4/22 LAB LECTURE mitosis/meiosisPopulation Growth, Resource Management, and Global Demographics

Population Growth Models: Exponential and Logistic Growth

• Exponential Growth Model

  • This approach describes how populations grow when there are no restrictions on their growth.

  • In a graph, the exponential growth line is the one that goes straight up (often described as a J-shaped curve).

  • According to the mathematical equation for exponential growth, populations would theoretically keep growing forever.

  • The model has limitations because it does not incorporate the concept of environmental limits.

• Calculating Growth Rate ($r$)

  • The growth rate is influenced by births and deaths.

  • Example using Santa Ana data (hypothetical): If an average of 10 people are born every day ($\text{birth rate}$) and an average of 9.5 people die every day ($\text{death rate}$), the net addition is 0.5 survivors.

  • In this scenario, the value for $r$ (the growth rate) would be $0.5$.

  • While individuals cannot be "half-alive" or "half-dead," these figures represent statistical averages across a population.

• Limitations and Carrying Capacity ($K$)

  • In the real world, populations do grow exponentially for a period, but not forever.

  • Eventually, populations get too big and run out of essential resources such as food, water, nesting space, or safe sleeping areas (like caves).

  • Carrying Capacity Definition: Referring to the maximum number of individuals that a specific environment can support.

  • Example: A farmer can only grow a maximum number of corn plants in a field based on the available space, water, nitrogen, and phosphorus in the soil.

  • Example: Santa Ana has a limit to how many residents can live there based on physical space and infrastructure; similarly, a classroom might have a limit based on the number of chairs (e.g., 40 chairs).

• Logistic Growth Model

  • When the concept of carrying capacity is incorporated into the growth equation, it is called logistic growth.

  • The graph for logistic growth goes up and then flattens out (S-shaped curve).

  • The flattening occurs because the population has reached its carrying capacity ($K$).

  • On a specific graph example (page 158), the flattening occurs at the $y$-axis value of $200$. Therefore, $K = 200$.

Sustainable Resource Management and Population Dynamics

• Steepest Point of Growth

  • In a logistic growth curve, the population grows at different rates depending on its current size.

  • In the provided example ($K = 200$), the population is not growing very fast at a size of $10$, and it is flat (zero growth) at $200$.

  • The line is steepest, and growth is fastest, when the population size is at $100$.

  • Mathematical Principle: The steepest point in a growth line is always at exactly half of the carrying capacity ($K/2$).

• Application to Natural Resources

  • Humans use plants and animals for food, construction, and income.

  • To manage resources sustainably (e.g., fishing), managers must ensure enough individuals remain to reproduce for future years.

  • The most efficient way to maximize harvest without depleting the resource is to reduce the population size to exactly half of the carrying capacity ($K/2$). This ensures the population will grow at its fastest possible rate for the following harvest.

Natural Resources Management Lab Activity: "Lentil Fishing"

• Materials and Setup

  • A container full of lentils represents the "Ocean."

  • The lentils specifically represent water in this imaginative scenario.

  • Three types of "fish" are placed in the ocean: Big, Medium, and Small fish.

• Reproduction Rules

  • Fish remaining in the ocean after a fishing season will reproduce.

  • Formula: For every 2 fish left, add 1 new fish.

  • Example: If there were 20 fish and 5 were caught, 15 remain. The 15 fish reproduce by adding $15 / 2 = 7.5$, which rounds up to $8$ new fish. The population for the next round becomes $15 + 8 = 23$ fish.

• Fishing Technology and Costs

  • The activity lasts for five seasons.

  • Season 1: All students must use forceps with their non-dominant hand (usually the left hand).

  • Subsequent Seasons: Students can purchase better technology:

    • Right to use dominant hand: $\$25$

    • Spoon: More expensive than dominant hand.

    • Fingers: Costs more than a spoon.

    • Full hand (scooping): The most expensive technology option.

• Economic Calculations

  • Students must calculate Profit. Formula: $\text{Total Income (from selling fish)} - \text{Costs (license, fuel, crew, maintenance, technology purchases)} = \text{Profit}$.

• Activity Goals and Constraints

  • Goal 1: Maximize total profit.

