Efficiency and Lethality: Survey Data Trends


The Aquarists' Data



Unfortunately, not much data has been gathered from typical home aquarists about their own aquarium systems. As such, the data that most aquarists rely on is oftentimes data that is derived from people unlike themselves. That is, scientists and the aquacultural industry have been dictating the why and how-to part of aquarium husbandry for many decades and the everyday aquarist has largely had to rely solely on such sources for the type of knowledge that is not often questioned. This is not to say that such sources are incorrect, but that they, by being the chief authority on the subject, relegate aquarist-derived knowledge to the realms of personal experience and opinion. Contrarily, this study seeks to support individual aquarist experiences by revealing certain statistical trends that can be verified by a large sample of self-reporting aquarists. This study is not designed to challenge long-held beliefs or reveal mysteries. Instead, this study simply summarizes and reports what many aquarists describe as their typical aquarium operation.
Additionally, this survey was conducted using certain calculations that, until now, were not verified as being reasonable facsimiles of the quantity they try to approximate except by limited observations. This being the case, this survey also adds validity to these particular calculations when they display the appropriate trend, but debunk certain measures when they fail to match the trends they attempt to replicate. In particular, the calculations that are at-issue in this study include the following:
  • IFUs MOD dtm / median (IFUMD): This is a more advanced version of the IFU base measurement and has already been implemented in some of the Fishsheet aquarium stocking spreadsheets. The idea behind this calculation is to not only approximate the biomass represented by the fish in the aquarium, but also account for the effect of varying feeding schedules upon that biomass. In theory, more food per unit of biomass should have a greater biological effect than less food per unit of biomass. At this stage, IFUMD is a relatively simple calculation that takes the number of IFUs per gallon and multiplies that quantity by the number of days per week that the fish receive food, the number of times per day the fish receive food on those days, and the number of minutes each feeding lasts divided by the median product of days, times, and minutes. Before this study was conducted, it was assumed that the dividing product should be 48 (6 days by 2 feedings by 4 minutes per feeding). For IFUMD to be a valid measure of the effect of feeding schedule upon biomass, it must, at minimum, trend in proportion to total nitrogen-compound production and, preferably, to daily nitrogen-compound production.
  • Gross Nitrogen Index (GNI): This calculation was proposed when the study was being conducted as a method of assessing how efficiently a given aquarium system processes its biological wastes, particularly nitrogen compounds (initial efficiency discussion). This method discounts nitrogen contamination via tainted tap water but does not discount nitrogen sources inherent to the aquarium system as a whole. In other words, if nitrogen is purposely added to the aquarium then it is assumed to be a valid part of the nitrogen contamination which the aquarium, in some way, must process. The GNI is calculated as the sum of the daily production rates of the three principal nitrogenous compounds: nitrate, nitrite, and ammonia. This daily production rate, in turn, is calculated as the average daily rates of differing measurement techniques (before water changes versus after water changes) (formula created via Maple12(TM)): 

      • r is the daily production rate of the substance being measured,
      • P is the decimal equivalent of the percentage of water removed per water change,
      • D is the number of days between water changes,
      • k is the average level of the substance normally found in the aquarium under normal operating conditions, and
      • A is the level of the substance found in the water that is used to replace the aquarium water.
Since the amount of nitrogen in each of the principal compounds is identical (one atom per ion), the GNI can be viewed as a simple sum of the total easily measured nitrogen that the aquarium system produces each day. Consequently, the ratio between biomass effect (IFUMD) and the GNI represents the efficiency with which the aquarium system absorbs, rather than transmits, biological wastes. For GNI to be a valid calculation that properly assesses the efficiency of a system, it would stand to reason that GNI efficiency would trend with very efficient filtration systems and items that absorb nitrogen compounds, like plants.

