problem very easy to model with the binomial distribution. if you were sick during math in high school, then the binomial is the little (n choose k) equation, where you predict the number of success or failures in N trials, assuming the probability of success or failure is constant. You can use the binomial to determine the probability of tossing a fair coin 20 times and getting only 5 tails for example.

In the context of fish jumping, we set the probability of success = daily probability of fish jumping, and ask how many times we observe 0 jumps over time... that gives us the probability of fish NOT jumping... 1- probability of fish NOT jumping is the same as the probability of fish jumping.

So here is the first model "“ assuming a fish has a 1% chance of jumping per day"¦ The probability that this fish would have jumped within the first year is close to 97.5%, The probability of this fish NOT jumping on you for a year is a measly ~2.5%... You NEED to get a cover if you want to keep this fish as the chance of keeping one in a tank with an open top for more than a few months are incredibly LOW.
273debbd8457b4976b8cb4e664f44f76.jpg


The second model has a daily probability of jumping at 3 in 10,000 (.03%); here we get into the grey zone. The chances of this fishing jumping by year one is about 10%, year 2 is about 20%, year 3 is about 30%, and year 5 is about 45%. The flip coin of this is you can almost certainly keep this fish alive in an open top tank (i.e. chance of fish NOT jumping) for a year, or two with only a small risk of it jumping). By 5 years though, it gets very dicey "¦ that is to say that half of the people that attempt this fish in an open top tank for 5 years will be successful while the others will not. This is where we tend to see a lot of debate between reefers; One will argue that I kept fish X for 5 years in an open top without it carpet surfing, so "œthey are not jumpers", while another will say, I tried fish X and it went carpet surfing, so "˜they are jumpers"; here is where the fallacy of observation bites us in the *** (with the binomial distribution laughing in the background).
74737c128bbf5a82a4773c97f098b574.jpg


Finally, the last model has daily probability of jumping at 1 in 100,000 (0.001%). This is the safe zone. You can keep this fish in an open top without any significant risk. At 5 years, the probability that this fish went carpet surfing is about 2%... you can take that risk.
adfb804baca9bfd224060ecd3f068f7f.jpg


While this model is very simple, I think it captures the stochastic nature of fish jumps.

In terms of real-world advice. It is just a matter of knowing the species you plan on keeping, their propensity for jumping, and how much risk you are willing to take with your fish. If you want to guarantee no jumping, then a well fitting / well constructed cover is necessary. For some species, the probability of jumping can be low enough, that it is very conceivable that you can keep them in an open top tank for a long period of time without any incidents... just keep in mind that rare events can and do happen given enough time.


If you are interested in running these simulations, here is some quick r code (r is free, but requires a bit of know how to access)

Just copy and paste this into r to explore different scenarios

dailyp=1/100000 #set this to the daily probablity

par(mfrow=c(1,2)) # initialize plot area

pjump=c() #initialize prob jump array

t=c() # initialize time in years array

for (time in c(0.5,1,1.5,2,2.5,3,3.5,4,4.5,5))

{t=c(t,time)

pjump =c(pjump,1-pbinom(0,size=round(time*365),prob=dailyp))

}

plot(t,pjump,main=c("Chance of Fish Jumping Over Time [",dailyp,"0.001% per day]"),xlab="Years in tank",ylab="Cumulative probability",pch=19,col='red')

plot(t,(1-pjump),main=c("Chance of Fish Jumping Over Time [",dailyp,"0.001% per day]"),xlab="Years in tank",ylab="Cumulative probability",pch=19,col="blue")



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Last edited:
With few exceptions fish generally jump to escape danger or confinement. It's usually a last resort solution. So if your fish try to get out of your tank on a regular basis check first what might be bothering them.
 
Not entirely sure I see the point of the 'exercise', nor the 'fallacy' of observation - other than by the time one observes a jumper it's usually too late? Seems to me less important why fish jump than the mere fact that they do. Just setup a nano in my son's room with a pair of clowns; no screen needed because clown don't jump, right! Wrong! Now it has a screen. I hear fish hitting the screens in my big tank all the time. Screens for me.
 
Not entirely sure I see the point of the 'exercise', nor the 'fallacy' of observation - other than by the time one observes a jumper it's usually too late? Seems to me less important why fish jump than the mere fact that they do. Just setup a nano in my son's room with a pair of clowns; no screen needed because clown don't jump, right! Wrong! Now it has a screen. I hear fish hitting the screens in my big tank all the time. Screens for me.

It was started because of what OrionN stated about his wrasses
http://www.reefcentral.com/forums/showthread.php?t=2369454&page=147

What you should of stated on this thread was please name the fish you have had over the years that have never jumped so you can compile a list of non jumpers? Very similar to the angels in a reef thread, which I think would be very helpful and useful?

http://www.reefcentral.com/forums/showthread.php?t=1661152&highlight=angels+in+a+reef+safe


FYI I would place OrionN pretty close to the top on being very knowledgeable in our hobby, and believe him on his word as an expert. But that is just me.
 
