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Y'know... I just did this very thing in another post, and I hadn't really considered why.
I like djtj's response, which makes a lot of sense to me.

I have to say though, I often don't adhere to the recommended group of 6 fish. If I have the space, I go for larger gorups, but sometimes it just doesn't work out, especially if you grabbed up some species you've never seen at the LFS before, and havn't seen since (why I have just 4 C. Reticulatus), or if a fish dealer sent you some freebees in the hopes you'd buy more (why I have only 3 green flame tetras), or because of die-off and you're either afraid to buy more or just havn't gotten around to it.

Sometimes small groups just don't work out as well. My 4 corys are timid and very shy, and they'd probably be better off in a larger group. On the other hand, my 3 tetras are robust and fearless, so sometimes I guess there's no harm in small groups.

Hoping that there must be a word for everything I mean...

Calla,

I am wondering why odd numbers would work better.

If at all, then I would say that the male/female proportions are important, usually with more f than m. But I guess it is hard to judge which juvenile fish are male or female in the LFS.

Ingo

---

Proud Member of the New Jersey Aquatic Gardeners Club

IMO, the number 6 use, came from the subject of breeding, and was just used there after as a small school number. And it then fits nicely into all the thoughts/ideas about it already mentioned.

Years ago, like 20 or so, there were several scientists that did a big study on what number would best get you at least a pair (male and female), out of a group of un-sexable fry. In other words, breeders don't want to have to buy 50 fry in hopes of getting just one pair. And most anyone knows that just buying two fry rarely gives you a pair in the end. It was determined that the lowest number of fry you could get that would have the greatest likelyhood of having at least one male and one female, was the number 6. Within this study, they worked with spawns that had ratios of even number females to males, as well as very lopsided numbers of male to female ratios. As there are many fish that ph and other parameters will determine the majority of the sex of the fry. This is the reason all clubs require 6 fry for their fry auctions, so others have a good chance of getting a pair. The study also went on to say that you had to go over the number 12 to make the odds any better. Which makes sense, because if 6 sets the odds best, and gives you the best chance of at least one from each sex, then you would have to have at least 6 more to get the odds to say you have at least 2 of each sex.

IMO, the number 6 for a school, started off the same way. When getting a school of fish, for better chances of getting at least one of each sex, the number 6 comes into effect.

_____________________________________________________________

There is always a bigger fish...

Whenever I've seen my cories breeding, the gravid female has always been courted simultaneously by two males. I've read other sources that say the same thing - the female prefers two males. So I guess to have a breeding school with more than one breeding female, you don't necessarily have to have odd numbers - just a multiple of three. (Fitting in nicely w/ the previously mentioned 6 and 12 school suggestions.)

I've been told and I've read that its perfectly fine to have a trio of cories. And I am planning on doing that unless someone can give me solid reasons I should get as many as six. I have a 20 gal, and I want other fish apart from cories...!

Acidrain, it doesn't take a "big study" to figure out what number is the best to get a pair - just a simple understanding of statistics.

Let's start with 1 fish: only two choices: 1 M or 1 F

so the chance of either case is 1/2 (I think everyone knew this)

Ok, let's do two fish:
4 choices in this case:
M&M or M&F or F&M or F&F. Note that it appears I have repeated myself, but statistically M&F is a different case than F&M. Even if the net result is the same.

So the odds are: M&M = 1/4, ending up with 1 F and 1 M = 2/4 or 1/2 and F&F = 1/4

So the odds of a pair are 50%

We can keep this exercise up: 3 Fish:

M&M&M, M&M&F, M&F&M, M&F&F, F&M&M, F&M&F, F&F&M, F&F&F

every case in the middle results in a pair: 6/8 or 75%

As you can see that this becomes very time consuming quickly, mathematicians have come up with a term: "combination" to describe this
the combination is works like this: you want the number of ways that choosing 5F in a group of 12 fish would be read "choose 5 of 12". Then you looks up C^12_5 (also deonted with parentheses sometimes). In fact, out of 12 fish, there are 792 ways that 5 of them are female. Out of 2^12 combinations, which is 4096. So end chance that if you select 12 unsexed fish that you have 5F is 792/4096 = 19.3%

Now, to get to the question acidrain proposed, you want to know that number of ways that you get all M or all F. Well that is choose 0 of N, where N is the total number of fish. From above, we see that if N=2, there is a 50% chance of all M or all F. N=3 is 25% of all M or all F.

