Question

How is the finite growth multiplier ( \(\lambda\) ) calculated from the population projection table?

Short answer

Answer: To calculate the finite growth multiplier (λ) from a population projection table, follow these steps: 1. Obtain the population projection table. 2. Calculate the number of survivors for each age class by multiplying the number of individuals at the beginning of the time period by the corresponding survivorship rate. 3. Calculate the total number of survivors by adding up the calculated number of survivors from all age classes. 4. Calculate the total number of individuals at the beginning of the time period by adding the number of individuals from all age classes. 5. Calculate the finite growth multiplier (λ) by dividing the total number of survivors at the end of the time period by the total initial population size.

Step-by-step solution

Obtain the population projection table

Obtain a population projection table, which generally includes the number of individuals in each age class at the beginning and end of a time period and the survivorship rate for that time period.

Calculate the number of survivors for each age class

For each age class in the population projection table, multiply the number of individuals at the beginning of the time period by the corresponding survivorship rate. This will give you the number of survivors for each age class at the end of the time period.

Calculate the total number of survivors

Add up the calculated number of survivors from all age classes to get the total number of survivors in the population at the end of the time period.

Calculate the total number of individuals at the beginning of the time period

Add up the number of individuals from all age classes at the beginning of the time period to get the total initial population size.

Calculate the finite growth multiplier (λ)

Divide the total number of survivors at the end of the time period by the total initial population size. This value represents the finite growth multiplier (λ). $$ \lambda = \frac{\text{Total number of survivors at end of time period}}{\text{Total initial population size}} $$ Please note that if the time period is not specified, the general formula for calculating λ will equal the net reproduction rate (R₀).

Key concepts

Population Projection Table

When ecologists want to predict the future size of a population, they often use a population projection table. This essential tool combines data on the current population structure with rates of survival and reproduction to forecast population dynamics over time. It typically consists of columns for age classes, survival rates, and fecundity rates, which may include additional factors like sex ratio in species where it's relevant.

For example, the table might show that 100 individuals who are one year old have a 90% chance of surviving to the next year. By multiplying the number of individuals by the survivorship rate, ecologists can predict how many individuals are expected to survive to the next age class. They do this for each age class to predict the population size and structure in the next time period. It's also crucial to include key factors such as immigration and emigration if applicable.

Population projection tables are not static; they are regularly updated with new data to refine predictions and reflect changes in environmental conditions, availability of resources, or impacts of human activities. Accurate tables are essential for effective population management and conservation efforts.

Survivorship Rate

The survivorship rate is a core metric in population ecology and demography, representing the proportion of a cohort that survives from one age to the next. It is typically expressed as a probability between 0 and 1. For instance, if out of 100 individuals, 85 survive from one year to the next, the survivorship rate for that period is 0.85.

Types of Survivorship Curves

There are generally three types of survivorship curves:

• Type I: High survival rates throughout most of the organism's life span, with high mortality at the end. Common in humans and large mammals.
• Type II: Constant survival rate throughout life. It's seen in some birds and reptiles.
• Type III: Low survival rates for the young, with a higher rate for individuals who reach adulthood. This pattern is common in many fish and invertebrates.

Ecologists use these rates to predict population changes and to understand the evolutionary strategies of different species. Effective conservation plans often depend on accurate survivorship data to target life stages that have the most significant impact on population growth.

Population Ecology

In essence, population ecology is the study of how populations of organisms change over time and space and the factors that influence these changes. It is a subsection of ecology which deals with the dynamics of species populations and how these populations interact with the environment.

Key concepts in this field include population size, density, distribution, age structure, and the rates of birth, death, immigration, and emigration. Population growth models, like exponential and logistic growth, describe how populations expand under certain conditions. The finite growth multiplier (λ) is an example of a metric used in these models to predict the future size of the population under study.

Population ecologists aim to understand these dynamics to manage wildlife and fishery stocks, control invasive species, and conserve endangered species. The interplay of factors such as competition, predation, resource availability, and human impact are complex and require sophisticated models and longitudinal studies to unravel.