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Different things may determine the population sizes within an ecosystem.
Non-living factors such as light intensity, temperature and humidity determine the number of organisms that a habitat can sustain. All species have a varying degree of ability to withstand harsh or fluctuating conditions, called resilience. If an abiotic factor changes dramatically in favour of a population – for example, plenty more light in a field – then the population will increase provided no other factors are limiting. The opposite is true if an abiotic factor changes against the resilience limit of a population – it will decrease.
“Living factors” refer to all interactions between organisms, be it a bunny rabbit being predated, or two shrubs competing for sunlight. All individual actions between organisms form a web which impacts on all populations in an ecosystem, therefore determining their sizes.
Interspecific competition refers to competition between members of different species for the same resources (food, light, water. etc.). Often when a new species is introduced in a habitat, say the American ladybird to the UK, if the invader species is better adapted, then the host population decreases in size. This may lead to extinction in some cases of the host species.
[Can’t remember the difference between interspecific and intraspecific? Interspecific is like the internet – different things come together.]
Intraspecific competition refers to competition between members of the same species. If a population of apple trees all compete for a source of light, then each apple tree is taking up some light that has now become unavailable to a different apple tree. There are only so many apple trees which that habitat can sustain. The maximum population size sustainable indefinitely in a habitat is called the carrying capacity.
Suppose you start off with equal populations of wolves and rabbits, and all the wolves rely on the rabbits for food. As the wolves start predating the rabbits, the rabbit population will decrease, while the wolf population will be sustained. Now there are fewer rabbits, so some wolves won’t have any food left. These wolves will die, so the wolf population will decrease. What will happen to the rabbit population now? Well, there are fewer wolves so they are predated less. The rabbit population will increase, followed by an increase in the wolf population, and so on.
The predator-prey relationship is very intricate, so the two affect each other and hence their population sizes rise and fall accordingly.