Question

The life table and the seed production of the winter annual plant Collinsia verna for \(1983-84\) was as follows (Kalisz 1991 ): $$\begin{array}{lccc} \hline & & \text { Average no. } \\ & \text { Age interval } & \text { Number } & \text { seeds produced } \\ \text { Life cycle } & \text { (months) } & \text { alive } n_{x} & \text { per plant } b_{x} \\ \hline \text { Seed } & 0-5 & 23,061 & 0 \\ \text { Seedling } & 5-7 & 6019 & 0 \\ \text { Overwintering } & 7-12 & 4617 & 0 \\ \text { plants } & & & \\ \text { Flowering } & 12-13 & 2612 & 0 \\ \text { plants } & & & \\ \text { Fruiting plants } & 13-14 & 692 & 10.754 \\ \hline \end{array}$$ Calculate the net reproductive rate for these plants and discuss the biological interpretation of this rate.

Short answer

Calculate \( R_0 = \frac{692}{23061} \times 10.754 \) to find the net reproductive rate and interpret its meaning.

Step-by-step solution

Understand the Life Table

The life table provides data on the number of plants at each life stage and the average seed production per plant. The stages are: Seed (0-5 months), Seedling (5-7 months), Overwintering plants (7-12 months), Flowering plants (12-13 months), and Fruiting plants (13-14 months). Only the Fruiting plants produce seeds, with an average of 10.754 seeds per plant.

Define Net Reproductive Rate

The net reproductive rate, represented as \( R_0 \), is calculated as the sum of the product of the proportion of individuals surviving to each age interval and the average number of offspring produced. It measures the expected number of offspring produced by an individual during its lifetime.

Calculate Proportion Surviving to Each Stage

To find the proportion of individuals surviving to each stage (\( l_x \)), divide the number alive at each stage by the initial number of seeds, which is 23,061. For example, \( l_0 = \frac{23061}{23061} = 1 \), \( l_5 = \frac{6019}{23061} \), and so on.

Compute Offspring for Each Stage

For each life stage, calculate the total offspring produced as \( l_x imes n_x imes b_x \). Since only the Fruiting plants produce seeds, for other stages, this will be zero. For Fruiting plants: \( l_{13} = \frac{692}{23061} \), then calculate \( l_{13} \times 10.754 \).

Sum Contributions to Net Reproductive Rate

Add the offspring contributions from all life stages to find \( R_0 \). Since only Fruiting plants contribute, \( R_0 = l_{13} \times b_{13} \). Substitute the values to compute it.

Interpret the Net Reproductive Rate

If \( R_0 = 1 \), the population is stable. If \( R_0 > 1 \), the population is growing, and if \( R_0 < 1 \), it is declining. We interpret \( R_0 \) based on its value after calculation.

Key concepts

Life Table Analysis

Life table analysis is a vital tool used in population ecology to understand different life stages of organisms and their survival rates and reproductive success. When studying a species, ecologists construct life tables to track the number of individuals living or dying during each stage of their life cycle. This helps in identifying which life stages are most critical for the population's growth and sustainability.

In the example of the winter annual plant Collinsia verna, a life table has been constructed to track the plant through different stages from seed to fruiting plant. Here, the table records the number of individuals alive at each stage and the average number of seeds produced by each plant. It includes detailed data collected over age intervals: from seeds, seedlings, overwintering plants, flowering plants, to fruiting plants.

By using the life table, you can calculate the survival rate at each stage by dividing the number of individuals alive by the initial number. This will provide insights into how many plants made it from one stage to the next. Understanding the transition through these stages is essential for predicting the future population dynamics of the species.

Net Reproductive Rate

The net reproductive rate, denoted as \( R_0 \), is a fundamental concept in population ecology that quantifies the average number of offspring a species is expected to produce throughout its lifetime. It is calculated by examining the survival and reproductive rates of each life stage. This gives insights into whether a population is likely to grow, decline, or remain stable.

To determine \( R_0 \), you first need the proportion of surviving individuals at each life stage. This is obtained by dividing the number of individuals alive at each stage by the initial population size. Next, you multiply this survival proportion by the average number of offspring (in this case, seeds) they produce at each stage.

In our exercise, only the fruiting plants contribute to the net reproductive rate since they are the only ones producing seeds. For Collinsia verna, calculating \( R_0 \) involves summing the contribution made by the surviving fruiting plants' seed production. Ultimately, the value of \( R_0 \) helps interpret the plant's population dynamics: a value greater than 1 suggests growth, less than 1 indicates decline, and equal to 1 means stability.

Plant Life Cycle

The plant life cycle is an essential subject in understanding plant reproduction and longevity. For species like Collinsia verna, the life cycle is divided into distinct stages where different biological processes occur. These stages usually begin with seed germination, followed by seedling development, overwintering, flowering, and finally, fruiting.

Each stage in a plant's life cycle serves a purpose.

• Seeds contain all the necessary materials to start a new plant and are the initial stage.
• Seedlings are vulnerable yet crucial for successful transition to the next stages.
• Overwintering enables plants to survive harsh conditions.
• Flowering is when the reproductive organs develop, crucial for attracting pollinators and spreading genetic material.
• Finally, fruiting produces seeds that can disperse and grow into new plants.

Understanding the plant life cycle offers insights into the timing and conditions that enhance successful growth and reproduction. Knowing the specific requirements and risks associated with each life stage helps ecologists and botanists develop conservation plans and predict how environmental changes might impact plant populations. This knowledge can also guide agricultural practices and ecological restoration efforts.