I want to know how to calculate the total aphid population in a plant or an ecosystem, where they occur in large numbers. Is there any formula to calculate total population or any work on this will help me for further research?
In Hungary the so called Banks scale is used. Unfortunately, I do not know by heart its units. Generally the visual counting was found to be the most accurate method, like 1 mm long infested twig = 10 aphids: http://www.eje.cz/pdfarticles/1083/
However, it is an assessment method for all aphid forms, to calculate only the winged ones is more difficult.
I do not think there is any reliable way of estimating, or calculating the total number of aphids if you (only) know the number (or density) of alates, because the proportion of alates is a) dependent on so many factors (such as plant species, aphid species, crowding, time of the year, plant physiology, natural enemies) and b) can fluctuate very strongly within a short period of time. E.g. imagine that the proportion of alates in a colony of a host alternating species in spring time increases in response to crowding and rising temperatures, but weather is just not good enough for them to fly off to find their summer hosts; then, as the weather turns, they will all leave the colony, so the proportion of alates drops dramatically, and depending on your sampling time you may completely over- or underestimate the total population, Also, you'd need to know the number (or density) of alatoid nymphs to be able to gauge the developmental stage. So I guess that there is no way round counting all morphs of the aphids.
In any case I think it would be good to do some preliminary sampling and analyse the spatial heterogeneity of the population and the variance, so that you can determine how many samples you need to achieve a given accuracy.
One piece of advice I got from one of the most experienced aphid researchers, Helmut van Emden, is to pool the efforts in time: Instead of weekly counts in your plants, with very low accuracy for each sampling time, you collect all your friends, colleagues, etc. and go out on one date to do a very intensive count - it will take a long time, but you can trust your numbers. Obviously it will then be crucial to get the timing right, because aphid populations fluctuate so enormously. Which means that you have to observe your plants or ecosystems regularly and you have to be quite clear about what question you want to know. Also it helps if you know from previous years when the population will peak in the year. In many cases it will make sense to plan the main sampling at the time just before the expected population peak.
You have illustrated actually almost all the difficulties of aphid population estimation. I would like to add to these that even the aphid species in question can influence the sampling.
There are absolute and relative assessment methods for a population estimate. The implementation of the absolute methodology is practically impossible, thus mainly the relative methods have been used.
Until now, I have estimated aphid population density for assessing the efficiency of some insecticides and for calculating correlation between natural enemies and their aphid prey. In the first case I have counted the number of aphids on several parts of the same length of shoots covered with aphids. I calculated the average with the fiducial limits and this value was applied for the measured shoot length. In most cases the efficiency of a pesticide could have been assessed. I used this method for Aphis spiraephaga, Aphis sambuci, Hyalopterus pruni, Hyalopterus amygdali (in case of Hyalopterus species the number of aphids on the leaves’ surface was estimated) and Aphis craccivora. Calculation the correlation between predator and aphid populations is more difficult. The collector places a flat container under the crop and with beating the plant the dropping predator and prey individuals are gathered. The harvested insects can be frozen and later they can be counted or measured (considering number of individuals or biomass). However, there are aphids which attach to the plant surface and this method does not work. Of course, the repetitions and subsequent calculations are important.
These are very old fashioned methods. It is possible to take digital photos from the plant parts covered by aphids and with the help of commercial computer programmes the aphid density can be assessed on the taken photo. These programmes calculate automatically also the statistics necessary.
For the measure of a surface the following method is suitable. However, this is a very simple and cheap technique and a lot of additional work is needed.
Jarou, Z. (2009): Measuring leaf area with Adobe Photoshop CS3.
Regarding the mentioned van Emden technique, how it is possible to follow the temporal change in the population density which is in permanent fluctuation as you wrote? Should be repeated the help of friends again and again? However, the aim of the investigation may determine it.