Main Points 1) Sources of population variability continued, and count-based PVA -- Example: geometric population growth and condor conservation -- Example: bootstrapping lambdas to estimate time-to-extinction 2) Demographic PVA -- age- and stage-structured matrices Pre-reading: Thursday 9 February: NA Tuesday 14 February: NA Syllabus updates: Tutorial #1 (Extra Credit #1) now due Tuesday 21 February. Help session for Tutorial/Extra Credit #1 now on Thursday 16 February. Jake will send Tutorial/Extra Credit #1 by tomorrow 5pm, he promises! Field Trip: Tuesday 14 February. Meet 920 sharp outside Berry Center entrance on Lewis. If you need Jake to contact your professor from an earlier class, let him know. Terms: bootstrap, age-structured (Leslie) matrix 1
Presentation Groups Thursday 2 March (schedule meeting with Jake by 23 February with outline) Justification, strategy, and successes of single-species conservation efforts -- Meghan B., Katerina, Emily R., Amber Justification, strategy, and successes of multi-species/ecosystem conservation efforts -- Taylor, Macy, Morgan Thursday 30 March (schedule meeting with Jake by 23 March with outline) Justification and strategy of proactive climate change mitigation through federal regulations -- Emily C., Abby, Trevor Economic perspectives of climate change mitigation -- Colman, Jessica, Andrea W. Thursday 20 April (schedule meeting with Jake by 13 April with outline) Justification for pro-animal welfare/anti-hunting worldviews -- Megan D., Reagan, Jaci Justification for consumptive use -- James, Patrick, Brittany Thursday 27 April (schedule meeting with Jake by 20 April with outline) Justification, strategy, and successes of conservation in protected areas -- Karly, Taelyn, Zach Justification, strategy, and successes of conservation in human-occupied landscapes -- Henry, Rhiannon, Jaide 2
Quality = Style + Content Style (45pts): 1) did all group members participate more or less equally in the presentation, and in answering questions? 2) was the delivery clear and professional? In other words, was jargon minimized, were terms well defined, was the delivery polished, and was the material wellunderstood by the presenters? 3) did all group members seem equally familiar with all of the material presented? In other words, were transitions between partners seamless, or did transitions seem awkward? 4) did speakers look at the audiences (as opposed to notes)? 5) did speakers end statements with question marks? Content (45pts): 1) was the presentation focused with a logical introduction, statement of controversy, references to the scientific literature (as opposed to the internet or magazine articles)? 2) were figures and tables explained clearly and succinctly? 3) were slides free of spelling errors and other mistakes? Was use of text on slides minimal? 4) were speakers able to answer questions posed by the audience? 5) did speakers ask the other group thoughtful questions? 6) were there lots of fallback words used (uh, um, like, sort of, etc)? 3
PVA of California Condor Morris and Doak. 2004. Quant. Conservation Biology. 4
Discussion Q: if I release 3 condors each with a p(survival) = 0.6, what are the chances that two individuals are alive after a year, assuming no breeding? Morris and Doak. 2004. Quant. Conservation Biology. 5
Geometric vs Arithmetic Means λ t = N t+1 /N t N t = N 0 λ t 6
Geometric vs Arithmetic Means λ t = N t+1 /N t N t = N 0 λ t, let N 0 = 1000 for this example Nt t lambda 1010 1 1.01 1020.1 2 1.01 1030.301 3 1.01 1040.604 4 1.01 1051.01 5 1.01 1061.52 6 1.01 1072.135 7 1.01 1082.857 8 1.01 1093.685 9 1.01 1104.62 10 1.01 7
Geometric vs Arithmetic Means λ t = N t+1 /N t 1100 1120 N t = N 0 λ t 1080 Nt 1060 Nt t lambda 1010 1 1.01 1020.1 2 1.01 1030.301 3 1.01 1040.604 4 1.01 1040 1020 1000 0 2 4 6 8 10 12 time 1051.01 5 1.01 1061.52 6 1.01 1072.135 7 1.01 1082.857 8 1.01 1093.685 9 1.01 1104.62 10 1.01 8
Geometric vs Arithmetic Means If: N t+1 = λ t N t Then: λ t = N t+1 /N t λ t 0.86 with p = 0.5 1.16 with p = 0.5 9
Geometric vs Arithmetic Means N t+1 = λ t N t 0.86 with p = 0.5 Nt t lambda 1000 1 0.86 λ t 860 2 1.16 997.6 3 0.86 1.16 with p = 0.5 857.936 4 1.16 995.2058 5 0.86 855.877 6 1.16 992.8173 7 0.86 853.8228 8 1.16 990.4345 9 0.86 851.7737 10 1.16 10
Geometric vs Arithmetic Means N t+1 = λ t N t 1100 1050 Nt t lambda 1000 1 0.86 860 2 1.16 997.6 3 0.86 857.936 4 1.16 995.2058 5 0.86 855.877 6 1.16 992.8173 7 0.86 853.8228 8 1.16 990.4345 9 0.86 851.7737 10 1.16 Nt 1000 950 900 850 800 0 2 4 6 8 10 12 time 11
