Population Parameters and Their Estimation Data should be collected with a clear purpose in mind. Not only a clear purpose, but a clear idea as to the precise way in which they will be analysed so as to yield the desired information. M.J. Moroney The greatest obstacle to discovering the shape of the earth, the continents, and the ocean was not ignorance, but the illusion of knowledge. D.J. Boorstin Poor data result in poor management recommendations. Thousands of biologists, originator unknown Why Estimate Population Parameters? Assess effects of management Track population trends Learn how populations function Uses of Survey Results you don t even know how many deer you have! Population trend Sex ratio Fawn survival Age structure Set harvest rates Scouting Intangibles (health, effects of drought, etc.) Estimate + Harvest recommendation + Difference in values = Conflict Make sure that you know the limitations of population estimates! Population Terms Population Estimation Terms Population Group of animals that occupy a certain area at a certain time This definition for population estimation Population size = total number of animals Population density: is the number of individuals per unit area (e.g., 45 white-tailed tailed deer per mi 2 ). Relative density: refers to the ranking of populations by density (e.g., Area A has 50% more white- tailed deer than area B). Census: a complete count of an entire population of animals. 1
Population Estimation Terms Population estimate: an approximation of the true population size based on some method of sampling animals, such as by capturing or counting them. A robust population estimate is still valid even when some of the assumptions of the estimation procedure are violated. Closed population: there are 2 components... demographic closure and geographic closure. Demographically closed populations have no births (natality)) or deaths (mortality) during the sample periods. Geographically closed populations have no movements into (immigration) or out of (emigration) the population during the sample periods. Population Estimation Terms Open population: a population that is not closed. Population index: a statistic that is related to population size. Use of indices is limited to comparisons between populations on the same area over time or between different areas at the same time because the exact relationship between the index and the true population frequently is not known. Population Parameters Births Deaths Population size and structure Abundance = numbers Density = animals/area Sex and age ratios = Males:Females, Fawns:Doe Demographic rates Birth = births per female Death = # deaths / # alive Population Males Adults Females Young Immigration Emigration These are frequently not considered, even by experienced biologists Immigration Dispersal Emigration Open or Closed???? Open or Closed??? 2
Open or Closed??? Open vs. Closed Populations Fenced Unfenced Open vs. Closed Population DISPERSAL All of these parameters are necessary to determine the rate of population growth (or decline) Population size (N Idealized, Theoretical model Time (t) Real Populations Observability and Sampling Management Good Rains Hurricane Observability Not all animals can be seen or captured Population Size (N Overharvest Drought Sampling Not all of area can be surveyed Time (t) 3
Observability Not all animals (N) in the area of interest are seen or captured. The probability (β) of sighting or capturing an animal is <1. Observability The relationship between a count (C), which is the number of animals seen or captured, and the true population is... C = β N Estimating the population size is a matter of dividing the count by an estimated observability... N = C β Observability - Example N = C β Count = C = 178 Observability = β = 0.47 Population Size = N =??? N = 178 0.47 N = 379 Sampling Usually, the entire area of interest cannot be surveyed. Therefore, biologists must sub-sample. C s represents the count on the sample area and represents the proportion of the entire area sampled. N = C s Observability and Sampling Combine the Observability and the Sampling equations and we get... N = C β + N = C Terminology Census* if the Observability (β) and Sampling ( ) coefficients = 1 Survey/Count if the Observability (β) and Sampling ( ) coefficients 1 N = C ( β ) * Note - A census is rarely possible in wildlife management. 4
Page 68, Fig. 3 Page 68, Fig. 3 Population Estimation Methods Population Estimation Methods All individuals seen β = 1 All individuals not seen β 1 All individuals seen β = 1 All individuals not seen β 1 Counts Recapture Removal Line Transect Drive Counts Thermal Scanners Population Reconstruction Lincoln Peterson Non-Selective Selective Spotlight Surveys Catch Per Unit Effort Change In Ratio In South Texas Helicopter Surveys Helicopter Spotlight Well researched by CKWRI DeYoung 1985 Beasom et al. 1986 Leon et al. 1987 DeYoung et al. 1989a DeYoung et al. 1989b Sullivan et al. 1990 Using Marked Deer. Basic approach in helicopter survey research was to use resightings of individually marked deer. Helicopter Transects (count in fixed strip or line transect) Fenced Unfenced 5
