Introduction

Estimating the size of wildlife populations is a fundamental task in conservation ecology. It allows us to evaluate population trends, assess species’ conservation status, and guide management actions. However, direct counts of all individuals in a population are rarely feasible—especially for small, cryptic, or mobile animals such as small mammals.

Instead, mark-recapture methods offer a practical and statistically robust way to estimate population size using repeated sampling. These methods involve capturing individuals, marking them in a non-harmful way, and then releasing them. On subsequent visits, researchers record how many individuals are recaptured (i.e., previously marked) and how many new, unmarked individuals are caught.

In this practical, you will estimate population sizes for each small mammal species you detected in the field, in two different areas of woodland at Svanninge Bjerge.

You will apply three classic estimators:

You will apply these calculations individually to each species in your dataset. For each species, you’ll need to extract the relevant data: how many individuals were captured and marked, how many were recaptured, and the sampling occasions.

Aim: Estimate population sizes and quantify uncertainty using your own data from Svanninge Bjerge.

Load Libraries

library(tidyverse)

Input Your Own Data

You should enter your data from the two areas below. Use data collected during capture-mark-recapture surveys.

For Two-Sample Estimators (Lincoln-Petersen & Chapman)

# Replace these numbers with your actual field values
M <- 50   # Number marked in first sample
C <- 40   # Number captured in second sample
R <- 10   # Number of marked individuals recaptured in second sample

Estimate Population Size

Lincoln-Petersen Estimate

\[ \hat{N} = \frac{M \cdot C}{R} \]

N_LP <- (M * C) / R
N_LP
## [1] 200

Chapman Estimate

\[ \hat{N}_{Chapman} = \frac{(M + 1)(C + 1)}{R + 1} - 1 \]

N_Chapman <- ((M + 1) * (C + 1)) / (R + 1) - 1
N_Chapman
## [1] 189.0909

Confidence Intervals

Lincoln-Petersen CI

SE_LP <- sqrt((M^2 * C * (C - R)) / R^3)
CI_LP <- c(N_LP - 1.96 * SE_LP, N_LP + 1.96 * SE_LP)
CI_LP
## [1]  92.64638 307.35362

Chapman CI

SE_Chapman <- sqrt(((M + 1) * (C + 1) * (M - R) * (C - R)) /
                   ((R + 1)^2 * (R + 2)))
CI_Chapman <- c(N_Chapman - 1.96 * SE_Chapman, N_Chapman + 1.96 * SE_Chapman)
CI_Chapman
## [1] 107.6129 270.5689

Estimating Population Size from Multiple Sampling Events (Schnabel Estimator)

If you collected more than two rounds of data, use the Schnabel method.

Example Simulated Data (Replace with your own)

# Example simulated data for illustration only
# You must replace this with your own data from Svanninge Bjerge
data <- data.frame(
  time = 1:4,
  C_t = c(40, 35, 50, 45),     # Captured individuals
  R_t = c(0, 5, 8, 10),        # Recaptured (marked) individuals
  M_t = c(50, 60, 75, 85)      # Number of marked individuals before capture
)

Estimate Using Schnabel Formula

\[ \hat{N} = \frac{\sum C_t M_t}{\sum R_t} \]

numerator <- sum(data$C_t * data$M_t)
denominator <- sum(data$R_t)
N_Schnabel <- numerator / denominator
N_Schnabel
## [1] 507.6087

Confidence Interval (Approximate)

SE_Schnabel <- N_Schnabel / sqrt(numerator)
CI_Schnabel <- c(N_Schnabel - 1.96 * SE_Schnabel, N_Schnabel + 1.96 * SE_Schnabel)

CI_Schnabel
## [1] 498.4009 516.8165

Reflection Questions

  1. Compare the population estimates from the three methods. How consistent are they?
  2. Do the confidence intervals overlap? What does that tell you?
  3. How do your results differ between the two woodland areas?
  4. Were the assumptions of these models (e.g., closed population, equal detectability) met in your fieldwork?
  5. How might violations of assumptions affect your estimates?

Summary

You’ve now:

These techniques form a fundamental part of quantitative conservation ecology.