Geometric vs Arithmetic Means N t+1 = λ t N t 1100 1050 Nt t lambda 1000 1 0.86 860 2 1.16 997.6 3 0.86 857.936 4 1.16 995.2058 5 0.86 855.877 6 1.16 992.8173 7 0.86 853.8228 8 1.16 990.4345 9 0.86 851.7737 10 1.16 Nt 1000 950 900 850 800 0 2 4 6 8 10 12 time 12
Geometric vs Arithmetic Means Arithmetic mean = 1.01 λ A = Σ x i t i=0 t Geometric mean = 0.99 λ G = x i t i = 0 p i 13
Geometric vs Arithmetic Means Arithmetic mean = 1.01 XXXX λ A = Σ x i t t i=0 Geometric mean = 0.99 λ G = x i t i = 0 1/t 14
Geometric vs Arithmetic Means N t+1 = λ t N t 1100 1000 Nt t lambda 1000 1 0.86 860 2 0.86 739.6 3 0.86 636.06 4 1.16 737.82 5 0.86 634.53 6 1.16 736.05 7 1.16 853.82 8 0.86 734.29 9 0.86 631.49 10 0.86 Nt 900 800 700 600 0 2 4 6 8 10 12 time 15
Bootstrapping to Conduct Count-Based PVA bootstrapping = resampling data to estimate properties of the data (like mean, variance, standard deviation, standard error, and confidence intervals). 16
Bootstrapping to Conduct Count-Based PVA bootstrapping = resampling data to estimate properties of the data (like mean, variance, standard deviation, standard error, and confidence intervals). We often bootstrap when we have a low n. 17
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Some Perspective: Extinct Genera of Mammals Caloprymnus, extinct 1935 hunted by introduced foxes and cats Prolagus, extinct 1774 hunted by humans Thylacinus, extinct 1936 human persecution, competition and disease from dogs Hydrodamalis, extinct 1768 hunted by humans Beatragus? 19
Hirola Declines Coincided With Elephant Extirpation Ali et al. 2017. J. Appl. Ecol. 20
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 1) From the data, calculate λ for each time step: N t+1 /N t = λ t 21
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 1) From the data, calculate λ for each time step: N t+1 /N t = λ t this will give you a vector of observed lambdas. 11,500/16,000 = 0.72 22
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 2) Draw randomly from vector of observed λ's, and simulate N 2, N 3, N 4, and so forth, until a desired year t: N 1 = N 0 λ 23
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 2) Draw randomly from vector of observed λ's, and simulate N 2, N 3, N 4, and so forth, until a desired year t: N 1 = N 0 λ drawn at random from vector of observed λ's 24
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 2) Draw randomly from vector of observed λ's, and simulate N 2, N 3, N 4, and so forth, until a desired year t: N 1 = N 0 λ starting population size from observed data 25
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 2) Draw randomly from vector of observed λ's, and simulate N 2, N 3, N 4, and so forth, until a desired year t: N b1 = N 0 λ bootstrap projection for population size after 1 year 26
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 2) Draw randomly from vector of observed λ's, and simulate N 2, N 3, N 4, and so forth, until a desired year t: N b1 = N 0 λ N b2 = N b1 λ N b3 = N b2 λ... N bt = N bt-1 λ 27
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 2) Draw randomly from vector of observed λ's, and simulate N 2, N 3, N 4, and so forth, until a desired year t: N b1 = N 0 λ N b2 = N b1 λ N b3 = N b2 λ... N bt = N bt-1 λ for each N b, λ is drawn at random from the observed vector 28
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 3) Repeat many times (100s or 1000s) to generate a distribution of projected population sizes t years into the future. 29
Bootstrapping to Conduct Count-Based PVA 10 years n = 230 95% CI = 100-341 4) Calculate summary statistics on distribution (e.g., mean, variance, standard deviation, CI, etc). 30
Bootstrapping to Conduct Count-Based PVA 10 years population size = 230 95% CI = 100-341 50 years pop size = 19 95% CI = 4-52 100 years pop size = 0 31
Tree Cover Has Increased ~250% Since Mid-1980s Extent of tree cover 1985 Extent of tree cover 2012 Ali et al. 2017. J. Appl. Ecol.
Resource selection coefficient + SE Hirola Avoid Trees Ali et al. 2017. J. Appl. Ecol. 33
Matrix Modeling to Conduct Demographic PVA Most populations in nature are age- or stagestructured; that is, their vital rates depend on age or stage Age and stage-structured matrices account for this variability 34
Matrix Modeling to Conduct Demographic PVA Leslie matrix = projection matrix of age-dependent survival rates and fecundities 6 5 1 >20 yr trees seedlings 15-20 yr trees 4 10-15 yr trees saplings 5-10 yr trees 2 3 35