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Related Concept Videos

Population Growth00:57

Population Growth

Population size is dynamic, increasing with birth rates and immigration, and decreasing with death rates and emigration. In ideal conditions with unlimited resources, populations can increase exponentially, which plots as a J-shaped growth rate curve of population size against time. This type of curve is characteristic of newly-introduced invasive species, or populations that have suffered catastrophic declines and are rebounding.However, realistic environmental conditions limit the number of...
Exponential Equations for Modeling Growth01:26

Exponential Equations for Modeling Growth

Exponential models are essential for describing rapid, multiplicative changes in natural systems, such as population growth. When a population doubles at regular intervals, the process can be modeled using a suitable base. For instance, a bacterial culture that doubles every three hours follows the model n(t)=n0⋅2t/3, where n(t) is the population at the time t.A more general model uses the natural base e, especially for continuous growth. This takes the form n(t)=n0⋅ert, where r is the relative...
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Modeling with Differential Equations

Population dynamics can be described mathematically by considering the population size P(t) as a function of time. The rate of change of the population is then represented by the derivative of P(t). A simple assumption is that the rate of growth is proportional to the size of the population itself. This leads to an exponential growth model, where the population increases rapidly without bound. While this is a useful first approximation, it does not reflect realistic long-term...
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Bacterial populations exhibit exponential growth when conditions such as nutrient availability and temperature are favorable. In this phase, cells reproduce through binary fission, where each cell divides into two identical daughter cells. This process causes the population to double at regular intervals, resulting in a growth rate that is directly proportional to the current number of cells. As the population increases, the number of new cells formed during each generation also grows, creating...
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Bacterial Growth Curve

The bacterial growth curve is a fundamental concept in microbiology that describes the dynamics of bacterial population growth in a closed system with controlled environmental conditions, such as temperature and nutrient availability. This curve is divided into four distinct phases: lag, log (exponential), stationary, and death phases, each reflecting a unique stage of bacterial adaptation and growth. During the lag phase, bacteria acclimate to their surroundings by synthesizing essential...
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Many human characteristics, like height, are shaped by both nature—in other words, by our genes—and by nurture, or our environment. For example, chronic stress during childhood inhibits the production of growth hormones and consequently reduces bone growth and height. Scientists estimate that 70-90% of variation in height is due to genetic differences among individuals, and 10-30% of variation in height is due to differences in the environments that individuals experience, such as differences...

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THE NATURE OF THE GROWTH RATE.

H S Reed1

  • 1University of California Graduate School of Tropical Agriculture and Citrus Experiment Station, Riverside.

The Journal of General Physiology
|October 30, 2009
PubMed
Summary

Organism growth rates, like chemical reactions, are proportional to remaining growth. Studies on pear trees, walnut trees, maize, and cattle confirm this autocatalytic model for predicting biological development.

Area of Science:

  • Biological Sciences
  • Biochemistry
  • Mathematical Biology

Background:

  • Organism growth can be modeled as a chemical reaction.
  • Growth rate is proportional to the amount of growth remaining.
  • Autocatalysis describes reactions where a product catalyzes its own formation.

Purpose of the Study:

  • To investigate the quantitative course of organism growth rates.
  • To determine if growth rates follow an autocatalytic pattern.
  • To assess the applicability of the autocatalytic model across different species and growth metrics.

Main Methods:

  • Weekly measurements of pear tree shoot length during the growing season.
  • Observation of growth cycles in young walnut trees over a single season.

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  • Analysis of maize growth using green weight, dry weight, and height.
  • Evaluation of cattle growth using weight and height data.

    • Main Results:

    • Pear tree shoot growth rates exhibited an autocatalytic pattern.
    • Walnut tree growth cycles followed an autocatalytic reaction rate.
    • Maize growth rates, measured by various metrics, aligned with the autocatalytic model.
    • Cattle growth, assessed by weight or height, also demonstrated autocatalytic characteristics.

    Conclusions:

    • Organismal growth rates can be quantitatively described by an autocatalytic model.
    • The autocatalytic model is applicable across diverse plant and animal species.
    • Growth rate is consistently proportional to the amount of growth yet to be achieved, regardless of the metric used.