Accuracy of Helicopter Surveys Measured extremes of 17% to 67% 600 Line Transect Method (strips) Example of Decline in Deer Counted with Increasing Distance from Flight Line, Faith Ranch, 1986 (DeYoung et al. 1989) Averages in the 35% range for 3-seat helicopters Many variables involved Height Speed Weather Experience Brush Time of year Helicopter model Deer behavior Coverage Number of Deer Counted 500 400 300 200 100 0 0-20 yds 21-50 yds 51-100 yds Distance from Flight Line Example of Repeated Counts (total deer) in same year on 5,000 acres 200 Simulated Deer Population Trends Randomly Selected from 4 or 5 Yearly Helicopter Surveys Flight 1986 1987 1988 1989 1 200 153 116 115 2 143 97 77 69 3 205 105 96 70 4 199 91 122 55 5 116 137 Number of Deer Counted 150 100 50 1986 1987 1988 1989 Year 0.300 Portion of female deer by age available (202 marked) and observed on repeated helicopter surveys 0.250 Portion of male deer by age available (112 marked) and sighted on repeated helicopter surveys Portion Available or Sighted 0.250 Observed 0.200 0.150 Available 0.100 0.050 1 2 3 4 5 6 7 Age Portion Available or Sighted 0.200 Sighted 0.150 Available 0.100 0.050 1 2 3 4 5 6 7 Age 6
Undercount of fawns greater than undercount of adults, 1986-88 Ranch Marked Sighted Camaron 0.20 0.14 Faith 0.26 0.21 Percent Accuracy of Classing Bucks as Mature vs. Young Ranch 1986 1987 1988 Camaron 82 100 79 Faith 96 89 92 Both 0.23 0.18 Helicopter Survey Summary Overall: Accuracy about 35% and variable Count-to-count variability high, use for trend Sex ratio unbiased but variable count-to-count Undercount of fawns compared to adults; variable Buck classification to young and mature good Population Estimation Methods All individuals seen β = 1 All individuals not seen β 1 Recapture Spotlight Surveys Removal Line Transect Counts Obtain counts on other species such as quail Good, quick feel of deer population Scouting Lincoln Peterson Non-Selective Catch Per Unit Effort Selective Change In Ratio Spotlight Surveys Spotlight Surveys Estimating Area Counted CKWRI has also researched Spotlight Counts Fafarman, K. R., and C. A. DeYoung. 1986. Evaluation of spotlight counts of deer in south Texas. Wildlife Society Bulletin 14: 180-185. Hahn technique Measure visible area perpendicular to line after count Line Transect technique Measure distance and angle of each sighting 7
Hahn : Standard Spotlight Counts Set up a route - Where? Mesquite Caliche Hills The transect has a fixed width (the maximum observation distance) that is measured at 0.1 mile increments for the length of the transect Mixed Brush Pasture Is your sample representative? Mesquite Caliche Hills Mesquite Caliche Hills Pasture Pasture Mixed Brush Mixed Brush Stratify your sample and sample the habitat proportionately. Spotlight Surveys Mesquite Caliche Hills There are more sophisticated ways to conduct a spotlight count Mixed Brush Pasture Line Transect Methods Sightability Functions Program TRANSECT Probability of sightin 1 2 3 4 5 6 7 8 Distance from transect 8
Line Transect Counts are assumed to be incomplete. The proportion of animals actually seen ($) must be estimated. $ is the sighting or detection probability Actual counts must be corrected using $ Requires perpendicular distance data or or both sighting distance and sighting angle Line Transect x i = perpendicular distance from the line to the detected animal i (or center of a group). r i = distance from the observer to the detected animal i at the moment of detection. 2 i = the angle between the line of travel and line of sight to the animal at detection. Sighting Distance and Angle r i x i 2 Line Transect Data Total number of animals detected (n) Corresponding perpendicular distances (x ), i or both the sighting distances and angles (r i and 2). Estimation uses these data and the known transect length (L) and width (2w). w is the maximum observation distance, so the width of the strip you surveyed is 2w Line Transect Assumptions In order from most to least critical: 1. All animals located directly on the line are detected (detection probability = 1.0) 2. Animals are fixed at the location where they are initially sighted (they do not move before being sighted) and none are counted twice 3. Distances (and sighting angles if taken) are measured exactly 4. Sightings are independent events (flushing of 1 animal doesn t cause another to flush) Line Transect Assumptions The basic idea behind line transect or similar distance sampling methods: The probability that you will see the animal decreases the farther it is from the line The distance data (x ) i are used to estimate this probability by treating it as a mathematical function g(x) g(x) is the conditional probability of seeing an animal when it is located distance x from the transect line: g(x) = Pr {animal observed x} 9
Maximum sighting distance w Detection Probability and Sighting Distance Expected Perpendicular Distance Data 8 7 6 Chances you will see the deer decrease with distance Number Seen 5 4 3 2 1 g(x) 0 0 10 20 30 40 50 60 70 80 90 100 110 120 Perpendicular Distance Deer on the line: detection probability = 1.0 If sample size is large and we see many animals, we can approximate g(x) Plot a histogram of animals seen grouped by distance from observer g(x) is approximated by drawing a smooth curve through the histogram Actual Perpendicular Distance Data Spotlight Counts Number Seen 9 8 7 6 5 4 3 2 1 0 0 10 20 30 40 50 60 70 80 90 100 110 120 Perpendicular Distance Works best in relatively open habitats On Welder Wildlife Refuge, was more accurate than helicopter, but still conservative In practice, samples are usually irregular. Critical: have sufficient sample 0.5 Fawns/Doe from Repeated Spotlight Counts by Month, Welder Wildlife Refuge (Fafarman and DeYoung 1986) 50 Effect of Time of Night on Spotlight Counts Fawns/Doe 0.4 0.3 0.2 0.1 Deer Counted (deer/sq. km) 40 30 20 10 0.0 August September October Month 0 0 13 33 55 69 Percent of Darkness Passed 10
