Life Tables and Survivorship Curves 1. Key Components of a Life Table A life table provides information about the survival and reproductive rates within a population at different age intervals. The key components are: • Age Interval (x): The age range or stage of individuals. • Survival Rate (Sx ): Probability of surviving from one age interval to the next. • Number of Survivors (lx ): Proportion of the original cohort still alive at the beginning of age x. • Fecundity (bx ): Average number of offspring produced by an individual of age x. • Net Reproductive Rate (R0 ): Sum of the products of survivorship and fecundity across all age intervals: X R0 = lx bx (1) 2. Survivorship Curves Survivorship curves illustrate the proportion of individuals surviving at each age for a given cohort. There are three main types: 1. Type I: High survival rates in early and middle life, with most mortality occurring in older age. 2. Type II: Constant mortality rate throughout the lifespan. 3. Type III: High mortality rates early in life, but those that survive early stages live much longer. 3. Example: Solving a Hypothetical Population Using a Life Table Age (x) Survivors (lx ) 0 1.0 1 0.5 2 0.4 3 0.28 4 0.168 Survival Rate (Sx ) Fecundity (bx ) 0.5 0 0.8 2 0.7 3 0.6 1 0.4 0 Table 1: Hypothetical Life Table Example Step-by-Step Solution: 1 Cumulative R0 0 1.0 2.2 2.48 2.48 1. Age 0: Survivors l0 = 1.0, fecundity b0 = 0. Contribution to R0 : l0 × b0 = 1.0 × 0 = 0 Cumulative R0 = 0. 2. Age 1: Survivors l1 = 0.5, fecundity b1 = 2. Contribution to R0 : l1 × b1 = 0.5 × 2 = 1.0 Cumulative R0 = 1.0. 3. Age 2: Survivors l2 = 0.4, fecundity b2 = 3. Contribution to R0 : l2 × b2 = 0.4 × 3 = 1.2 Cumulative R0 = 2.2. 4. Age 3: Survivors l3 = 0.28, fecundity b3 = 1. Contribution to R0 : l3 × b3 = 0.28 × 1 = 0.28 Cumulative R0 = 2.48. 5. Age 4: Survivors l4 = 0.168, fecundity b4 = 0. Contribution to R0 : l4 × b4 = 0.168 × 0 = 0 Cumulative R0 = 2.48. Analysis: • Net Reproductive Rate (R0 ): From the calculations above, R0 = 2.48, meaning each individual is expected to replace itself 2.48 times over its lifetime. • Population Growth: Since R0 > 1, the population is expected to grow. 4. Example Life Table from Textbook (Figure 7.1) Age (x) Survivors (lx ) 0-1 1.0 1-2 0.7 2-3 0.56 3-4 0.504 4-5 0.428 Survival Rate (Sx ) Fecundity (bx ) 0.7 0 0.8 2.5 0.9 4.0 0.85 1.0 0.6 0 Cumulative R0 0 1.75 3.99 4.494 4.494 Table 2: Life Table Example from Textbook (Figure 7.1) 2 5. Steps to Create and Use a Life Table 1. Determine the cohort size and follow it through successive age intervals. 2. Calculate lx as the proportion of individuals surviving to each age interval. 3. Calculate Sx as the ratio of survivors in one age interval to the previous. 4. Determine bx from reproductive data. 5. Multiply lx and bx for each age interval and sum the values to calculate R0 . 6. Applications of Life Tables and Survivorship Curves • Understanding population dynamics and predicting growth trends. • Managing conservation efforts for endangered species by identifying critical life stages. • Comparing survival and reproductive strategies across species. 3