Here is a table:

N % all F or all M

2 50%
3 25%
4 12.5%
5 6.25%
6 3.12%
7 1.56%
8 0.78%
9 0.39%
10 0.19%
11 0.097%
12 0.049%
13 0.024%
14 0.012%
15 0.0061%

You make the odds better with each additional unsexed fish, not just going from 6 to 12. Apparantly fish clubs have decided that a 3% chance of all F or all M is acceptable at auction, which is why they require 6 fry.

I've been told and I've read that its perfectly fine to have a trio of cories. And I am planning on doing that unless someone can give me solid reasons I should get as many as six. I have a 20 gal, and I want other fish apart from cories...!

Just look around at this post. If you had the cories in a 5 gallon by themselves or something, then it would be ok to have only 3. But in a commnuity setting, it would be best to have more cories so the other fish don't intimidate them. Besides, a 20 gallon can easily hold 6 cories and a variety of other fish.

Yes, ok, there is a behaviour difference, but I'd hazard there is a behaviour difference between 6 and 24 too, and so why isn't the minimum school 24?

Good point, but I think it's asking too much of the adverage fishkeeper to make 24 fish a solid minimum. That would mean that you couldn't have schooling fish unless you owned a 30 gallon tank. 6 is a more realistic number that many more people will listen to.

Remember that old Tv show, "Why is it so"

Your answer is easy "Some one said so" and the rest are just following along.

In most types of design work it has been considered that an uneven number looks more pleasing, reason the eye is not looking to pair things up.

One makes a statement.
Two make it even, and three make it interesting.

Well that's the way I work anyway.


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Keith

Near enough is not good enough, therefore good enough is not near enough, and only your best will do.
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If you had the cories in a 5 gallon by themselves or something, then it would be ok to have only 3. But in a commnuity setting, it would be best to have more cories so the other fish don't intimidate them.

Best, but not vital? Like ideally they'd also be in a 55gal tank with only species of the same region?

I think it's asking too much of the adverage fishkeeper to make 24 fish a solid minimum. That would mean that you couldn't have schooling fish unless you owned a 30 gallon tank. 6 is a more realistic number that many more people will listen to.

Having 6 as a minimum is very limiting in its own way, as if you had a 20 gal, you would severely reduce the number of other fish could could have if you took into account adult size and activity of 6 corydoras. 5 is a pretty realistic number too...


I suppose what i'm asking is for the average fishkeeper with no care about M:F ratios or breeding, is the number 6 an ideal number or something with a very good reason?

To me, 3 is adequate, 6 is a bit more adequate, and so on and so forth down the line. Aiming for 'natural' with 6 doesn't make sense, so what exactly are we aiming for? do any of us know the natural behaviour of these fish or just behaviour that we have seen in tanks when the fish appear to be content? Is it a certain type of fearless behaviour that we are aiming for? Least signs of stress?
I think I could stick 4 cories in a heavily planted tank and have them more content than 6 in a sparsely decorated purple gravel/plastic plant arrangement.

6 is fine, love it, wonderful number, but when it comes to other numbers should we be taking into account other things that could affect the outcome? And do we have an ideal outcome in mind?


Ingo, unsure about the uneven number thing, but it was very popular a while back. It has to do with the pecking order. I don't see much difference between odd and even once you get over 4 fish, there is almost always a runty one if you watch long enough. 3 fish its the same, but the one down the pecking order is much easier to pick.