  • Lethal Nitrogen Index (LNI): This calculation is probably the least controversial measure and is a weighted sum of the principal three nitrogen compounds (nitrate, nitrite, and ammonia) as they present a threat to the aquarium fish. Nitrite and ammonia are often considered to have similar lethalities with regard to freshwater fish (Ines Schuermann) and thus can be similarly weighted. Further, nitrate and nitrite have a roughly 40-fold difference in lethality when combined with the same cation in solution (nitrate LD50, nitrite LD50) and it was decided for purposes of this study that nitrite and ammonia should be weighted at 40 times the significance of nitrate. This calculation is self-validating to the point that it identifies which aquariums are safest with regard to nitrogen compound content.
  • Remaining Waste Index (RWI): The remaining waste index, as per this study, is a calculation that compares the relative effects of frequency and percentage removed with regard to water changes. Ostensibly, aquarium systems with similar RWIs have similar cleanliness levels. Particularly, a high RWI represents high levels of waste remaining in the aquarium while a low RWI represents low levels of remaining waste. However, the RWI calculation does not account for the effect of stocking density, just percentage removed and frequency, and is thus not very useful for comparing aquarium systems that are dynamically different. Nonetheless, the overall trend should be that aquariums that are safer for the fish should have low RWIs. The formula used to calculate the RWI of a particular system is the days between water changes divided by the decimal equivalent of the percentage removed per water change. In other places, the RWI has been referred to as the RWI factor. Also, many of the Fishsheets do not use RWI in the way this study does, they interchange RWI with the RW (discussed hereafter).
  • Remaining Waste (RW): The remaining waste is similar to the RWI except that it accounts for the effect of stocking density by multiplying the RWI by the IFUMD, ceasing to be an index and becoming a more complete approximation of how much waste is actually in the aquarium. In order for RW to be a reasonable calculation, it must trend along with the lethality of the germane aquarium systems.
This study was conducted via an online survey that requests basic aquarium information from willing aquarists. All data presented in this study is self-reported and thus is not suitable for determining correlation, just trends. Also, the biomass calculation used in the study relies on there being a suitable relationship between a biomass estimation based on the average length and number of fish being kept and the actual biomasses of the individual fish being kept. To determine if there does exist such a relationship, a program was created via PASCAL that creates random aquarium scenarios with fish numbers ranging between limits set by the user and is so arranged that the average number of fish in each tank, if the sample is large enough, approximates an average level set by the user (IFUER2[MOA]). This program assigns an actual biomass calculation to each fish in every simulated aquarium and compares the overall biomass calculation of every aquarium to the approximated biomass calculation based on SAVI theory. This program then determines the average error in calculation so that the approximation can be made more accurate.
As it turns out, the fish number limits for the study were 1 and 130 (meaning that the lowest number of fish in the data sample was 1 fish per tank and the highest was 130 fish per tank; see data spreadsheet attachment). Additionally, the average, whole number of fish per aquarium in the data sample was 19 (19 fish per aquarium on average). When these parameters were entered into the PASCAL program and scenarios were run for 100,000 aquarium stocking configurations, the average error was determined to be 19.1 percent. When this adjustment was made to the biomass approximation, the error boundary configuration was as follows:
  •   0-10% Error: 50.056% of the Sample
  • 10-20% Error: 28.746% of the Sample
  • 20-30% Error: 11.962% of the Sample
  • 30-40% Error:   4.830% of the Sample
  • 40-50% Error:   1.918% of the Sample
  • 50-60% Error:   0.969% of the Sample
  • 60-70% Error:   0.531% of the Sample
  •    70+% Error:    0.988% of the Sample
As the above configuration shows, the biomass approximation used by this study is within 20 percent of the true biomass about 80 percent of the time when the 19.1 percent adjustment is used. This relative consistency demonstrates that the study can be conducted using the biomass approximation provided that the data is considered en mass. Consequently, the study does not address specific aquarium configurations but rather examines the data by pentatiles (one-fifth of the entire data sample). Using pentatiles (as opposed to quartiles) assures that every variable considered will have a perfect median value. In general, median values were used in this study due to the median's insusceptibility to extreme data points whereas the average can change drastically if one data point is extremely high or low.
Lastly, much of the data from the survey has been summarized on a separate page containing all the major data graphs and some data entries were omitted. The summarizing page can be opened here. The figures can be enlarged by clicking on them. As to the omitted data entries, they were stricken for one of the following reasons:
  • Not pertaining to freshwater environments
  • Users did not follow entry directions and thus constituted unreliable sources
  • Multiple tanks were entered on a single form
  • Nitrogen compound data was missing
  • Data entries made no sense (i.e., fluorescent lighting with no wattage, etc)


