It depends on their habitat. You can measure the specific growth rate, relative growth rate which I think are the most important growth parameters. If you want to growth promoting parameters, you can investigate water temperature, pH, secchi depth and dissolved oxygen. You may also measure the dissolve suspended solid (DSS) and suspended solid.(SS) if you have facility. These would be from your surrounding water where fish lives. 

First of all, I think it is most important how your estimation values of the natural mortality and growth rate are accurate. Very frequently, we mistakenly estimate K and M values. It needs to reinvestigate your estimation values again.

2.6 is very high and I would be very skeptical of whichever source you drew that from. The "standard" value for teleosts is 1.5. (Try a Google search for "Beverton-Holt life history invariants". There is a substantial modern literature.) Many species have other values of M/K but it should be possible to suggest reasons (such as protogynous hermaphroditism) for why a particular species differs. Estimating K is possible (though it is often very hard to get a precise value) but estimating M is rarely practical, so empirical confirmation of M/K is not often an available option.

dear Dr Kenchington & Dr Kim

yes the value of M/K 2.6 is very high for teleosts.

however I come across a study conducted by  Etim et al. (1996) on another species of mudskipper (Periophthalmus barbarus) in Cross River Nigeria.They reported that the K =  0.51 and M = 1.341. thus M/K values = 2.63

A similar study on the same species (P.barbarus) by Chukwu & Deekae (2010) in New Calabar River, where they reported the K=  0.65, M = 1.68, M/K = 2.58. Can this be considered as  a normal m/k value for the mudskipper species?

It may be best to return to basic principles: M is a measure of how fast fish die (in a "natural" or unexploited condition). If M is high, most fish die young. K is a measure of how fast fish grow towards their asymptotic size. If K is low, they have several or many years during which they put much of their energy into somatic growth. If M/K is high, then M is high relative to K and most individuals die at ages when their species is still growing actively (besides the eggs, larvae and younger juveniles, most of which die at much younger ages). Since the population must include spawners, most of the spawning must be done by fish that devote their energy to growth rather than production of eggs and milt. That seems inefficient and typical teleosts do not do it. They have M/K≈1.5. Mudskippers are very atypical and there may be something about their life history that makes M/K>2.5 optimal. I would not rule that out but I would not place much confidence in it unless there was either (a) a plausible explanation of why it is advantageous for mudskippers to go on growing quickly after reaching sexual maturity or (b) solid empirical evidence that they do that.

I have found a copy of Chukwu & Deekae (2010). I cannot find Etim et al. (1996) but the same authors have a 2002 paper in Fisheries Research which looks to be a final report on similar (or perhaps the same) work. I only have access to the abstract of that. It seems that both studies estimated K (and the other parameters of the von Bertalanffy function) using length data. That raises a problem. Given some length-at-age data, it is usually easy to estimate K/L[inf] with reasonable accuracy. It is much harder to estimate either parameter individually. K is a measure of how quickly the fish approach L[inf] and data on mid-sized fish cannot distinguish a slow approach to high L[inf] from a swift approach to low L[inf]. Estimating either parameter really needs data from fish of similar sizes but different (high) ages, which can support estimates of L[inf]. But if the sizes of different age-classes are similar, then those classes cannot be distinguished in a length-based analysis. (That would need otolith ages or something similar.) For many purposes, knowledge of K/L[inf] is enough and you do not need an accurate estimate of other parameter alone. To estimate M/K, however, you obviously need to know what K is and that's hard to get from length data alone. The two studies provide some indication and I would not dismiss either of their estimates of K but neither would I place great reliance on them.

Estimating K with useful accuracy is challenging but accurately estimating M is very much more difficult. Chukwu & Deekae (2010) used Pauly's method, which was probably the best approach that they could have chosen, though still highly uncertain. (See my 2014 review of M-estimation methods for data-poor fisheries in Fish & Fisheries 15:533-562.) However, Pauly's method estimates M from K and, at its best, cannot be any more accurate than the estimate of K. Much more seriously for present purposes, it means that Chukwu & Deekae's estimate of M/K does not come from empirical data but only from the structure of Pauly's estimator. That generates an estimate of M≈(K)^0.68, with some modification based on L[inf] and environmental temperature. For long-lived cold-water fish, which were the source of most of Pauly's data, (K)^0.68 is very roughly equal to 1.5K and so yields the expected M/K≈1.5. Chukwu & Deekae's M=1.68 came from applying the estimator to a very different fish. I would not say that that estimate was wrong but I would not place much trust in it. [Etim's paper probably explained how he estimated M but his abstract only gives the estimate: 1.35.]

Combining those various thoughts: Mudskipper is a very unusual teleost and may have a very unusual life history. Therefore, I would not say that M/K>2.5 is impossible but, without an explanation of why such a high value is optimal for mudskipper, I would not simply accept that value without strong empirical evidence. Estimating K really needs ageing of individual old fish, which may be impossible with (heavily-exploited) mudskipper. Reliably estimating M needs a huge research effort over many years, which is not an available option. Hence, the empirical evidence is necessarily weak. In short, I think you should keep in mind two possibilities, both M/K>2.5 and M/K≈1.5. Then you should shape your research so that you get results that would be correct for either value of M/K.