Last edited by Callatya at 16-Jan-2006 22:05

For animals, the entire universe has been neatly divided into things to (a) mate with, (b) eat, (c) run away from, and (d) rocks. - Terry Pratchett

robbanp, please don't take this to be too rude, but did you even read the previous posts? B/c you got both what I and acidrain said backward.

acidrains said: "Now, the only way to better your odds in this scenerio is to jump up to the 12 number." in which he was saying the only way to improve the odds is to go from 6 to 12 unsexsed fry. Which I proved conclusively wrong. Again, every single individual you add increases the chance of having one pair.

An then, in fact, every single individual you add increases the chances of having 2 pairs. By the exact same arguments. I think I and Cup are still waiting for a reference on this big study that acidrain keeps alluding to.

Bignose, I may have said it in confusing words, but actually what I was meaning was exactly what robbanp stated. True, the math shows that with each individual fish you add to the mix, your odds grow. And I understand this, and believe it to be true. But, what I was meaning with the odds and such, and confused as well, was like if you add one or two more than six, your odds go from 96.9% (6fry) to 98.4% (7fry) to 99.2% (8fry) of getting a pair. Not even a 3% increase with the addition of 2 fish. Where as, if you just simply get 2 fish, your odds are 50% likelyhood of getting a pair. But, if you get 6 in one bag, and 6 in another, well I am no math expert, but to me that is twice as good as a 96.9% chance of getting two pairs. This is were my confusion comes in, lol. As for getting a second set of 6, would you not agree, there is a substantial difference in the chance of getting a second pair vs the smaller chances of adding one at a time up to the 6?
A friend of mine turned me on to this equation; 1-(2/(2^n)) and ask you what you thought? How similar is this to yours?

Mainly, making statements like "Now, the only way to better your odds in this scenario is to jump up to the 12 number" is not right. It is a horrible misapplication or misunderstanding of statistics.

I totally agree, and apologize for this statement. I was meaning to be more general.

What you’re saying is that numerous studies have concluded that six fish is the ideal number by which one can obtain a fair sex ratio

Don't twist my words Cup, I stated there was one big study about 20 years ago where they determined this. I later stated that there have been numerous studies done on the sex ratios of the fry of fish bred in different water parameters.

As for the articles, they were 20 years ago. I have no idea which mag I read them in. And I will not claim I know where they are. So Cup you can continue your old wives tale idea.

And Cup, I never called you a liar. I simply asked you for more sound info so that I could maybe change some of my speaker programs. That is all. As I cannot give talks at other clubs with info that I cannot back up. Whether it be bogus or not, I must have a reference to use. Then you came back with smart ellic remarks refering me a liar. I simply stated to you to bring the facts if that is so. And, as usual, you did not. You simply come back saying I called you a liar. This conversation with you is done. If you have any further problems with it, you can take it up with Adam.


_____________________________________________________________

There is always a bigger fish...

You didn't really answer my questions, but okay...

Which smart aleck comments? The ones in which you utilized my own quotes to refer to my argument with so much cynicism you could cut it with a knife when I had initially posted? Regardless; no one is twisting any words. That is the impression that I thought (and evidently was not the only one) was conveyed by your post, which is why I had commented in the first place, with no attempt to purposely change the meaning of your post. I apologize if I came across in that manner.
“As, he said, and she said, and a prominent cichlid breeder said, etc etc, just don't make it so.” I doubt anyone can argue that the above quotation was accusatory in tone. There is no hesitation in my mind that you insinuated that I had made up such breeders for the sake of my argument (lying), and whether or not that was your intention, I felt it to be so. And this is one and many instances that you called into question the veracity of my statements without giving me a chance to explain myself or even assuming that what I had stated actually might possibly be correct. Ehnce, this is why I felt you were IMPLYING that I was fallacious, not that you had outright said it.

But no, you are correct, this talk is indeed done.

In any case, back to the topic at-hand. Suitable numbers vary on a species-by-species basis. I don’t think this stance, at least, will be debated by many individuals.


Last edited by Cup_of_Lifenoodles at 18-Jan-2006 23:31

Origional posting

I am seeing a whole bunch of posts saying that if you plan on having cories, they must be in a group of 6 or more. Its starting to spread to other schooling fish too.

