The Scenario. From today s lecture (and readings!) you should be able to : Steps in Conducting an Assessment using Inventory and Monitoring

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1 Goals: Sampling Populations with Incomplete Counts Mark-Recapture Methods 1. Understand the concept of indices of abundance and their limitations. 2. Understand the concept of mark-recapture methods, their strengths, and limitations. 3. Appreciate how these methods can be applied to wildlife issues that are likely to confront wildlife biologists Readings: Elzinga Ch. 13 Wedn lab on Nov 17 will allow hands-on experience with today s topics; see class web site for links to further materials on mark-recapture Bring to lab Donovan and Weldon s chapter on mark-recapture (in Quinney Reserve) From today s lecture (and readings!) you should be able to : Understand the difference between: Sample vs Census Actual vs relative population size Understand what is meant by detection probability and why it is an important issue for monitoring animal populations Be able to explain strengths and limitations of mark-recapture methods Know what is meant by assumptions of a model Understand the concept behind the Lincoln-Petersen estimator Steps in Conducting an Assessment using Inventory and Monitoring 1. Develop Problem Statement may include goals 2. Develop specific objectives 3. Determine important data to collect 4. Determine how to collect and analyze data When incomplete counts are expected The Scenario 5. Collect data 6. Analyze data 7. Assess data in context of objectives 1

2 The Verdict The transport company was found responsible for the spill Required to provide funds for restoration efforts. It was agreed upon that efforts would continue until tadpole density was within % of the average number of tadpoles of the 5 adjacent ponds Problem Statement Were restoration efforts successful in increasing tadpole numbers to a similar level to non-impacted ponds 5 years after the spill? Beagley and Associates, a private consulting firm with headquarters in Logan UT, was contracted to conduct the surveys (due in part to FRWS 3700 Certification) Tadpole Density Low High Graphically Identify the Question Impacted Pond % difference? Yes No Adjacent Ponds Done Phase II The Problem Tadpoles are nearly impossible to census (recall census?) Design a study to estimate the actual or relative population size of tadpoles 2

3 Estimation Population Assessment Techniques Many estimators exist; each has its own set of assumptions, limitations, and field costs. The common issue is simple, important, and usually forgotten: probability of detection Population Estimation Methods All Individuals Seen B = 1.0 Complete Census Counts on Sample Plots Not All Individuals Seen B < 1.0 Indices Capture Distance-based Methods Capture Recapture Removal Modified from Lancia et al Indices of Relative Abundance Definition: A measure that has a proportional relationship to abundance No. Tadpoles/trap= B * Pop. Size of Tadpoles an index to abundance may be potentially useful Lets explore this. Abundance Index (e.g.,tadpoles/trap) Low High Low What does the slope represent? 2X 2X High What does the slope represent? Recall the equation for a straight line: Y = mx + b Y = abundance index m = slope X = actual abundance b = Y-intercept [value of Y when X=0] Abundance Index (e.g.,tadpoles/trap) Low High Low High 3

4 Indices of Relative Abundance Y = mx + b In our case, Index = 0 when abundance=0, so b = 0 and Y = mx Look familiar? Index (tadpoles/trap) = B * The slope, m, = B, the proportionality constant Assumptions The index assumes that the proportionality, B, is constant among ALL comparisons (in this case, ponds). And at all densities examined see Elzinga for discussion on this issue High Thus, m = B = change in Y / change in X What happens when B changes? Low Abundance Index (e.g.,tadpoles/trap) What does the slope represent? Index (Tadpoles/Trap) 15 Detection probabilities (or proportionality) may differ among observers, ponds, or methods Index (Tadpoles/Trap) As long as comparisons are made within the context of a constant B, inferences are valid Why would detection probabilities potentially vary among these ponds? Consider the biology of the situation and sampling issues 4

5 If detection probability (or proportionality) varies, then we need to (1) change (and test) sampling technique to ensure it doesn t Or (2) use a method that does not require equal detection probabilities among comparisons. Trap Design A mark-recapture design was decided upon. Tadpole traps were to be placed at 5 m intervals Tadpoles were to be marked with vi-alpha tags An Example with a Mark-Recapture Method The Lincoln-Petersen Estimator An Example with a Mark-Recapture Method The Lincoln-Petersen Estimator A frequently used example because of its clear conceptual basis for us, a starting point (page 234 in Elzinga) Allows us to test the assumption of equal detection probabilities of the index to abundance Allows us to take the differences in capture probability into account The estimator in its most conceptual form: n1/n=m2/n2, N=number tadpoles in a given pond n1=number tadpoles captured and marked in first day of trapping n2=total number of tadpoles captured in 2nd day of trapping m2=number of marked (from day 1) tadpoles in second sample 5

6 The Key Concept Behind the Lincoln-Peterson Method The proportion of animals marked in the second sample should be equal to the proportion marked in the entire population, and an estimate of the total population size is thereby obtained. Elzinga et al. chapter 13 A Closer Look Does this ratio make sense? n1/n=m2/n2 To make it clear, we ll cheat: We know the truth that N=12 The number captured and marked at the first sample, n1=.. What? 6 it is, n1=6 which is half of the true population Because we captured 50% of the population, the detection probability, p1 = 0.5 (6/12) n1/n = m2/n2 Key Point: we KNOW the number of marked animals that we COULD detect again and that is all we would normally know right? If p2=p1, then what percent of the marked frogs should be caught ( detected ) in the second sample???? m2/n2=n1/n So : N=12, n1=6, n2=6, m2=3 3 is to 6 AS 6 is to 12 The ratio of marked animals to N (n1/n) will be the same as the ratio of marked animals in the sample (m2/n2) Written to solve for N, ^ N = (n1*n2)/m2 Composition of Frog Population After First Sample ^ N = (6*6)/3 =12 6

7 The LP estimator is valid if and only if: Assumptions: What are assumptions? 1. Closure a. demographic b. geographic 2. Tags are not lost 3. Equal prob. of detection among ALL individuals (marked and unmarked alike) Two issues to ponder.. What happens when you violate these assumptions? If detection probability is 0.5, will 50% of the population ALWAYS be detected? Consider a coin flip? Effect on estimates? We will explore these issues in lab Back To Indices Mark-Recapture is ONE of several methods that estimate detection probabilities And is ONE of several ways to evaluate the constant proportionality assumption of indices of abundance Redesigning the Tadpole Study Use a mark-recapture design that allows estimation of pondspecific capture probabilities Evaluate how well assumptions of LP method are met Evaluate study design through simulation exercises. 7