well actually Crackerbee this little chart is the whole ball of wax rolled up into one little graph <lots of good stuff here. I also want to reference folks to Randy Oliver article in the Sept 2011 ABJ 'Varroa Management-Getting Down to the Brass Tacks'... which is essentially the same kinds of graphs with varroa population included. Mr Oliver's graphs are generated from simulation model based on altering certain assumption. <lots of good stuff here also so everyone should try to give this article a read.
I tossed this hive population curve in here first to illustrate the ideas of rate of growth* which we had loosely discussed in a prior thread and which at the time I didn't know how to illustrate.
*Mr Oliver calls these 'r's in his article and as he suggest the r's (bees and varroa) is where it at when it comes to controlling or understanding how to control varroa...
My attached graph:
The black line (total population) between January and May is a classic growth curve (sometimes call a sigmoid growth curve) and fairly represents population growth for a lot of biological organisms. If you draw a tangent line (straight line intersecting the curve) to the curve starting in January the tangent line is below the curve up till about Feb 15 and that the angle of the tangent line at any point along this part of the curve is increasing steadily (angle of the tangent line is getting steeper). So for the illustrate graph the rate of population growth is increasing at an increasing rate. Essentially the small beginning population is being 'added to' with progressively larger chunks.
then about Feb 15 the tangent line to the curve is above the curve and the angle of the tangent line is decreasing steadily till total population reaches a maximum on about May 1 to 15. this part of the graph represents where population growth is increasing at a steadily decreasing rate. The chunks are still being added to total population but the chunks are getting progressively smaller. We tag this part of the graph as increasing at a decreasing rate.
At or beyond about May 1 to the 15 total population reaches it peak... beyond this point the rate of growth is simply termed decreasing.
Mr Oliver's graphs are a bit more stretched that the one I presented above... which really only means the one above is for Southern Arkansas and Mr Olivers is for somewhere in California. I do suggest everyone who can read Mr Oliver's article... Mr Oliver has also included 'computer generate' results of various bee keeper manipulations and interventions.
likely somewhat clearer than mud... but none the less everyone than can should get their hands on Mr Oliver's little article.
Thank you Tec.for taking the time to explain that in further detail.Not many folks on forums will take the extra time the way you did to explain a subject in easy to understand detail.I fully understand now the point you've made.Your post has given me an epiphany toward understanding another level of knowledge needed to achieve better beekeeping practices,and I thank you for that.
I read that same post months ago but it's content really didn't register until I read it(with your added explanation)the second time.
Definitely food for thought and thanks again for taking the time to post it.
glad it was one shade cleared than mud. do try to get your hands on Mr Oliver's article and I think perhaps the application of this simple idea will become somewhat clearer than mud. Mr Oliver operated some virtual space that is ScientificBeeKeeping.com. I have not looked there to see if the referenced article is there, but I assume it should be at some point in time.