This is all well and good, but WHY 6? It seems somewhat arbitrary.

Why not 5? I'm seeing people get told that 5 cories isn't enough and that they should really get one more to make it a school of 6. Huh?

Is it that vital that one fish will make all the difference?
***********************************************************

Maybe I am out of line but this is getting way off line.

Taking this out of context
they "must" be in a group of 6 or more.

The word here is "must" Who said so and why does it actually matter it is a personal choice its your tank its your choice.



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Keith

Near enough is not good enough, therefore good enough is not near enough, and only your best will do.
I VOTE DO YOU if not WHY NOT?
VOTE NOW VOTE NOW

"A friend of mine turned me on to this equation; 1-(2/(2^n)) and ask you what you thought? How similar is this to yours?"

This is exactly what I used to calculate the chances in the first long post with the table entries: N fish & chance of getting all one sex.

The second equation is a generalization of the first one, where each sex is not 50:50. That is the p^m*(1-p)^f. If p were 0.5, and (m+f)=n, then you get exactly the same answer.

Finally, if yes you can only get multiples of 6, then 6 to 12 is the only ways of increasing you odds. So, the confusion was right there.

And yes, the odds fall of pretty quickly. Hence my statement that "fish clubs must think that 3% chances are a good compromise, which is why they require bags of 6"

Now, let me address another statement you just made: "But, if you get 6 in one bag, and 6 in another, well I am no math expert, but to me that is twice as good as a 96.9% chance of getting two pairs."

This is true, and false! You change the distributions when you get 12 fish... there is more to spread out. What I mean, there are 6! = 720 different way of distributing 6 fish between M & F. But 12! = 479,001,600 different ways if distributing 12 fish between M & F.

Let me show you a few calculations:

For six fish:
Split -- chance of getting at least 1 pair

50:50 -- 96.9%
60:40 -- 94.9%
70:30 -- 88.2%
80:20 -- 73.8%
90:10 -- 46.8%

For 12 fish:
Split -- chance of getting at least 1 pair -- chance of getting at least 2 pairs

50:50 -- 99.9% -- 99.4%
60:40 -- 99.7% -- 98.0%
70:30 -- 98.6% -- 91.5%
80:20 -- 93.2% -- 72.5%
90:10 -- 71.1% -- 34.1%

Look what happened. Up to the 70:30 split, you actually have a better chance of getting 2 pairs from 12 fish than getting 1 pair from 6 fish. But then look, after the 80:20 split, you have a worse chance of getting 2 pairs from 12 fish than getting 1 pair from 6 fish. Though, for all of the 12 fish, you have a much improved chance of getting at least 1 pair. This is because these distributions are so skewed. In fact, for 12 fish, at 80:20 you have a 6.9% chance of getting all 80's, at 90:10 you have a 28% chance of getting all 90's.

So sometimes getting 12 fish is better than twice as good, and sometimes it is worse. This is tricky thing with statistics And now everyone can see exactly why the cynic saying "you can prove anything with statistics" ain't too far from the truth.

Last edited by bignose at 19-Jan-2006 05:51

Right.

Well.

In the nicest possible way gents, I'm not feeling the love here...
There is no need for all this swordfighting.



So, i'm buying 3 cories. Couldn't give a toss about rex ratios or pH or whathaveyou.

Anyone going to tell me why I am a horrible terrible person for not buying 6?

I'm going out to buy 6 cories, anyone want to tell me why i'm a horrible terrible person for not buying 24?



As far as I can figure, to the average hobbyist who is not at all interested in breeding or sex ratios, it doesn't really matter if the fish are in a school of 6 or not. It matters that they aren't singular, or paired, but above that, I am having difficulty seeing the difference between 5 and 9 and 12. Obviously more is better for communal fish, but as a minimum, 6 seems kinda strange. Optimumof 6 or above might be a better way of presenting it. Perhaps?

