A normal distribution is a very important statistical data distribution pattern occurring in many natural phenomena, such as the height or longevity of a member of a population, e.g., human beings. For this discussion we are focused on the life cycle of Cryptocaryon irritans, otherwise known as marine ich. Certain data, when graphed as a histogram (data on the horizontal axis, amount of data on the vertical axis), create a bell-shaped curve known as a normal curve, or normal distribution.
Normal distributions are symmetrical with a single central peak at the mean (average) of the data. The shape of the curve is described as bell-shaped with the graph falling off evenly on either side of the mean. Fifty percent of the distribution lies to the left of the mean and fifty percent lies to the right of the mean. The average life cycle of Cryptocaryon irritans is 3 weeks.
The spread of a normal distribution is controlled by the standard deviation. The smaller the standard deviation the more concentrated the data. Unfortunately, there is no published value for the standard deviation of the life cycle of Cryptocaryon irritans.
Now let's look at the percentages of population members of the normal distribution with a mean μ and a standard deviation σ. We are interested only in populations that exceed the given lifespan, so we see that
• 84.1% of the distribution lies to the right of μ + σ
• 97.7% lies to the right of μ + 2σ
• 99.8% lies to the right of μ + 3σ
Assuming a one-week standard deviation, leaving a tank fallow for 4 weeks will give you an 84.1% chance that you have eradicated the parasite, leaving a tank fallow for 5 weeks will give you a 97.7% chance of eradication, but if you want a 99.8% chance, you must leave the tank fallow for 6 weeks. That is the reason you see different numbers being used on Reef Central and in the literature.
For those that are analyzing this post on the subject, I must admit to simplifying in the interest of understandability. For any given salinity, temperature, light cycle, and most importantly, strain of Cryptocaryon irritans, the life cycle distribution is much more likely to be Poisson rather than normal. But for the population (collection) of those distributions, as with most biological processes, the overall statistical description is likely to be normal.
For those who are uncomfortable with the original analysis, simply assume the longest reported period, which is 72 days. That is probably going to be ok the vast majority of the time. That, too, is a simplification as it is only for one strain of Cryptocaryon irritans in one set of circumstances.
Normal distributions are symmetrical with a single central peak at the mean (average) of the data. The shape of the curve is described as bell-shaped with the graph falling off evenly on either side of the mean. Fifty percent of the distribution lies to the left of the mean and fifty percent lies to the right of the mean. The average life cycle of Cryptocaryon irritans is 3 weeks.
The spread of a normal distribution is controlled by the standard deviation. The smaller the standard deviation the more concentrated the data. Unfortunately, there is no published value for the standard deviation of the life cycle of Cryptocaryon irritans.
Now let's look at the percentages of population members of the normal distribution with a mean μ and a standard deviation σ. We are interested only in populations that exceed the given lifespan, so we see that
• 84.1% of the distribution lies to the right of μ + σ
• 97.7% lies to the right of μ + 2σ
• 99.8% lies to the right of μ + 3σ
Assuming a one-week standard deviation, leaving a tank fallow for 4 weeks will give you an 84.1% chance that you have eradicated the parasite, leaving a tank fallow for 5 weeks will give you a 97.7% chance of eradication, but if you want a 99.8% chance, you must leave the tank fallow for 6 weeks. That is the reason you see different numbers being used on Reef Central and in the literature.
For those that are analyzing this post on the subject, I must admit to simplifying in the interest of understandability. For any given salinity, temperature, light cycle, and most importantly, strain of Cryptocaryon irritans, the life cycle distribution is much more likely to be Poisson rather than normal. But for the population (collection) of those distributions, as with most biological processes, the overall statistical description is likely to be normal.
For those who are uncomfortable with the original analysis, simply assume the longest reported period, which is 72 days. That is probably going to be ok the vast majority of the time. That, too, is a simplification as it is only for one strain of Cryptocaryon irritans in one set of circumstances.
