background-color: #fdf6e3 background-image: url(../image-library/royalsociety//penguin-swim.jpg) background-position: center background-size: 120% class: center, top # Conservation decision-making under long transients ## Carl Boettiger ### *UC Berkeley* --- layout: true background-color: #fdf6e3 class: top --- class: center, top # What could possibly go wrong? <img src="../image-library/royalsociety//penguin-swim.jpg" width="500px"> ??? Image credit: [Royal Society Photo Competition](https://royalsociety.org/journals/publishing-activities/photo-competition/) --- <div style='float:left;width:50%'> <img src='img/city-slice.jpeg' style='transform:translate(-22%, -10%);height:100%;object-fit:cover;overflow:hidden'> </div> # in an era of predictive black-box models... --- <div style='float:left;width:50%'> <img src='../image-library/royalsociety//pensive-polarbear-slice.jpg' style='transform:translate(-22%, -10%);height:990px; width:1329; overflow:hidden'> </div> # ... a need for theory & process-based models --- background-image: url(../image-library/royalsociety//snake.jpg) background-position: center background-size: 120% class: center, top # Ghost Attractors --- class: center # Ghost Attractors ![](img/ghost.png) <br/> Hastings et al. *Science* (2018) --- # A Ghost Attractor ![](index_files/figure-html/unnamed-chunk-3-1.png)<!-- --> --- # Simple ARIMA forecast: ![](index_files/figure-html/arima_data-1.png)<!-- --> --- # Simple ARIMA forecast: ![](index_files/figure-html/arima_forecast1-1.png)<!-- --> --- # Simple ARIMA forecast: ![](index_files/figure-html/arima_forecast-1.png)<!-- --> --- class: left # Statistical Issues .pull-left[ - sufficient data - accurate measurements - appropriate model - numerical/computational issues - ... ] .pull-right[ <img src="../image-library/royalsociety//ballons.jpg" width="400", style="float:center"> ] --- class: left # Theoretical Issues .pull-left[ ... Issues run deeper: transients hard to infer *even under idealized conditions* #### *Stochastic* dynamics *qualitatively* alter the picture ] .pull-right[ <img src="../image-library/royalsociety//pensive-polarbear.jpg" width="400", style="float:center"> ] -- Knowing the correct model is not enough --- ### A look at a candidate model `$$X_{t+1} = X_t + \underbrace{X_t r \left(1 -\frac{X_t}{K} \right)}_{\textrm{logistic growth}} - \underbrace{\frac{a X_t ^ Q}{X_t^ Q + H ^ Q}}_{\textrm{saturating consumption}} + \underbrace{\xi_t X_t}_{\textrm{environmental noise}}$$` ![](index_files/figure-html/theory_f-1.png)<!-- --> --- ## potential well diagram ![](index_files/figure-html/theory_U-1.png)<!-- --> --- ## deterministic skeleton timeseries ![](index_files/figure-html/det-1.png)<!-- --> --- # Stochastic simulations ![](index_files/figure-html/stoch1-1.png)<!-- --> --- # Stochastic simulations ![](index_files/figure-html/stoch2-1.png)<!-- --> --- # Stochastic simulations ![](index_files/figure-html/stoch_all-1.png)<!-- --> --- # Stochastic simulations ![](index_files/figure-html/ensemble-1.png)<!-- --> --- # Stochastic simulations ![](index_files/figure-html/wtf-1.png)<!-- --> --- # Stochastic simulations **First-passage times** ![](index_files/figure-html/fpt-1.png)<!-- --> --- class: top, left ## Long transient dynamics can ## also create stochastic phenomena -- - Emergent ensemble dynamics not predicted by the deterministic model -- - But intuition is simple: noise helps 'jump' the ghost -- - Noise creates dynamics that are deeply challenging for both inference & decision-making... --- background-image: url(../image-library/royalsociety//reef-shark.jpg) background-position: center background-size: 120% class: center, top # Challenges to Model Inference --- # Model Inference Given time-series observations, *can we distinguish* **ghost** attractors from **real** ones? ![](index_files/figure-html/disc_sims-1.png)<!