It does seem that with each additional fish you change the behaviour of the group, but as very few of us would know the differences between 6 and 24, or 24 and 100, it seems a bit presumptuous to say that you cannot have 4 fish be happy, but with 6 they'll be happy like they are in the wild. The behavioural difference between 3 and 6 is noticable, i'll say that, but who is to say that the behaviour difference between 6 and 24 is any less noticable? If its just as marked, or moreso, would it not translate that it would also be unfair to keep fish in schools of 6 and if you couldn't do that in the size tank that you had you should buy one large enough to hold 24 cories or not have them at all?


Really, as much as I can see great benefits to having more fish for species that naturally school, I also can see that in home aquaria we are never ever going to get remotely close to 'natural' either in environment or school size, and I don't see why such a kerfuffle is made out of having to have a minimum of 6 when 3+ will suffice. I guess 'suffice' sounds harsh, but I mean a 20 gal will suffice whereas a 6x2x2 is optimum. Its all a matter of perspective I guess.


The purpose of this thread was an attempt to a) find out where the number 6 came from and b) get people to question themselves as to why they respond the way that they do to group stocking questions. I get concerned that sometimes a whole lot of authorititive parrotting goes on without any real substance to back it up. If you have anectodotal evidence, GREAT! that really is what forums are all about Explain to the person why higher numbers are better You don't need X papers by Dr Bigwig phD, thats whats so awesome about forums, you just need to tell people your experience. It is kinda nice to have reasons for your answers though helps with the whole believability factor

Fishkeeping is as much an art as a science, and sometimes you can be flexible on things in order to make a tank work efficiently. Having a cookie-cutter response puzzles me, as so many people were say it regardless of what other fish were planned/owned or the type or size of the tank. Some weren't even asking about tank parameters/decor/filtration *eek*


What is the worst case scenario of giving the absolute minimum number of cories at 3 assuming the tank falls into the well planted suitable tankmate category? Guy goes and buys only 3 fish and doesn't see the same behaviour as he would if he bought 6. Is that so bad?



Last edited by Callatya at 19-Jan-2006 13:08

For animals, the entire universe has been neatly divided into things to (a) mate with, (b) eat, (c) run away from, and (d) rocks. - Terry Pratchett

First, addressing the original question. The magic number 6 was arrived at as being a 'perceived minimum' from the standpoint of the welfare of shoaling fishes. Don't forget fishkeeping has been an actively pursued hobby for a long time - there is even a book by an author called Warrington who penned a tome in the 1880s entitled The Balanced Aquarium, which though naive by today's standards, was the first attempt to approach the aquarium as an ecosystem. in all that time, the number 6 has probably been arrived at first by trial and error, and later subject to the kind of analyses seen above. Plus, from the standpoint of a breeder faced with the task of obtaining at least one breeding pair from a group of fishes with no obvious external gender differentiation, 6 is a number that both provides an excellent chance of obtaining a male/female pair, and is manageable in the case of larger fishes - it's easier to find replacement homes, for example, for 4 surplus Oscars than for 20!

Seecond, Callatya. If you are subject to various practical constraints that force you to build up shoals piecemeal, then I have no objections to you doing so. If you intend to obtain, say, 6 Corys of a given species, but that species is expensive (or you're left with just 3 individuals at the dealer's because everyone else has snapped them up before you) then I'm not going to jump on you for getting 3 to start with. Of course, I'll advise you to get as many as you can to make the Corys happy, based upon my own experience with my Pandas. In the case of my Pandas, because they are more avowedly social than many other Corys, I've found that the 'magic number' whereupon they transform into bouncing happy hyperactive little hamsters with fins frolicking about the aquarium, is actually 8, not 6. Now that I have 11 in the Panda Fun Palace™, they're very content!

I hope this settles a few things for you!


Panda Catfish fan and keeper/breeder since Christmas 2002

Obviously more is better for communal fish, but as a minimum, 6 seems kinda strange. Optimumof 6 or above might be a better way of presenting it. Perhaps?

Exactly, and this makes it look like 6 are a "nice thing" while in reality they are very important. If you tell everyone that 6 is minimum, they will be more inclined to get 6 than if you said optimum.