A population cannot grow forever, and will reach some kind of growth-limit eventually. How does this occur? Why do some populations grow quickly, and others only slowly? Why do populations stop growing at different sizes? Answering questions like these will force us to think about the factors influencing birth and death, and how these factors interact to determine the population’s density.
Under ideal conditions, any population can grow exponentially (that is to say, with an accelerating rate), growing faster the bigger it gets (like compound interest in a trust fund). Exponential growth may be extremely fast (e.g. bacteria provided with fresh medium), or moderately fast (mice at harvest-time in the fields), or rather slow (humans since about 1700). The rate will be set by the time it takes an individual to become a breeder, by the number of offspring produced by an individual, and by the nature and intensity of mortality factors acting upon the population, among other things. Ideal conditions, however, do not persist. As a population becomes larger, the presence and activities of its members will alter the conditions, for example depleting food faster than it is renewed.
Fast-multiplying organisms (such as a population of bacteria) do not differ much in their individual ability to access resources, and have little or no capacity to use their behaviour to beat out rival individuals. When the population becomes unsustainably large, nearly all individuals are equally (and perhaps fatally) inconvenienced by food shortage, and the density crashes abruptly. The few lucky survivors may then be able to initiate a fresh phase of growth, if the food supply recovers, but their fate will be similar. This “lid on growth”-effect is referred to as limitation, literally suggesting that there is a ceiling or upper limit to density imposed by an outside force and acting indifferently upon the individuals present. The “lid” won’t necessarily always be held in the same position over the growing population, but on average there will be a normal ceiling against which the population will bash itself.
Many factors aside from sudden food-shortage can impose limitation: the onset of bad weather conditions (cold, extreme heat, drought), disturbances like fires or floods, and in some instances predation or disease. A population whose size is set only by limitation will never achieve a stable, near-constant density, and will instead fluctuate through time in a series of spikes and crashes, often referred to as a cycle of “boom and bust”. This is an example of a relatively “r-selected” life-history.
A population in which growth is “limited-only” is in no way controlled by its own actions. The forces which end up limiting such a population would act whether the population was present, or not; consider limitation imposed by the weather – the onset of winter will kill off mosquitoes, but the winter cannot know that it is doing this, and winter will not “hold off” if mosquitoes are absent! But there are factors whose actions are influenced by the presence and state of the population, and their influence may be such as to stabilize the population’s density just as a thermostat can stabilize the temperature of air in a house.
When a factor acts at an intensity set in part by the state of the population it is affecting – i.e. when a factor’s strength depends on the size or growth-rate of the controlled population – the factor is referred to as a potentially regulatory factor. If the factor actually does produce a stable, controlled density, and maintains it over time, the process if referred to as regulation. The main difference between regulation and limitation is that regulation imposes both upper and lower limits on population density, not just a ceiling. Regulation can do this because the factor in some way “notices” the density of the population and acts accordingly.
For example: imagine a population regulated by a constant food supply, in which the stable state is that every individual manages to acquire just barely enough food to survive. If a few extra individuals were to be added to this population (by extra births, or the arrival of immigrants), the weakest would fall short of nutritional adequacy and would die, and the remaining individuals would stabilize at a density near the previous stable value. Now imagine the effect of removing a few individuals (either by accidental deaths, or emigration, or an experimenter’s action): the remaining individuals would be able to produce more offspring, because more food would be available, but this would increase density only to the previous stable value, and no further. Similarly, if food supply were to be altered, density would stabilize at the same food-per-individual value as before, either more individuals with increased food-supply or fewer with reduced supply. In this extended example, competition for food is clearly the mechanism of regulation. Other potentially-regulating forces are interspecific competition, predation, and disease – biotic factors generally.
Regulated populations, when they are at low density, grow more or less exponentially, but as they get larger the influence of their own members’ presence, and/or the increasing intensity of extrinsic regulatory forces acting upon them, prevents exponential growth from continuing. The slowing-down of growth causes the initial exponential rise to deflect until the growth-curve levels off, that is to say until the population density achieves a stable, unchanging value. The result on the density-over-time graph is a shape like a flattened S, usually referred to as a pattern of S-shaped or sigmoid growth. This is the form of growth-curve characteristic of K-selected populations, and the stable maximum density achieved at the end of the S is the carrying capacity, or K-value.
Just because a factor is biotic, this does not prove that it is regulatory. All regulatory factors are biotic, but not all biotic factors are regulatory. [“All crows are black, but not all black things are crows.”] Biotic factors at least have the potential to alter their action according to the population’s condition, though they do not necessarily do so.
Remember that all populations, whether regulated or not, are subject to limitation. Thus some populations are limited-only, some are mostly limited and a bit regulated, and some are limited and strongly regulated (perhaps by several regulatory factors, not just one).
