Estimating Animal Numbers Uses Definitions Types of methods and analyses

Estimating Animal Numbers Populations vs. Experimental Units N N N N N N N N N

Estimating Animal Numbers Population Abundance or population size (N) Density Relative abundance/density

Estimating Animal Numbers Types of methods Estimation methods Censuses All individuals observed Complete Sample plots Surveys All individuals not observed Indices Pros & cons Cost Precision & Accuracy

Estimating Animal Numbers Indices Estimating Animal Numbers Censuses Surveys DISTANCE METHODS

Estimating Animal Numbers Censuses Aerial photography/counts Waterfowl Deer Large animals

Estimating Animal Numbers Censuses Thermal IR Large homeotherms

Estimating Animal Numbers Censuses Drive counts Large animals

Estimating Animal Numbers Censuses Total mapping of territories Spot or Territory mapping

Estimating Animal Numbers Censuses Radar

Estimating Animal Numbers Censuses Point counts

Estimating Animal Numbers Censuses Various total counts on plots

Estimating Animal Numbers Surveys Mark-recapture Distance sampling Line transects & point counts Distance methods Removal methods

Estimating Animal Numbers Mark-Recapture Used to estimate abundance and density for many different species Some methods also allow the estimation of survival, population change, and harvest effects Many methods Lincoln-Peterson Schumacher Jolly-Seber Other

Estimating Animal Numbers Mark-Recapture All methods require capturing, marking, and recapturing individuals Capture and marking may not require making contact with animals Natural markings, e.g., jaguars Electronic or photo sensors for recapture Radio-telemetry

Estimating Animal Numbers Mark-Recapture Sample Size & Precision # captures & capture probability # marked # sampling occasions Population size Survival rates

Estimating Animal Numbers Mark-Recapture Lincoln-Peterson Simplest method Mark animals on 1 occasion and record the proportion of animals recaptured on second capture occasion Assumptions Equal catchability among animals and trapping occasions Animals do not lose their marks Marking does not influence survival All marks are correctly recorded Closed population (i.e., no B, D, I, or E during study)

Estimating Animal Numbers Mark-Recapture Lincoln-Peterson Original model N = CM/R Better model N = ((M+1)(C+1)/(R+1))-1 95% CI = …. With and without* replacement where: N = population size at time of marking. M = number of animals marked as a result of the first trapping occasion. R = number of marked animals captured during the second trapping occasion. C = total number of animals (marked and unmarked) captured during the second t rapping occasion.

Estimating Animal Numbers Mark-Recapture Lincoln-Peterson Example: In July, 27 box turtles were marked and released. In September, 23 were recaptured, of which 17 had been marked. Therefore: M = 27, C = 23, and R = 17. Density (N) = ((M+1)(C+1)/(R+1))-1 = ((27+1)(23+1)/(17+1))-1 = 36.3 turtles 95% CI = 31.8 – 45.4 turtles

Estimating Animal Numbers Mark-Recapture Schumacher Method Variation of the Lincoln-Peterson method, using several mark and recapture occasions Assumptions similar to L-P method

Estimating Animal Numbers Mark-Recapture Schumacher Method Model where: Mi = # marked in population prior to the ith day. Ci = # captured (total) on the ith day. Ri = # captured with marks (recaptures) on ith day. Ui = # marked for first time and released on ith day (needed to calculate Mi) N = Σ (CiMi2) Σ RiMi 95% CI = …

Estimating Animal Numbers Mark-Recapture Schumacher Method A frog population sampled over 5 days Day Ci Ri Ui (# newly marked less deaths) Mi 1 32 2 54 18 36 3 37 31 6 68 4 60 47 13 74 5 41 87 N = 93.1 frogs 95% CI = 81.7 – 108.1

Estimating Animal Numbers Mark-Recapture Jolly-Seber Method Animals are marked and recaptured on several occasions Population can be open Each animal must carry a unique mark so it can be determined when each individual was last captured Allows estimation of N & survival (Φ)

Estimating Animal Numbers Mark-Recapture Jolly-Seber Method Assumptions Animals do not lose their marks Captured animals are correctly recorded as marked or unmarked Marking does not affect survival and all animals have the same survival during intervals between samples Equal catchability* Very important & testable Sampling time is negligible in relation to intervals between samples Assumptions can be changed (e.g., survival constant vs. survival different between sampling occasions).

