Amanina , your question is vey good and deserves scientific explanation . Photosynthetic  carbon assimilation and transpirational loss of water play an important role in crop yield, irrespective of species. Water availability and stomatal structural limitations  upon photosynthesis needs to be looked into. According very good publication of Broectx et al 2013 (Tree Physiology , 34(7) : 701-715) , there is a trade off between WUE and Photosynthesis N-use -efficiency. I am furnishing some other links also to look into . These are : https://books.google.co.in/books?isbn=140514999X /https://books.google.co.in/books/isbn=3642676375. Hope , they will be useful to you.

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Amanina,

This is a very good question. I think Anoop has mentioned a very interesting reference. Also just have a look on the recent review by  Oula, 2016, J Exp Bot (attached)   If you think about leaf based  intrinsic TE (transpiration efficiency, according to Passiora  increased A or decreased gs can improve iTE. Also if you look at internal and ambient C balance (1- ci/ca), reduced Ci will lead to high TE. WUE is a collective response of the leaf canopy to available soil water.  If you increase Photosynthesis by reducing gs eventually you are saving water but increasing C fixation and biomass accumulation.  That way you could expect +ve correlation between A and WUE. But this process is very complex and A and gs also show a curvilinear relationship; slopes due to stomata limitation and the limitation in carboxylation reactions.  There are many papers reporting contradictory evidence on TE and WUE relationship for many crops. However please read some good papers and arrange your experiments to test your hypothesis

Ghannoum O. 2009. C-4 photosynthesis and water stress. Annals of Botany 103, 635-644.

Gilbert ME, Zwieniecki MA, Holbrook NM. 2011. Independent variation in photosynthetic capacity and stomatal conductance leads to differences in intrinsic water use efficiency in 11 soybean genotypes before and during mild drought. J Exp Bot 62, 2875-2887.

Amanina,

Positive correlation between Photosynthesis and WUE(i)? Yes and No.

Basically AN/gs (Net assimilation / srtomatal conductance) simply indicates the amount of carbon fixed / stomatal conductance if it is  derived from stable  carbon isotopes. Or Carbon fixed / unit water lost if derived from gas exchange measurements. Nevertheless you can find the following: a) increase in WUE with an increasing A while gs remains constant or increases moderately. b) an increase in WUE if A remains constant but gs decreases c) decreasing AN and gs decreases significantly. The latter usually occurs under drought situations. An incerease in WUE does not necessarily mean an increase in AN or increase in Biomassproduction. E.g. Tree rings often show a decrease while WUE increases (mostly found under increasing or chronic drought). You can find further details under

Saurer, M., R. T. W. Siegwolf, and F. Schweingruber, 2004: Carbon isotope discrimination indicates improving water-use efficiency of trees in northern Eurasia over the last 100 years. Global Change Biology, 10, 2109-2120.

Interesting Jayampathi , what is your opinion , what kind of relationship would you expect when you compare such relation in a situation of high density versus normal density crop raising ?

Here we are discussing only gas exchange parameters,  the other part is photosystem I and II where the light is important to drive the chemical reactions. The quantity and  quality for light is important for chemical reactions. I think plant density make more differences in light interception by the canopy. Shading reduces both An and gs and one reason may be photo-inhibition  and feed back. This is again vary with crops and many other crop factors such as canopy architecture, leaf orientation, light duration etc.