The purpose of this thread was to use some math and modeling to study the likelihood of fish jumping in an open water tank. The model is obviously very simple and can undoubtedly be improved. The exact motivation was several experts giving the opposite opinions on the same topic. The typical argument goes like this:

Expert 1:I kept fish x for y years without jumping, therefore fish x is safe in an open top
Expert 2: fish x jumped after y time, therefore fish x needs a cover.

You will see that my second model predicts situations such as this (experts having different opinions based on real experiences). When species of fish jump at intermediately low probabilities, jumping and non-jumping can be equally likely outcomes by the 3 year mark.

The 'fallacy of observation' is used to refer to problems with deducing general laws from a small number of observations.
Consider the classic:
I smoked all of my life and I don't have cancer. Therefore smoking does not cause cancer; this is a fallacy because one is making a general claim based on a single or few observations

In fish terms: this can be easily stated as: I kept fish X in an open top tank for a long time without it jumping. Therefore it is not a jumper.

We actually see a lot of this type of thinking on the forums; I did 'this' and I never had a problem, therefore 'this' works or is safe. (Eh. Substitute this with quarantine. I am sure many people don't qt and don't have issues, but that is also a probabilistic problem)

So i developed the models as a way to generalize without having to use personal observation.

I am in no way attacking the opinions or legitimacy of specific members or experts. I just want to show how probabilistically discrete events can sometimes lead to varying opinions that are both correct and valid.

Now if we had a good way of estimating probability of jumping for a specific species of fish, you can easily plug them into the models and estimate the chances of keeping this fish in an open top long term.


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The 'fallacy of observation' is used to refer to problems with deducing general laws from a small number of observations.

Ah, OK, in other words the statistical significance of a given sample size - maybe you said that and I just missed it. It is, BTW, a fundamental problem in this hobby - too many anecdotal observations masquerading as facts. In that sense you are correct, one person's conclusion that a fish is not a jumper because theirs has not jumped is statistically invalid. FWIW, any fish can end up on the carpet, though some are far more likely to do so than others. More likely would be wrasses, basslets and anthias. Less likely tangs, angels and clowns.
 
Ah, OK, in other words the statistical significance of a given sample size - maybe you said that and I just missed it. It is, BTW, a fundamental problem in this hobby - too many anecdotal observations masquerading as facts. In that sense you are correct, one person's conclusion that a fish is not a jumper because theirs has not jumped is statistically invalid. FWIW, any fish can end up on the carpet, though some are far more likely to do so than others. More likely would be wrasses, basslets and anthias. Less likely tangs, angels and clowns.



Glad you see the value. The probabilistic models help solve the observational problem by looking at the outcome of a large number of events. Also I think you hit the nail on the head with your last sentence on likelihood of fish jumping. It obviously differed between species / genera and will influence overall success in an open top tank.
Cheers!


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Many fish use a three to four foot vertical leap to escape predators.
This works great in the open ocean.
Not so much in a 24 inch tall tank.

You just need a nice 4 foot tall tank. 😀



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tenurepro and everybody,

At least we all agree some species of fish are more likely to jump than other in our tank. A lot of it have to do with the species and some the individual.
There are many reason why a fish jump out. Some of the reasons I can think off is as below:

Spawn behavior. Many species dart up release eggs and sperms and dart down. This will surely result in jumping out in our tank since 99.99% of our tanks are not deep enough.

How timid is the species, being chased or even too aggressively chase other fish, either con-specific or more aggressive species.

Being an open swimmer does not like the confine of the tank.

What the behavior of the species in the face of danger or startle like light being suddenly turn out, vibration or motion or movement near the tank. Some species take to the air, other dive for the sand and still other dive into the rock structure.

Tank condition is intolerable to the fish for one reason or another.


I do not think your model will be of any use because we do not have accurate probability of a fish jumping out of the tank, essentially garbage in garbage out. Even with the same fish, the probability of him jump out is different in different condition. For example, two Mandarin dragonettes in a 120 gal tank, the chance of them jump out is essentially nil if there are no fish that bother them and they are a mated pair. Remove the female and put in another male and the chance of one of them jump out is almost certain after 2 weeks, even if all the other fishes are the same.

This is my 2 cents worth of though.


 
Minh sums it up pretty nicely.
I forgot about the spawning, but then that's accidental and not intentional jumping.
In the past I lost most of my sixline wrasses due to accidentally overshooting while spawning. Generally all pelagic spawners are at risk.

For most fish that just want to get out of the tank, euro-braches are 70 to 90% effective in preventing carpet surfing, simply because most fish that want out try jumping in corners. A screen will only be effective with such fish when it is a really tight fit. The smallest gap between the screen and the glass may allow smaller fish to slip through.
This is one of the reasons why I don't like rimless tanks.

Fish that want to get out will find the smallest holes in your cover and exploit them. That's why I usually stuff even the smallest holes and gaps with filter foam pieces on my jawfish tanks.

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Hi All,

I thought it would be fun to put this out there after some discussions on the leopard wrasse thread. Essentially; some folks claim that a certain group of fish never jump (because of personal experience of keeping a few fish) while others claim that the same group of fish are jumpers and are thus ultimately doomed to certain death in an open top tank. This little writeup shows how both view points can be reconciled with some simple math.

