## 2 Related Work  
Ref. [7] performed a comparative study between two different aquaponics systems using the Life Cycle Assessment. The authors grew Lettuce and Rainbow trout in a raft aquaponics and media-filled system. They found that floating systems are less effective than those with cultivation in gravel. Ref. [8] studied the growth promoting effect of earthworms on tomato plants. The authors tried different concentrations of vermiwash and discovered that the vermiwash treatment outperformed the normal fish water treatment. A project was conducted by the authors of [9] on the effect of vermiwash as a vermiponics medium on the growth of biochemical indices of Amaranthus. They compared different percentages of vermicompost and identified that 100% of vermiponics performed best with statistically significant improvements at \(\alpha=0.05\). Ref. [10] determined an optimal freshwater replenishment rate of 19% on a 100-liter aquaponics system and found that a regular water replenishment system helps to maintain fish--that water quality. Aquaponics fish and plant production performance were analyzed when the authors of [11] studied the optimal hydraulic loading rate on plant ratios. The authors of [12] conducted an evaluation of the growth of the different plants added to small-scale aquaponics systems to obtain adequate concentrations. They used basal, chard and chive plants with different concentrations of vermicompost added to each plant. Ref. [13] performed a hematobio-chemical response and intestinal histomorphology of Nile-tilapia with earthworm meal and concluded that elevating the diversity of protein sources is imperative for fish growth improvement. Earthworms with a favourable content of amino acids are natural food for numerous species of fish, especially bentophagous fish such as Cyprinids. They have a beneficial effect on the fish, leading to fish immunity [14; 15]. Ref. [4] suggested that aquaponics productivity could be enhanced using earthworms and vermicompost from vegetable waste. The authors proposed that the earthworms can be cultivated from vegetable waste. A study [16] outlined that the use of vermiliquers from earthworms in aquaponics leafy vegetable production improves nutrient uptake and supports immunity, thereby boosting growth.  
Regular water replenishment may help in improving the efficiency of aquaponics productivity [10; 17] than conventional aquaponics without water replenishment. Although studies have been performed on conventional aquaponics and vermiponics systems separately, to the best of our knowledge, there is no study comparing aquaponics and vermiponics with and without water replenishment. The present study attempts to cover this research gap by performing a comparative study of standard aquaponics and vermiponics performance and the effect of earthworms in vermiponics productivity. The major contributions of this research are as follows: a unique dataset of a comparison of standard aquaponics and vermiponics systems along with novel algorithms and mathematical formulae; an analysis regarding the impact of water replenishment on yield productivity with gold carp fish and Swiss chard plants; and an attribute-wise productivity evaluation of both systems.