One of the principal goals of this study when it was begun was to see what factors affect the efficiency of the system with regard to nitrogen compound absorption/production. When the data is arranged in ascending order with regard to transfer percentage (the percentage of the IFUMD that is transferred to the GNI), certain trends can be observed (Efficiency sheet of spreadsheet; Figure 11 and Figures 1 through 5). Generally, these trends can be separated into one of two basic categories: 1) unsurprising results and 2) surprising results. The unsurprising results help to validate the GNI method of nitrogen compound assessment, but the other results raise some interesting for aquarists to ponder.
With regard to the unsurprising results, one of the first trends that was noticed is that canister-type filtration systems coincide very nicely with good transfer numbers (Figures 1 through 5). For example, there was an approximately 35 percent difference in canister filter use between the first and fifth pentatiles when the data was arranged according to efficiency. Further, the percentage of canister filters used steadily dropped with each pentatile. Given this trend, what many aquarists have known for years has been confirmed: canister filters are very efficient systems. The other unsurprising trends include the following (Figure 11):
  • Large aquariums tend to be more efficient than smaller ones.
  • Well-lit tanks (with high wattage per gallon) tended, slightly, to be more efficient than tanks with fewer watts per gallon.
  • Heavily planted or moderately planted tanks (as per the users' own appraisal) were more likely to be associated with efficiency than non-planted or sparsely planted tanks.
  • Lethality (LNI) increased as efficiency decreased.
Despite how many trends matched conventional expectations, some trends were a bit odd. Two trends, in particular, that were surprising were the relationships between snail and fertilizer presence and aquarium efficiency. In cases where the efficiency was good (the transfer was low), the presence of snails and fertilizer followed. From the outset of this study it was assumed that since the GNI did not account for nitrogen compound contamination via fertilizer that some planted tanks would not fair very well with regard to efficiency, yet it is the opposite case that actually occurred. Similarly, since snails were not included in the biomass measurements it was thought that the omission would diminish the efficiency of aquarium systems containing snails, but snails actually seem to be a moderate indicator of efficiency. As to other surprising trends, they include the following (Figure 11; Figures 1-5):
  • A large water removal percentage had a slight tendency to be associated with inefficient tank systems. This condition is odd in that water changes are often thought of as being good for most freshwater systems, or at least that is the conventional wisdom. It may also be the case, though, that large water changes, those above 30 percent in particular, remove so many nutrients at a time that the beneficial bacteria populations responsible for biologically processing nitrogenous wastes may be upset. Nonetheless, this trend does not apply to lethality and is thus of minor consequence to the average aquarist.
  • The overall markers of waste (RWI and RW) tended to be higher in more efficient aquariums. As with the water change percentage, this condition may be due to a greater consistency in nutrient levels for the beneficial bacteria, producing greater system efficiency, but this result is also a consequence of the definition of efficiency used in this study. That is, by definition, a system is more efficient if its stocking density (IFUMD) is proportionally greater than its daily production rate (GNI).
  • Lastly, HOB+ filtration systems tended to be more strongly associated with inefficient aquarium systems than with efficient aquarium systems. HOB+ filters are Hang-On-Back filters that either have a biowheel device or space for extra biological filter media. These additions to HOB+ filters supposedly make them more efficient, but this study does not support that hypothesis. It may be that HOB+ filter systems give aquarists a false sense of security in that aquarists with HOB+ systems are more likely to not maintain their system appropriately, assuming that the filter can handle the neglect. As with the water change percentage, this trend does not hold when lethality is considered.


