Population dynamics

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Population dynamics are branches of life science that study population size and composition as a dynamic system, and the biological and environmental processes that drive them (such as birth and death rates, and by immigration and emigration). Examples of scenarios are aging population, population growth, or population decline.

Video Population dynamics

Histori

Population dynamics have traditionally been the dominant branch of mathematical biology, which has a history of more than 210 years, although more recently the scope of mathematical biology has been greatly developed. The first principle of population dynamics is widely regarded as Malthus exponential law, as modeled by Malthus's growth model. The early period was dominated by demographic studies such as the work of Benjamin Gompertz and Pierre FranÃÆ'§§ois Verhulst in the early 19th century, which refined and adapted Malthus's demographic model.

A more general modeling formula proposed by F.J. Richards in 1959, which was later expanded by Simon Hopkins, in which Gompertz, Verhulst and Ludwig von Bertalanffy's models were discussed as special cases of general formula. The Lotka-Volterra predator equations are another well-known example, as well as the alternative Arditi-Ginzburg equation. Computer games SimCity and MMORPG Ultima Online, among others, are trying to simulate some of the dynamics of this population.

In the last 30 years, population dynamics have been complemented by evolutionary game theory, developed first by John Maynard Smith. Under this dynamic, the concept of evolutionary biology can take a deterministic mathematical form. Population dynamics overlap with other active research areas in mathematical biology: mathematical epidemiology, the study of infectious diseases that affect populations. Various models of viral spread have been proposed and analyzed, and provide important results that can be applied to health policy decisions.

Maps Population dynamics

Intrinsic increase rate

Tingkat di mana suatu populasi meningkat dalam ukuran jika tidak ada kekuatan tergantung kepadatan yang mengatur populasi dikenal sebagai laju peningkatan intrinsik . ini

${\ displaystyle {\ dfrac {dN} {dt}} {\ dfrac {1} {N}} = r}  ÂÂ$

di mana derivatif ${\ displaystyle dN/dt}  ÂÂ$ adalah laju peningkatan populasi, N adalah ukuran populasi, dan r adalah intrinsik tingkat peningkatan. Jadi r adalah tingkat teoritis maksimum peningkatan populasi per individu - yaitu, laju pertumbuhan populasi maksimum. Konsep ini biasa digunakan dalam biologi populasi serangga untuk menentukan bagaimana faktor lingkungan mempengaruhi tingkat populasi hama meningkat. Lihat juga pertumbuhan populasi eksponensial dan pertumbuhan populasi logistik.

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Model matematika umum

Pertumbuhan populasi eksponensial

Exponential growth represents unregulated reproduction. It is very unusual to see this in nature. In the last 100 years, the growth of the human population seems to be exponential. However, in the long run, it is not possible. Paul Ehrlich and Thomas Malthus believe that human population growth will lead to overpopulation and starvation due to resource scarcity. They believe that the human population will grow at a rate where they exceed the ability of humans to find food. In the future, humans will not be able to feed large populations. The biological assumption of exponential growth is that the per capita growth rate is constant. Growth is not limited by scarcity of resources or predation.

Simple discrete time exponential model

$Â\; Â{\displaystyle Â\; Â\; Â\; Â\; Â\; Â\; Â}$ _{    Â¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯½¯¯¯¯¯¯¯¯¯¯ïÂ.½ïÂ.½ïÂ.½ïÂ.½ïÂ.½ïÂ.½ï                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½     Â    Â 1                          =         ?            Â¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯¯½¯¯¯¯¯¯¯¯¯¯ïÂ.½ïÂ.½ïÂ.½ïÂ.½ïÂ.½ïÂ.½ï                ÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂÂï <½                                {\ displaystyle N_ {t 1} = \ lambda N_ {t}}  Â}

where ? is the discrete-time per capita growth rate. On ? = 1, we get a linear line and a zero-discrete time-per-cap growth rate. In ? & lt; 1, we get a decrease in per capita growth rate. In ? & gt; 1, we got an increase in per capita growth rate. In ? = 0, we get species extinction.

Ongoing version of exponential growth.

Beberapa spesies memiliki reproduksi berkelanjutan.

${\ displaystyle {\ dfrac {dN} {dT}} = rN}  ÂÂ$

di mana ${\ displaystyle {\ dfrac {dN} {dT}}}  ÂÂ$ adalah laju pertumbuhan populasi per satuan waktu, r adalah tingkat pertumbuhan per kapita maksimum, dan N adalah ukuran populasi.

At r & gt; 0, there is an increase in per capita growth rate. At r = 0, the per capita growth rate is zero. At r & lt; 0, there is a decline in growth rate per capita.

Logistics population growth

"Logistics" comes from the French word logistique , which means "counting". Population regulation is a process that depends on density, which means that the rate of population growth is governed by population density. Consider the analogy with a thermostat. When the temperature is too hot, the thermostat turns on the air conditioner to lower the temperature back to homeostasis. When the temperature is too cold, the thermostat turns on the heater to raise the temperature back to homeostasis. Similarly, density dependence, whether high or low population density, population dynamics returns population density to homeostasis. Homeostasis is a set point, or carrying capacity, defined as K.