  • Goal 2: Maintain steady income. High variability (e.g., $\$1,000,000$ one year and $\$50,000$ the next) makes business planning like buying new boats difficult.

  • Goal 3: Avoid extinction. If any of the three fish types go extinct, the group is disqualified ("sent to fishing jail").

  • The winning group receives 6 points instead of 5.

  • Winning Formula: Aim for a high number on top (profit) and a small number on the bottom (variance/steadiness of income).

• Cleanup Procedures

  • The lentils and fish must be separated using a sieve and trays.

  • Lentils must be returned to their original bin.

  • Spilled beans on tables or under computers can be picked up by hand or using a "high-technology" handheld sweeper.

Global Human Population Statistics (2024 Estimates)

• Population Size by Country (in millions)

  • United States: $336.6\text{ million}$

  • Canada: $41.4\text{ million}$

  • Mexico: $129.4\text{ million}$ (noted as approximately $130\text{ million}$)

  • China: $1,408.6\text{ million}$

  • India: $1,441.7\text{ million}$

  • Vietnam: $101.1\text{ million}$

• Regional Statistics

  • Highest Population Region: Asia.

  • Country with highest population within Asia: India.

  • Highest Population Subregion of Africa: Eastern Africa, with a population of $490\text{ million}$.

• Population Densities and Experiences

  • Vietnam is noted for being extremely crowded relative to its size compared to Mexico.

  • Saigon Traffic Example: Crossing the street is compared to the game Frogger because of the "river of motorcycles." The recommended strategy is to walk blindly next to a local person and trust they know when to move.

Key Demographic Definitions

• Total Fertility: The average number of children a woman will have during her life.

• Infant Mortality Rate: The annual number of deaths among children less than one year old per $1,000$ live births.

• Life Expectancy: The average number of years that a newborn can expect to live.

Demographic Data and Health Disparities

• High Fertility Countries (Africa)

  • Somalia: $6.1$

  • Democratic Republic of the Congo (DRC): $6.1$

  • Chad: $6.1$

  • Central African Republic (CAR): $6.4$

• Modern Contraception Use

  • Somalia: $1\%$

  • DRC: $18\%$

  • Central African Republic: $14\%$

  • United States: $80\%$

  • Barriers in Poor Countries: Lack of money, difficult transportation (living days away from clinics), and ongoing civil wars.

• Infant Mortality Statistics

  • Guyana (South America): $21$ per $1,000$ births.

  • Pakistan (South Asia): $49$ per $1,000$ births.

  • For comparison: Afghanistan (historically high).

• Life Expectancy Disparities

  • Lowest (Women): Central African Republic ($59$), Chad ($57$), Nigeria ($55$).

  • Nigeria (Men): $54$.

  • Highest (Men in Europe): Sweden ($82$), Norway ($81$).

  • United States: Women are expected to live to approximately $79$ and men to $75$. This is a slight decrease compared to those born around 2005 (where it was $80$ for women and $76$ for men).

History of Human Population Growth

• Timeline to 1 Billion

  • Our species appeared approx. $300,000$ years ago.

  • It took the entire history of the species ($300,000$ years) to reach a population of $1\text{ billion}$ in the year $1800$.

• Population Pyramids and Pillars

  • Graphs that break down populations by gender and age groups are called population pyramids.

  • The shape of the pyramid indicates how fast a population is growing.

• Doubling Time

  • This refers to the amount of time it takes for a population to double in size.

Questions & Discussion

• Question: Is the population growing faster when the size is 10, 100, or 200?

  • Answer: At 100, because that is half the carrying capacity of 200.

• Dialogue on Cultural Differences: The speaker emphasizes the importance of travel to understand how different countries function, noting that people in countries with governments the US has friction with (like Pakistan) are often very friendly to US citizens personally.

• Closing Anecdote on Labor: The speaker notes a group from the previous day where two students left early, leaving the remaining two to do all the cleaning, emphasizing that cleanup is a group effort.

• Student Commentary and Speculation: Near the end, students discuss population numbers per hour ($70$ additions per population per hour/$2.75\text{ hours}$) and engage in speculative/conspiracy-theory dialogue regarding COVID-19 and war as methods for population control, which the instructor does not explicitly validate but acknowledges as "hard decisions."