This week the professor handed us a review article from the Royal Society about using insects as models for determining the cost-benefit relationship involved in learning and memory. As it explains, there is much evidence supporting a link between hippocampus size and learning in larger, more complex animals. But causation is not clear, and determining the size and neural density of such large brains is very difficult, because they are so large. The mushroom body, a higher processing center in insect brains, only tends to have a few hundred thousand neurons. Research into the costs of learning has expanded in the past decade with a lot of help from insects.
The brain is an expensive organ, taking up a lot of energy. One cost mentioned is the energy cost of maintaining resting potential. So, if learning is correlated to brain size and neural density, it is not necessarily adaptive. However, some insects perform surprisingly complex cognitive tasks. This may mean that more connections between neurons is better and more efficient than using more neurons. There is also evidence that higher order processing units may have at least as good an effect as upping the size of an entire brain. If we can learn the energy costs and performance of different units of nervous systems, we can understand how their relationship effected their evolution.
There is also an analysis of two basic types of costs of learning. Constitutive costs are costs that an animal pays whether or not it uses the memory. This can be a structure in the brain or even simply a lengthened axon resulting from a learning experience. There are also induced costs of learning. which are paid during the act of learning. There is a lot of evidence backing up the induced costs of learning, which may mean behavioral costs or the costs of processing information in the brain. Some studies on Drosophila have suggested that only crucial, repeated information makes it into the more costly type of memory storage. As well as encoding memory, deleting memory may be very expensive.
These studies have show gaps in that performance in a particular task does not necessarily translate into fitness. There is still a lot more to explore in this field.
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Neuro-Tick 
Interesting. You state “the brain is an expensive organ”. Expensive to build or expensive to maintain? In metabolic terms it might be useful to compare to the expense of a liver, the expense of active muscle or the expense osmoregulation. Isn’t the brain rather good value for money? Good luck with your course.
In answer to the question, yes. It is expensive both to build and to maintain. The costs are development time and energy. Thanks for the well-wishing.