class: left, title-slide .title[ # Counting animals ] .subtitle[ ## EFB 390: Wildlife Ecology and Management ] .author[ ### Dr. Elie Gurarie ] .date[ ### September 10, 2024 ] --- <!-- https://bookdown.org/yihui/rmarkdown/xaringan-format.html --> .pull-left-60[.content-box-blue[ ## Goals of wildlife management 1. make them increase 2. make them decrease 3. keep them stable 4. do nothing - but keep an eye on them ]] -- .pull-right-60[.content-box-yellow[ ## What do we need to know!? ]] --- # A count can be simple .pull-left.footnotesize[ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 127, 128, 129, 130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141, 142, 143, 144, 145, 146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157, 158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169, 170, 171, 172, 173, 174, 175, 176, 177, 178, 179, 180, 181, 182, 183, 184, 185, 186, 187, 188, 189, 190, 191, 192, 193, 194, 195, 196, 197, 198, 199, 200 ] .pull-right[] --- # ... or a count can be pretty darned complex Variance on the estimator of the variance of a **Pacific cod** count based on on-deck observations of harvest in pots:  .center[Miller 2005 (Ph.D. dissertation)] --- # An observation .center[] .large.center.blue[Counting **fish** is just like counting **trees**, except they're *invisible* and they *move* ...] .center[] --- background-image: url('images/aerialcount.jpg') ### .white[Three broad approaches (with sub-categories)] .pull-left-60[.full-width[.shadow[.content-box-yellow[ 1. **Compete census** (total count) 2. **Sample count** - Counts along transects or variable plots 2. **Mark-racapture/resight** 3. **Population index** - count *signs* or *correlates*, not *animals* ]]]] --- background-image: url('images/aerialcount.jpg') ## .white[Some considerations] .pull-left-70[.full-width[.shadow[.content-box-yellow[ - Do I **need** absolute numbers? - How **precise** of an estimate do I want? - How **accurate** of an estimate do I need? - What is the **cost** of the estimate? - Is an **index** sufficient? - How **frequently** do we need to survey/census? ]]]] --- ## Two important considerations:  --- .pull-right-60[] ### Accuracy Is the estimate .blue[**biased**]? - .green[On average, on target] Determined by **design**. - .green[how well you throw the dart?] Can be difficult to assess. - .green[because there isn't usually a dartboard!] -- ### Precision What is the .green[*error*] or .green[*variance*] or .green[*spread*] on the resulting estimate? Quantified with .green[**Confidence Intervals (C.I.)**] (or .green[coefficients of variation (C.V.)]) Determined by **effort** and computed with (sometimes very fancy) **statistics**. .center.content-box[ Generally: bigger the **sample** = smaller **error** = higher **precision**. ] --- ### Very accurate, but very imprecise:  .content-box-green[ *“It could be anything ranging from **something that would endanger the lives of hundreds of millions** of people to something that **has no impact on anything whatsoever**. That’s how vague the classified categorization is,” Alex Wellerstein, a historian of science and nuclear weapons, told me.*] --- ### General Goal of Abudance Estimation .large.content-box-blue[ Increase both **accuracy** and **precision** as contraints on **effort** (& costs). *Generally*, there a higher premium on **accuracy** - (i.e. better an unbiased but imprecise estimate, than a highly precise but biased estimate). ] -- ### When might BIAS not be so important? -- .large.content-box-yellow[ If the bias is consistent, repeated measures can tell you how things are *changing* ] --- ### Method I: Total Count, aka. **Census** .pull-left-60[ #### Pros - Simple to explain! - Simple math (*arithmetic*)! - Very precise #### Cons - Usually - VERY difficult / expensive to perform - Only possible for certain kinds of animals - Almost always biased! .red[***What kinds of animals can we census?***] ] .pull-right-40[] --- background-image: url('images/elephantcensus.jpg') background-size: cover ## .white[**Census Examples**] .full-width[.shadow[.content-box-yellow[ - U.S. Census - Hippopatomuses in clear rivers* - Large game (elephants, rhinos, wildebeest) within some parks / game reserves in African savanna* - Apparently - until the 1950's - many deer / elk herds in the West.* *- .small[*examples from Fryxell book ... but a bit tricky to confirm.*]]]] --- ### Northern Fur Seals *Callorhinus ursinus* .pull-left[  ] .pull-right[  ] .pull-left[ .small[ - Once extemely abundant - VERY heavily harvested - Paid off 1867 purchase Alaska in 30 years - Reproduce (essentially) in only 6 **rookeries** worldwide - At heart of the first international wildlife management treaty. ]] .pull-right[] --- background-image: url('images/countem_tuleny.jpg') class: bottom .white.center[ ###**Count 'em!** Tyuleni Island] --- background-image: url('images/LyoshaCounts.jpg') background-size: cover ## Lovushki Island Fur Seal Pup Count **technology:** Count Clickers | Notepad --- background-image: url('images/bamboopoles.jpg') background-size: cover ## Lovushki Island Fur Seal Pup Count **technology:** Bamboo poles for self-defense --- ## Fur seal count: Source of variation? -- ### Individual counters  Pretty good agreement. --- ## Fur seal count: High Precision! .pull-left-60[  ] .pull-right-40[ **Point Estimate:** `\(\widehat{N} = 28,792\)` **Standard Error (s.e.):** `\(\sigma_e = 216\)` **95% Confidence Interval** `\(\widehat{N} \pm 2 \sigma_e = (28,630 - 29,220)\)` **Coefficient of variation** `\({\sigma_e \over \widehat{N}} = 0.75 \%\)` ] --- background-image: url('images/WikiFurSeals.jpg') background-size: cover ## .white[**Fur seal count: what about accuracy?**] .pull-left-40[.content-box-blue[ What are potential sources of *error* (bias)? What *direction* is that bias in?] ] --- background-image: url('images/WikiFurSeals.jpg') background-size: cover ## .white[**Fur seal count: Ecological question?**] .pull-left[.content-box-blue[ What does **the number of pups** really tell you about a population? ]]