Population Growth - Basic Information All populations change in size with time - if births exceed deaths, the population grows - if deaths exceed births, the population shrinks - only when births equal deaths does the population stay the same Other Population Growth Factors Populations can also change size if organisms move in (immigration) or leave (emigration)
Putting It All Together We can write a simple equation to show population growth as:
Change in Population Size = (Births + Immigration) - (Deaths + Emigration)
Expressing Population Changes as a Percentage Suppose we had a population of 100,000 individuals. Suppose in one year there were 1000 births, and 500 deaths. What percentage of the population were births? 1000/100,000 = 0.01, or in percentage terms, this is 1% of the population.
What percentage of the population were deaths? 500/100,000 = 0.005, or in percentage terms, this is 0.5% of the population.
Assume immigration equals emigration. If so, then they cancel out of our population equation. We'll come back to this assumption later.
Now, subtract deaths from births but express as a percentage: 1000-500/100,000 = 500/100,000 = 0.005, or 0.5% net growth
Thus, this population would be growing by 0.5% this first year. That means that after one year, there will be 500 more individuals than the previous year. So, after one year, the population would be 100,500 individuals.
The Net Reproductive Rate The net reproductive rate (r) is the percentage growth after accounting for births and deaths. In the example above, the population reproductive rate is 0.5%/yr.
Net reproductive rate (r) is calculated as: r = (births-deaths)/population size or to get in percentage terms, just multiply by 100.
Suppose we came back many years later, the net reproductive rate was still the same, but now the population had grown to 1,000,000. How many new individuals would be added each year now? Simply multiply the population by the reproductive rate: 1,000,000 x 0.05 (which is 0.5%) = 50,000
This means that now 50,000 new individuals are added in one year!! The net reproductive rate is the same as before, but because the population is so much bigger, many more individuals are added.
Exponential Growth If a population grows by a constant percentage per year, this eventually adds up to what we call exponential growth. In other words, the larger the population grows, the faster it grows!! A curve of exponential growth is an upward sweeping growth curve.
The Hardy-Weinburg equation is p + q = 1, or p^2 + 2pq + q^2 = 1, where p is dominant and q is recessive. If 10 out of 100 rabbits have white fur, 10% of the rabbits have white fur. Therefore, 90% of the rabbits have brown fur, which can be substituted into the first equation to become 0.9 + 0.1 = 1. Now that we know what p and q equal, we can solve the rest of the equation.
0.9^2 = 0.81
0.9 * 0.1 * 2 = 0.18
0.1^2 = 0.01
Therefore, the allele frequency of the recessive allele is 0.1
Citral is a typical essential oil used in the food, cosmetic, and drug industries and has shown antimicrobial activity against microorganisms. Citral is unstable and hydrophobic under normal storage conditions, so it can easily lose its bactericide activity. Nanoemulsion technology is an excellent way to hydrophilize, microencapsulate, and protect this compound. In our studies, we used a mixed surfactant to form citral-in-water nanoemulsions, and attempted to optimize the formula for preparing nanoemulsions. Citral-in-water nanoemulsions formed at So 0.4 to 0.6 and ultrasonic power of 18 W for 120 seconds resulted in a droplet size of < 100 nm for nanoemulsions. The observed antimicrobial activities were significantly affected by the formulation of the nanoemulsions. The observed relationship between the formulation and activity can lead to the rational design of nanoemulsion-based delivery systems for essential oils, based on the desired function of antimicrobials in the food, cosmetics, and agrochemical industries.