Another way to describe the action of regulatory factors is to describe them as density-dependent in their action: they differ in intensity is such a way that they stabilize the population. Competition for food acts gently at low density (lots of food, few individuals, thus a weak force to control growth) and strongly at high density (less food relatively speaking, to the point where bare survival becomes difficult, as there are more hungry mouths present). Contagious disease spreads slowly at low density (hard to transmit when individuals are sparse) and easily at high density (perhaps aided and abetted in killing victims by starvation and other high-density problems). A density-dependent (or “DD”) mortality factor kills a greater percentage of a large population than it does a small one, and this tends to stabilize density; density-dependent birth makes fewer babies per mother in a large population than in a small one, again stabilizing but from the opposite effect. Some regulated populations are controlled mainly by DD mortality, some mainly by DD birthrates, and some by both; all will of course also be influenced by limiting factors.
Limiting factors in contrast, as described above, act in a manner which must be described as density-independent (“DI”). DI mortality factors certainly cause an increasing number of deaths as density increases, but always in proportion to the size of the population – they act much like sales-tax on items of different cost! (You pay more sales-tax on a $10 item than on a $1 item, but the increase is by a factor of 10 exactly, just like the item-price.) Thus although DI mortality factors can slow the exponential growth of a population, they cannot by themselves change it to sigmoid growth, so they cannot regulate. This is true even when a DI factor like a major catastrophe strikes a population – it may kill 95 or 99% of the individuals present, yet it is limiting only. Very limiting, to be sure, but not likely to lead to any regulated stable density; instead, it will simply set the stage for steady recovery, or it will drive the population extinct – in neither case is there regulation.
It is also possible for factors to act in a manner that varies with density, but not in the mode which promotes stability; consider an example. Imagine a house thermostat which responds to warm air by turning the furnace ON, and responds to cool air by turning the furnace OFF. Such a device, far from creating a stable temperature, would either burn the house down, or allow it to freeze solid! It would be responding differentially to temperature, but “the wrong way around”, promoting instability. In ecological terms this would be analogous to a factor killing a smaller fraction of a large than a small population, or one promoting more births per female in a crowded population than in a sparse one. We refer to such factors as inverse-density-dependent (“IDD”) factors. Such factors obviously cannot regulate, and in fact are counter-regulatory, but they can be consistent with overall regulation as long as their effects are relatively weak.
We can best assess the rates of birth and death of a population as a value “per individual”, or if you prefer the fractional rate: for death, how many individuals die per individual present per unit time? This is the same as saying what fraction of individuals present die per unit time? If ten die of one hundred present in a time period, you can then say “ten per 100 die”, or equivalently “one-tenth (or ten per cent) die”, per time period. Similarly for birth, we say (for instance) twenty offspring are produced per hundred breeding females per unit time, or equivalently “one-fifth of females breed per time period”, or “twenty per cent breed per unit time”, or “on average one-fifth of an offspring is produced by each female in a time period”.
If you graph out these “fractional rates” over density, the shape of the resulting line tells you if the factor is DD or DI. A DI mortality, for example, would always kill the same fraction of individuals irrespective of density – say 10 per cent of a small population, of a medium-sized population, or of a large one. Thus the fraction, 1/10 or 10%, would stay constant with density, and the line would be parallel with the density-axis.
On the other hand, a DD mortality factor would act increasingly strongly at higher densities: it might kill 10% of a small population, 30% of a medium-sized one, and 70% of a large one. Such a line will have a positive slope with density. Of course, since a birth-rate factor has the opposite effect on density to that of a death-rate factor, a DD birth-rate will show a negative slope with density. If a population exhibits birth- and death-rate lines which cross on the graph – and to achieve this, one rate at least must vary with density – there will be a point of density at which the rates are equal, and at this density the population will have zero growth.
Be warned! – just because a crossover point exists, this does not necessarily mean the population will be stable at that point. The overall slopes of the birth and death rate curves must sum to a DD state, otherwise there will be no regulation and no stability. When there are DI factors, they will contribute nothing to regulation, and just increase “noise” (variance) in the population-control situation. When there are IDD factors present, they will undercut the strength of DD factors, and must be taken into consideration when evaluating the overall mode of control. Only when all factors of significance are analyzed for their density-relations can we confidently assert that a population’s growth is understood.
Whether a population is regulated or merely limited, lives at a stable consistent density or jerks all over the map in boom-and-bust chaos, this is no indication of the success of the organism! Many stable K-selected organisms like pandas and whales are highly endangered species, while the majority of spike-and-crash r-selected organisms are ineradicable pests like bacteria or mosquitoes – a population’s mode of growth and density-control is independent of how well it may do in its environment.