Estimating Animal Numbers Mark-Recapture Jolly-Seber Method Field voles sampled on 11 days Time of capture Time of last capture 1 2 3 4 5 6 7 8 9 10 11 15 37 61 75 77 69 14 19 Total marked (mt) 16 64 79 81 76 Total unmarked (ut) 22 26 32 45 25 12 Total caught (nt) 41 48 82 89 101 107 91 27 Total released (st) 21 46 88 99 106 90 m6

Estimating Animal Numbers Mark-Recapture Jolly-Seber Method Sample Prop. marked Size of marked pop. N 95% CI of N Prob. of Φ 95% CI of Φ 1 0.832 0.546-1.000 2 0.381 17.5 45.9 41.1-69.5 0.395 0.270-0.575 3 0.347 17.2 49.5 48.0-57.9 0.862 0.751-0.961 4 0.458 40.7 88.8 84.4-100.0 0.824 0.739-0.908 5 0.722 70.5 97.7 94.6-104.0 0.925 0.859-0.983 6 0.784 87.5 111.6 108.0-118.7 0.853 0.769-0.937 7 0.759 91.7 120.8 115.3-132.0 0.651 0.565-0.748 8 0.837 76.0 90.8 90.8-194.4 0.104 0.058-0.194 9 0.450 9.3 20.7 19.0-28.9 0.738 0.550-0.927 10 0.571 15.0 26.2 26.2-47.7 11 0.870

Estimating Animal Numbers Mark-Recapture Tests of equal catchability Zero-Truncated Poisson Leslie, Chitty, and Chitty Others Causes of unequal catchability The behavior of individuals in the vicinity of the trap Learning by animals already caught (trap-shy or trap-happy) Unequal opportunity to be caught because of trap position

Estimating Animal Numbers Mark-Recapture Zero-Truncated Poisson Test of Equal Catchability Snowshoe hares captured during 7 days # of times caught (x) # of hares caught (fx) Expected frequency 1 184 174.6 2 55 66.0 3 14 16.7 4 3.2 5 0.5 6 0.1 7

Estimating Animal Numbers Mark-Recapture Zero-Truncated Poisson Test of Equal Catchability Snowshoe hares captured during 7 days Χ2 Goodness of fit test Ho: equal catchability (rejected) Observed Χ2 = 7.77 Critical Χ2 = 5.99 df = 2 (x - 2; x groups combined so all frequencies > 1) α = 0.05 Total individuals captured = 261 Mean # of captures per individual = 1.425 Estimated mean # of captures = 0.756

Estimating Animal Numbers Line Transects & Point Counts Sometimes referred to as Distance Sampling If probability of detection incorporated Used to estimate abundance and density for many species, particularly birds Relatively easy to apply, but labor intensive Involves observing (both sight and sound) individuals within an area of known or estimated size

Estimating Animal Numbers Line Transects Assumptions Animals on the line will never be missed Animals do not move before detection Animals are not counted twice Position and distance to animals are correctly estimated (Hayne & Emlen) Individual observations are independent events Larger counts yield better estimates (>60)

Estimating Animal Numbers Line Transects General methods w c b a L Θ where: D = animal density L = transect length 2w = transect width ai = position of observer bi = sighting distance (distance between animali and observer) ci = perpendicular distance between animali and transect line Θi = sighting angle n = number of individuals counted

Estimating Animal Numbers Line Transects Basic Density Estimate D = n/2Lw Counts usually biased low due to missed individuals Example: Five transects (500m each) were run and 53 scaled quail were counted within 50m of the transect line. D = n/2Lw = 53/(2)(2500)(50) = 0.00021 quail/m2 = 2.1 quail/ha 95% CI or other estimate of variation ?

Estimating Animal Numbers Line Transects Emlen’s Method Assumes that all individuals within a threshold distance are observed. After determining the threshold distance only individuals within this distance are used in calculations Detection probability Models Correction to transect & point estimators (also mark-recapture and other estimators) Radio-telemetry

Estimating Animal Numbers Line Transects Emlen’s Method Scaled quail data 0-10 11-20 21-30 31-40 41-50 51-60 61-70 71-80 81-90 91-100 101-110 111-120 121-130 Perpendicular distance from transect (m) 1 2 3 4 5 6 7 8 # birds D = 40 birds/(2)(60m)(2500m) = 0.000133 birds/m2 = 1.33 birds/ha

Estimating Animal Numbers Line Transects Hayne Density Estimate ≥2 of 3 needed Sighting distance Perpendicular distance Sighting angle DH = … 95% CI = …

Estimating Animal Numbers Point Counts Basic Density Estimate Emlen correction & detection probability (Relative) Abundance estimates (unlimited radius) r D = n/πr2p where: D = animal density n = number of animals counted r = radius of plot p = number of points/plots

Estimating Animal Numbers Distance Methods Called plotless sampling methods Use distance measures Typically, used on plants and sessile animals Estimate abundance, density, and dispersion All methods assume random dispersion (each has test for dispersion) T-square Point quarter Byth & Ripley Ordered distance Variable area transect

Estimating Animal Numbers Distance Methods T-square Measure the distance (xi) from random point (O) to nearest organism (P); then measure the distance (zi) from the organism (P) to its nearest neighbor (Q) with the restriction that the angle OPQ (= the T-square) must be >90° Sample size Random location of points