As useful as an examination of efficiency may be, the primary concern of most aquarists is lethality, or how suitable the aquarium is for its inhabitants. As mentioned previously, the lethailities of the aquarium systems in this study were determined using the Lethal Nitrogen Index (LNI), which is a weighted sum that gives more effect to ammonia and nitrite than to nitrate. When the data set of the study is arranged so that the LNI of each aquarium system is in ascending order, almost all of the expected trends are confirmed (Lethality sheet of the spreadsheet; Figure 12 and Figures 6-10):
  • Canister filters are most strongly associated with low LNIs.
  • HOBs (those without additions) are more strongly associated with high LNIs.
  • RW tends to increase as lethality increases but RWI has no distinguishable pattern. That is, the effect of biomass (IFUMD) and cleanliness (RWI) together constitute a trend but cleanliness, by itself, does not determine how suitable the aquarium environment is.
  • Stocking density (IFUMD) increases as lethality increases.
  • Efficiency (transfer from IFUMD to GNI) tends to increase as lethality (LNI) decreases.
  • Well-lit, planted tanks have less lethaility than poorly lit or non-planted ones.
Of course, arranging the data by lethality did not produce only expected outcomes. One of the strangest trends was that tank size tended to increase as the lethality increased. This is directly contradictory to conventional wisdom and even defies the findings when the data was arranged according to efficiency. This result seems to indicate that either aquarium size is not a reliable indicator of efficiency or lethality (a false trend) or that there is some factor not addressed by this study that coincides with large tank sizes but circumvents any advantage a large tank may provide. Also, as with efficiency, snails and fertilizer tended to be indicative of less lethal systems.


This study has brought a few interesting trends to light, but, for the most part, this study illustrates what aquarists have known for decades. Consequently, the overall effect of this study is to validate some of the more obscure calculations contained herein and to present average aquarists with the median conditions of their peers. Specifically, this study confirms IFUMD as a valid calculation for measuring the effect of feeding schedule on biomass, but it was found that the old divisor was incorrect in that the median dtm (days, times, minutes) was 21, not 48 as was previously believed (cell N1 of the data spreadsheet). Furthermore, RWI was disproved as being a suitable means of determining the lethality of an aquarium system, but RW was shown to display the correct trend. 
As to information that the average aquarist can use, the overall assessment of the data reveals these median values as being the most indicative of a functional, safe aquarium system:
  • Median Tank Size: 37 Gallons (inconclusive)
  • Median Stocking Density: 13 Fish at 2 Inches Each (more being worse with regard to lethality but not necessarily efficiency)
  • Median Water Change Frequency: 7 Days (inconclusive, no trend)
  • Median Water Change Percentage: 30% (very large water changes may be detrimental to efficiency, but not lethality)
  • Median Lighting Wattage: 40 Watts (more watts being better)
  • Median Plantedness: Moderately Planted (more plants being better if appropriately cared for)
  • Average Snail Presence: 53% (snails seem to be associated with better efficiency and lower lethality)
  • Average Fertilizer Presence: 48% (fertilizers seem to function like snails)
  • Best Overall Filter Type: Canister (HOBs are the most prevalent, worst filter type with regard to lethality while HOB+ filters are the most prevalent, worst filters with regard to efficiency)
These results do not indicate that any other parameters will not work, but these results do indicate that the most common successful system is close to matching these parameters. Hopefully, more data will come to light and some of the odd results discovered by this study will be better understood in the future. Moreover, this study largely confirms the new calculations used herein and thus offers the aquarium world more means of assessing and describing various aquarium systems.
More data can be submitted here.
Questions/comments can be sent to MOA (email on home page) or can be left on his Fishsheet forum (also found on home page).

Subpages (1): Efficiency Graphs
MOA Fishkeeper,
May 25, 2010, 10:35 PM