Spotlight Count Summary Accuracy depends on cover Decent in open habitats Poor in dense brush Population Estimation Methods All individuals seen β = 1 All individuals not seen β 1 Density estimates variable Repeated counts advised Counts Sex ratio accuracy poor, variable Fawns/doe accuracy poor, variable Depending on month Lowest counts just after dark Recapture Lincoln Peterson Non-Selective Catch Per Unit Effort Removal Selective Change In Ratio Line Transect Spotlight Surveys Research Advance Photo The density of cameras determines the sampling coefficient ( ) and the observability coefficient (β). Bring the deer to you! The relationship between the number of unique bucks photographed and the total number of bucks photographed eliminates double sampling. 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1 / 100 acres Winter Fall The sampling coefficient ( ) observability coefficient (β) changes with the number of days the cameras were operational 1 2 3 4 5 6 7 8 9 10 11 12 13 14 DAYS Total Bucks Photographed = 178 Unique Bucks Photographed = 37 Proportion of Unique Bucks = 37 178 = 0.208 This is called the Population Factor This is used to determine the number of unique does and fawns photographed 11
If the cameras were run in the winter for 7 days at a density of 1 camera per 100 acres... The combined Sampling Intensity ( ) and Observability (β) coefficient = 0.8 (from graph) 100% 90% 80% 70% 60% 50% 40% 30% 20% 10% 0% 1 / 100 acres Winter Fall 1 2 3 4 5 6 7 8 9 10 11 12 13 14 DAYS Determine the number of unique deer Total bucks photographed = 178 Total does photographed = 236 Total fawns photographed = 124 178 0.208 = 37 236 0.208 = 49 = 112 Total Deer 124 0.208 = 26 Finally, determine how many deer occupy your tract of property Divide by the combined sampling and observability coefficient ( β) 112 0.8 = 140 deer Surveys Basic approach is to identify number of bucks by antler characteristics Adjustments needed if a lot of spikes are present *****Assume***** does and fawns are sighted at same rate as bucks Calculate population size Number of Bucks Identified During Surveys in Experimental Enclosures on the Comanche and Faith Ranches Ranch Density Long-term 12-day Comanche High 21 6 Medium 10 7 Low 7 4 Faith High 9 8 Medium 9 3 Low 7 10 *** Not all deer come to bait or are photographed 12
Preliminary Population Estimates in Experimental Enclosures on the Comanche Ranch Ranch Density Long-term 95% CI 12-day Comanche High 29 21-42 9 Medium 25 17-46 8 Low 18 4-48 9 Summary Promising in published Literature Preliminary results from S Texas (Comanche-Faith study) suggest undercount Appears best suited for small ranches High camera density needed for good results Population Estimation Methods All individuals seen β = 1 All individuals not seen β 1 Population Reconstruction Counts Population Estimation Methods Recapture Removal Line Transect All individuals seen β = 1 All individuals not seen β 1 Lincoln Peterson Non-Selective Selective Closed Models 2-sample: Lincoln Peterson Multiple Samples: Program CAPTURE Spotlight Surveys Drive Counts Thermal Scanners Population Reconstruction Open Models Jolly-Seber Putting Population Estimates in Perspective Even when estimates are useful, they do not provide all the answers. Proper estimates of population size before and after management action give strong inferences about ability of the action to influence population size. Putting Population Estimates in Perspective Fundamental explanations of how and why the population responded may be more important. All changes in population size are the result of 4 basic demographic variables: Mortality Reproduction Emigration Immigration 13
Summary When animals can be seen easily, observationbased methods are preferred. When large areas must be surveyed and animals are visible, aerial surveys are used. When all animals can be observed, total counts may be obtained. Summary Methods involving development of a sighting probability model are suited to mobile animals, animals in groups. If animals are visible from the ground, distance sampling methods are used. In hunted or trapped species, removal methods may be useful. Summary There is no single best method to estimate population size. All methods are potentially useful under some conditions. Selection of a method depends on biology and habits of the species, how the data will be used. Using Survey Data Regardless of the survey technique, data must be used carefully Use as trend data, DO NOT CALCULATE HARVEST RATES FROM YEARLY COUNTS!! Deer populations seldom change dramatically from year-to-year Use in conjunction with other information on deer herd for management decisions Final Thought There are ALWAYS more deer than you think there are! 14