Estimating Animal Numbers Distance Methods T-square Sample # xi (m) zi (m) 1 12.6 8.7 2 9.3 16.4 3 7.5 4 16.2 5 8.8 3.5 6 10.1 11.2 7 6.2 13.6 8 1.5 9.1 9 14.3 2.7 10 9.6 8.6 11 11.3 7.9 12 8.9 12.1 13 6.3 15.6 14 13.9 9.9 15 10.8 13.7 16 7.6 8.4 N = 2n/π Σ(zi2) = 0.004 tree/m2 95% CI = … = 0.003-0.005 tree/m2 Random dispersion pattern where n = # samples/points Tree example

Estimating Animal Numbers Distance Methods Point Quarter Locate random points; divide area around each point into 90° quadrants; measure the distance to the nearest individual in each quadrant Points must be far enough apart so that the same individuals are not measured more than once

Estimating Animal Numbers Distance Methods Point-Quarter N = 4(4n-1)/π Σ(rij2) = 193 tree/ha 95% CI = … = 140-263 tree/m2 Where: n = # samples/points r = distance from point I to the nearest organism in quadrant j Distance from point to tree (rij; m) Point (i) Quadrant 1 (j) Quadrant 2 (j) Quadrant 3 (j) Quadrant 4 (j) 1 3.05 4.68 9.15 7.88 2 2.61 12.44 19.21 3.87 3 9.83 5.41 7.55 11.16 4 7.41 9.66 1.07 3.93 5 1.42 7.75 3.48 1.88 6 8.86 11.81 6.95 7.32 7 12.35 9.00 8.41 3.16 8 10.18 7.14 2.73 9 3.49 5.70 9.12 8.37 10 5.88 4.15 13.95 7.10 Tree example

Estimating Animal Numbers Removal Methods In these methods, part of the population of interest is removed and the original population is estimated from the progressive decrease in size after subsequent removals. Typically used to estimate density and survival of small mammal and harvested populations. Advantages of removal methods are that they are relatively quick and inexpensive techniques to estimate wildlife populations. These techniques have the obvious disadvantage of significantly affecting the population. Leslie Change-in-ratio

Estimating Animal Numbers Removal Methods Assumptions the probability of being caught is constant for all animals on each harvest occasion capture or removal of one individual does not interfere with capture of other individuals no births, deaths, immigration, or emigration during the trapping period (closed population)

Estimating Animal Numbers Removal Methods Leslie Method This method, also known as the Regression Method, uses simple linear regression to estimate the population before any removals have taken place For reliable estimates of population size, this method requires that a large proportion of the population be removed during each trapping period, and that enough sampling periods are obtained to fit a reliable regression line through the points

Estimating Animal Numbers Removal Methods Leslie Method Example: Snap traps were used to catch short-tailed shrews for 8 days. Trap Day (n) # Shrews Harvested (y) Cumulative Harvested (x) 1 125 2 72 3 91 197 4 82 288 5 55 370 6 90 425 7 48 515 8 40 563

Estimating Animal Numbers Removal Methods Leslie Method Alternatively: Abundance/density estimated by knowing catch and effort at each occasion

Estimating Animal Numbers Removal Methods Change-in-ratio Method Assumptions The population has 2 types of organisms (e.g., males & females) A differential change in the numbers of the 2 types of organisms occurs during the observation period

Estimating Animal Numbers Removal Methods Change-in-ratio Method Ring-necked pheasant data where: P1 = proportion of group 1 before removal R1 = proportion of group 1 after removal K1 = proportion of group 1 in total kill U = overall mortality rate P1 = proportion of females prior to harvest = 550/717 = 0.767 R1 = proportion of females after harvest = 296/349 = 0.848 K1 = proportion of females in total harvest = 185/548 = 0.338 U = │(P1 - R1)/(R1 - K1)│= │(0.767 - 0.848)/(0.848 - 0.338)│ = 0.159 Sex-specific Mortality Females: (U)(K1/P1) = (0.159)(0.338/0.767) = 0.07 or 7% Males: (U)(1 - K1)/(1 - P1) = (0.159)(1 - 0.338)/(1 - 0.767) = 0.45 or 45% Preseason Population = Harvest/Sex-specific mortality Females: 185/0.07 = 2643 pheasants Males: 363/0.45 = 807 pheasants Total: 3450 pheasants Females Males Total Preseason survey 550 167 717 Harvest 185 363 548 Post season survey 296 53 349

Estimating Animal Numbers Indices Types Constant proportion* Frequency Track counts Scat counts Call counts Scent-stations Catch-per-unit effort Flush counts Questionnaires Roadside counts Spotlight counts Aerial counts