Exponential growth ("J" growth)
Thomas T. Myers, a famous demographer, put forward an exponential growth model. He believes that population growth is not a simple additive relationship, but a multiple growth. Later, the biologist Charles Robert ·C·r· Darwin confirmed this growth model again by studying the elephant population. This objective growth pattern shows that all populations have the ability of explosive growth [1].
The function of exponential growth is an exponential equation, the variable is time t, and the constant is a multiple of population density growth. This growth model has no upper limit, and complete exponential growth only exists in the ideal situation that there are no natural enemies and food and space are absolutely sufficient (so there is no intraspecific struggle). In real life, when bacteria, invasive organisms (such as Eichhornia crassipes) and cyanobacteria just inoculated in Petri dishes erupt, the population will increase exponentially for a considerable period of time, and then tend to be stable or die in large numbers.
Logical growth ("S" growth)
Main project: logical growth model
Exponential growth is an ideal situation. After a period of exponential growth, the number of many creatures will remain stable, which can be described by another mathematical model.
test result
Example: Russian ecologist G.W. Gowther once did an experiment. Five giant paramecium were put into 0.5ml culture medium, and the population density of the population was counted every 24 hours. The result is shown on the right. As can be seen from the figure, after rapid growth, the number of giant paramecium is stable at 75 (K value). [ 1]?
Logistic growth model can better guide the regulation of artificial population.
environmental carrying capacity
There is an upper limit for the number of populations growing logically. This upper limit is called environmental carrying capacity, abbreviated as "K value", which represents the maximum carrying capacity of populations without damaging the environment, or the maximum number of populations in the environment. When the population density is K/2, a population grows fastest, which can guide the collection of economic organisms and keep the population density within the range of K/2 all the time. "Redundant" collection can make economic organisms grow at the fastest speed. [ 1]?
Natural rise and fall
In nature, the quantitative change of a population is not only incremental, but also may not completely conform to the above mathematical model, and its quantitative change has some basic characteristics.
periodical change
① Seasonal change
Generally, the species with seasonal reproduction, after the last reproduction in a year, the maximum population density often drops, and then reproduction stops, so the population density drops, and this decline continues until the beginning of the next breeding season, when the population number is the lowest, resulting in seasonal changes.
Example: In the cold regions of Eurasia, many small birds and mammals usually stop breeding in winter, and their populations are the lowest before they start breeding in spring. After breeding began in spring, the population number kept rising, and reached the highest level in a year before stopping breeding due to cold in autumn. Larger animals, such as badgers and marmots, breed only once a year. Their breeding season is in spring, and their number reaches its peak after birth. Later, due to death, the number gradually decreased.
When investigating populations with seasonal changes in population density, it is usually done twice.
② Annual variation
Under relatively stable environmental conditions, the population density of seed plants and large vertebrates changes periodically in a long time span. For example, common trees such as poplar and willow blossom and bear fruit once a year, and the number of seeds is relatively stable; Another example is large ungulates, which generally have 1 ~ 2 babies every year, and the population is relatively stable. The population of Canadian argali has changed in 36 years, and the ratio of the highest to the lowest is only 4.5 times. In the past 20 years, the ratio of the highest number to the lowest number of American red deer in winter is only 1.8 times.
Irregular fluctuation
There are also some kinds of animals whose numbers fluctuate violently, but not periodically. The most famous species is the house mouse. It lives in houses, farmland and threshing floors. According to the statistical data of Chinese Academy of Sciences 16, the annual average capture rate fluctuates between 0. 10 ~ 17.57, that is, the highest-lowest ratio is several hundred times. Another example is the Brandt vole, which also has irregular quantitative changes. In the lowest year, there were only 1.3 per hectare on average, and in the highest year, there were 786 per hectare, which was more than 600 times worse. There are birth and death in the population, and its members are constantly updated, but this change often revolves around an average density. In other words, when the population is increased or decreased by some interference, it often returns to the original level. This situation is dynamic equilibrium.
Population outbreak
Population outbreaks may occur in organisms with irregular or periodic fluctuations, and red tide is an example of this situation.