Model of sustainable logistics growth

${\ displaystyle {\ dfrac {dN} {dT}} = rN {\ Big (} 1 - {\ dfrac {N} {K}} {\ Big)}}$

di mana ${\ displaystyle {\ Big (} 1 - {\ dfrac {N} {K}} {\ Big)}}  ÂÂ$ adalah ketergantungan kepadatan, N adalah jumlah dalam populasi, K adalah titik set untuk homeostasis dan daya dukung. Dalam model logistik ini, tingkat pertumbuhan penduduk tertinggi di 1/2 K dan tingkat pertumbuhan populasi nol sekitar K . Tingkat panen optimal adalah tingkat yang mendekati 1/2 K di mana populasi akan tumbuh paling cepat. Di atas K , laju pertumbuhan penduduk negatif. Model logistik juga menunjukkan ketergantungan kepadatan, yang berarti tingkat pertumbuhan populasi per kapita menurun dengan meningkatnya kepadatan penduduk. Di alam liar, Anda tidak bisa membuat pola-pola ini muncul tanpa penyederhanaan. Ketergantungan kepadatan negatif memungkinkan untuk populasi yang melampaui kapasitas membawa untuk menurunkan kembali ke daya dukung, K .

Menurut teori seleksi R/K mungkin khusus untuk pertumbuhan yang cepat, atau stabilitas lebih dekat ke daya dukung.

Model logistik waktu diskret

${\ displaystyle N_ {t 1} = N_ {t} rN_ {t} (1- {N_ {t}/K})}  ÂÂ$

This equation uses r instead of ? because per capita growth rate is zero when r = 0. Since r becomes very high, there is oscillation and deterministic chaos. Deterministic chaos is a major change in population dynamics when there is very little change in r . This makes it difficult to make predictions with high r values ​​because very small errors r result in massive errors in population dynamics.

Population always depends on density. Even independent events of heavy density can not regulate the population, although it can cause it to become extinct.

Not all population models always depend on negative density. The Allee effect allows for a positive correlation between population density and per capita growth rates in communities with very small populations. For example, fish that swim by themselves are more likely to be eaten than fish swimming between schools of fish, as the pattern of school fish movements is more likely to confuse and create stun predators.

Individual-based model

Cellular automata is used to investigate the mechanisms of population dynamics. Here is a relatively simple model with one and two species.

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Management of fisheries and wildlife

In fisheries and wildlife management, the population is affected by three dynamic level functions.

• Equality or birth rate, often recruitment, which means reaching a certain size or stage of reproduction. Usually referring to the age of a fish can be captured and counted in the net.
• Population growth rates, which measure individual growth in size and length. More important in fisheries, where populations are often measured in biomass.
• Mortality, which includes harvest mortality and natural death. Natural deaths include non-human predation, disease and old age.

Jika N ₁ adalah jumlah individu pada saat 1 lalu

${\ displaystyle N_ {1} = N_ {0} B-D I-E}  ÂÂ$

where N ₀ is the number of individuals at time 0, B is the number of individuals born, D the number is dead , me the number that was immigrating, and the E number emigrated between time 0 and time 1.

If we measure this level for some time interval, we can determine how the population density changes over time. Immigration and emigration are present, but are usually not measured.

All of this is measured to determine which surpluses can be harvested, which is the number of individuals that can be harvested from a population without affecting long-term population stability or average population size. Harvest in a harvestable surplus is called a "compensation" of death, in which the death of the harvest is replaced for death to occur naturally. Harvest above that level is called "additive" death, because it increases the number of deaths that will occur naturally. These terms are not always judged as "good" and "bad," respectively, in population management. For example, fish & amp; Game agencies may aim to reduce deer population size through additive deaths. Bucks may be targeted to increase money competition, or may be targeted to reduce reproduction and thus the size of the population as a whole.

For the management of many fish and other wildlife populations, the goal is often to achieve the largest long-term sustainable crop, also known as maximum sustainable yield (or MSY). Given the population dynamic model, like one of the above, it is possible to calculate the size of the population that produces the largest surplus of harvest in equilibrium. While the use of a dynamic population model along with statistics and optimization to set harvest boundaries for fish and games is controversial among scientists, it has proven to be more effective than the use of human judgment in computer experiments where both models are faulty and management of students' natural resources compete to maximize yield in two hypothetical fisheries. To give an example of non-intuitive results, fisheries produce more fish when there is the closest shelter of human predation in the form of a nature reserve, which results in a higher catch than if the whole area is open for fishing.

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For control apps

Population dynamics have been widely used in several applications of control theory. By using evolutionary game theory, population games are widely implemented for different industrial and life contexts. Most are used in multi-input multiple-output systems (MIMO), although they can be adapted for use in single-input-output (SISO) systems. Some examples of applications are military campaigns, resource allocation for water distribution, distributed generator shipments, laboratory experiments, transportation problems, communication problems, among others. Furthermore, with adequate contextualization of industrial problems, population dynamics can be an efficient and easy-to-apply solution to problems related to control. Various academic research has been and continues to be done.

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See also

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Note

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References

• Introduction to Social Macrodynamics: Macromodel Compact World System Growth by Andrey Korotayev, Artemy Malkov, and Daria Khaltourina. ISBNÃ, 5-484-00414-4
• Turchin, P. 2003. Population Dynamics Complex: Theory/Empirical Synthesis. Princeton, NJ: Princeton University Press.
• Weiss, Volkmar (2007). "The Population Cycle Encourages Human History - from the Eugenic Phase to Dysgenic Phase and Finally Collapse". Journal of Social Studies, Politics, and Economics . 32 (3): 327-58.

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External links

• GreenBoxes share network code. Greenboxes (Beta) is a repository for open-source population modeling and PVA code. Greenbox allows users an easy way to share their code and look for other shared code.
• Virtual Handbook on Population Dynamics. The online compilation of state-ot-the-art basic tools for the analysis of population dynamics with emphasis on benthic invertebrates.
• Creatures! An interactive high school simulation program that implements simulations based on grass, rabbit and fox agents.

Source of the article : Wikipedia