Kinetic parameters affecting effluent water quality including half saturation constant (K-s), maximum specific growth rate (mu(max)), and specific affinity (a(A)(0), defined as mu(max)/K-s) were investigated using three types of anaerobic sludge (raw anaerobic digestion sludge referred to as unacclimated sludge, unacclimated sludge after endogenous decay, and sludge acclimated to low-strength wastewater in an anaerobic membrane bioreactor (AnMBR) for 360 days). Long-term acclimation to low-strength wastewater resulted in sludge with high specific affinity (1.6 x 10(-3) L/mg COD/day for acclimated sludge compared to 4.1 x 10(-4) L/mg COD/day for unacclimated sludge). The mu(max) values for unacclimated sludge and acclimated sludge were 0.08 and 0.07 day(-1), respectively. The K-s values for unacclimated sludge and acclimated sludge were 194 +/- 81 mg COD/L and 45 +/- 13 mg COD/L, respectively. Although the K-s of unacclimated sludge after endogenous decay increased to 772 +/- 74mg COD/L, mu(max) increased to 0.35 day(-1) as well, resulting in no statistically significant difference of a(A)(0) between the two types of unacclimated sludge. Overall, a(A)(0) is a better indicator than mu max or K-s alone for determining effluent water quality, as effluent substrate concentration is approximately inversely proportional to the specific affinity. 16S rRNA sequencing data analysis indicated a high abundance (85.8% of total archaea) of Methanosaeta in the microbial community after long-term acclimation. High a(A)(0) associated with the enrichment of Methanosaeta appears to ensure successful anaerobic treatment of low-strength wastewater.