Ok, we hear a lot of general statements about certain fish being jumpers versus others that are not. But obviously, there are some individual specific tendencies (personality), species specific tendencies, genera specific tendencies, and all of this is modified by the tank environment (etc. size of tank, depth, interactions with other fish). I don't really think that fish are either jumpers or not jumpers... way too binary. For the simplicity of the model developed below, lets think of fish have a 'probability' of jumping for any given day; this probability depends on species (some species of fish/wrasse have higher probabilities of jumping than others) and tank environment / scape. We can probably all agree that most fish can in theory jump, so the probability of jumping is almost always a number that is greater than zero.

If the probability of jumping is greater than zero and substantially high. (say 10% a day), then it is inevitable that the fish will jump given enough time, and that a cover is absolutely needed to keep the fish alive in a tank.

Even if the probability of jumping is really low, say, 1 in 100,000 (0.001%) a day... it doesn't mean that the fish will never jump. Given enough time, rare events will occur (think of people winning the lottery, or getting struck by lighting... it happens, but it is rare). When we are dealing with such low probabilities, then it is totally conceivable to see how some reefers can keep the same species in an open top without them ever jumping, while others having them jump a few times... (just like some people win the lottery while most don't; you can't argue that just because you didn't' win the lottery, that nobody wins the lottery; also, you can't argue that if you win the lottery, than every one will win the lottery)...

So i decided to explore some models of fish jumping in an open top tank given a CONSTANT (assumption) daily probability of jumping. The constant assumption and the discrete nature of jumping (and dying) vs. not jumping (and living) make this problem very easy to model with the binomial distribution. if you were sick during math in high school, then the binomial is the little (n choose k) equation, where you predict the number of success or failures in N trials, assuming the probability of success or failure is constant. You can use the binomial to determine the probability of tossing a fair coin 20 times and getting only 5 tails for example.

In the context of fish jumping, we set the probability of success = daily probability of fish jumping, and ask how many times we observe 0 jumps over time... that gives us the probability of fish NOT jumping... 1- probability of fish NOT jumping is the same as the probability of fish jumping.

So here is the first model "“ assuming a fish has a 1% chance of jumping per day"¦ The probability that this fish would have jumped within the first year is close to 97.5%, The probability of this fish NOT jumping on you for a year is a measly ~2.5%... You NEED to get a cover if you want to keep this fish as the chance of keeping one in a tank with an open top for more than a few months are incredibly LOW.
273debbd8457b4976b8cb4e664f44f76.jpg


The second model has a daily probability of jumping at 3 in 10,000 (.03%); here we get into the grey zone. The chances of this fishing jumping by year one is about 10%, year 2 is about 20%, year 3 is about 30%, and year 5 is about 45%. The flip coin of this is you can almost certainly keep this fish alive in an open top tank (i.e. chance of fish NOT jumping) for a year, or two with only a small risk of it jumping). By 5 years though, it gets very dicey "¦ that is to say that half of the people that attempt this fish in an open top tank for 5 years will be successful while the others will not. This is where we tend to see a lot of debate between reefers; One will argue that I kept fish X for 5 years in an open top without it carpet surfing, so "œthey are not jumpers", while another will say, I tried fish X and it went carpet surfing, so "˜they are jumpers"; here is where the fallacy of observation bites us in the *** (with the binomial distribution laughing in the background).
74737c128bbf5a82a4773c97f098b574.jpg


Finally, the last model has daily probability of jumping at 1 in 100,000 (0.001%). This is the safe zone. You can keep this fish in an open top without any significant risk. At 5 years, the probability that this fish went carpet surfing is about 2%... you can take that risk.
adfb804baca9bfd224060ecd3f068f7f.jpg


While this model is very simple, I think it captures the stochastic nature of fish jumps.

In terms of real-world advice. It is just a matter of knowing the species you plan on keeping, their propensity for jumping, and how much risk you are willing to take with your fish. If you want to guarantee no jumping, then a well fitting / well constructed cover is necessary. For some species, the probability of jumping can be low enough, that it is very conceivable that you can keep them in an open top tank for a long period of time without any incidents... just keep in mind that rare events can and do happen given enough time.


If you are interested in running these simulations, here is some quick r code (r is free, but requires a bit of know how to access)

Just copy and paste this into r to explore different scenarios

dailyp=1/100000 #set this to the daily probablity

par(mfrow=c(1,2)) # initialize plot area

pjump=c() #initialize prob jump array

t=c() # initialize time in years array

for (time in c(0.5,1,1.5,2,2.5,3,3.5,4,4.5,5))

{t=c(t,time)

pjump =c(pjump,1-pbinom(0,size=round(time*365),prob=dailyp))

}

plot(t,pjump,main=c("Chance of Fish Jumping Over Time [",dailyp,"0.001% per day]"),xlab="Years in tank",ylab="Cumulative probability",pch=19,col='red')

plot(t,(1-pjump),main=c("Chance of Fish Jumping Over Time [",dailyp,"0.001% per day]"),xlab="Years in tank",ylab="Cumulative probability",pch=19,col="blue")



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In my case I observed that jumping decreases with time.
Jumping after a week is exceptional.
 
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