-- --> --- class: left # Model Inference Hierarchical Bayesian estimation of stability ```r library("greta") mean <- x_t + r * x_t * (1 - x_t / K) - a * x_t ^ q / (x_t ^ q + b ^ q) distribution(x_t1) <- normal(mean, sigma_g * x_t) a <- uniform(.25, .34) # Prior draws <- mcmc(model(a), n_samples = 1000, warmup = 3000, chains = 4) ``` Using TensorFlow(R) via `greta` R package, <https://greta-stats.org> --- class: left # Model Inference ![](index_files/figure-html/posteriors-1.png)<!-- --> --- # Model Inference (Full ensemble 500 length-3000 replicate timeseries) ![](index_files/figure-html/unnamed-chunk-6-1.png)<!-- --> --- background-image: url(../image-library/img/chess.jpg) background-position: left background-size: 120% class: center, bottom # Decision Theory --- class: center # Decision Theory .pull-left[ ## Societal Dynamics Utility function `\(U(x_t,a_t)\)` Given state `\(x_t\)` and action `\(a_t\)`, balance costs and benefits. <img src="../image-library/royalsociety//balance.jpg" width="300px"> ] -- .pull-right[ ## Ecological Dynamics Transition function (forecast probabilities) `\(f(x,a)\)` <img src="index_files/figure-html/posteriors-1.png" width="400px"> ] --- class: middle, center # Potential contexts -- *Tipping point or ghost?* --- background-image: url(../image-library/royalsociety//forest-fire.jpg) background-position: center background-size: 120% class: center, top --- background-image: url(../image-library/royalsociety//methane_bubbles.jpg) background-position: center background-size: 100% class: center, top --- background-image: url(img/flickr-vsmoothe-pine-beetle.jpg) background-position: center background-size: 100% class: center, top --- ## True model: weak ghost attractor ![](index_files/figure-html/true_a-1.png)<!-- --> --- ## Incorrect belief of bistable system ![](index_files/figure-html/a29-1.png)<!-- --> --- ## Incorrect belief of stronger bistable system ![](index_files/figure-html/a31-1.png)<!-- --> --- ## Simulation under *no intervention* ![](index_files/figure-html/unnamed-chunk-9-1.png)<!-- --> --- ## Mistaken ghost for alternate stable state ![](index_files/figure-html/mistaken_ghost-1.png)<!-- --> --- class: center # Adaptive Management: ### Updating beliefs <img src="../image-library/royalsociety//waiting-in-the-shallows.jpg" width="450"> -- *Reinforcement Learning* -- (Markov Decision Process over possible models with Bayesian updating) --- ## Prior beliefs ![](index_files/figure-html/priors-1.png)<!-- --> --- ## Learning late ![](index_files/figure-html/learning-1.png)<!-- --> --- ## Outcome ![](index_files/figure-html/unnamed-chunk-10-1.png)<!-- --> --- ## More agnostic prior beliefs ![](index_files/figure-html/priors_wide-1.png)<!-- --> --- ## Less learning, more caution ![](index_files/figure-html/less-learning-1.png)<!-- --> --- ## Less learning, more caution ![](index_files/figure-html/unnamed-chunk-11-1.png)<!-- --> --- class: middle # An emergent precautionary principle? <!-- Better to be ignorant than wrong --> --- class: top, left # Conclusions <img src="index_files/figure-html/arima_forecast-1.png" width="100px" height="60px"> Ghost attractors look like real attractor but behave differently -- <img src="index_files/figure-html/wtf-1.png" width="100px" height="60px"> Stochastic ghosts `\(\neq\)` deterministic ones -- <img src="index_files/figure-html/posteriors-1.png" width="100px" height="60px"> This makes model inference hard! -- <img src="../image-library/royalsociety//forest-fire.jpg" width="100px" height="60px"> .. and can lead to very bad decisions! -- <img src="index_files/figure-html/learning-1.png" width="100px" height="60px"> Reinforcement learning can help deal with uncertainty -- <img src="index_files/figure-html/less-learning-1.png" width="100px" height="60px"> Precaution is sometimes better than knowledge --- class: center, top background-image: url(../image-library/royalsociety//penguin-swim.jpg) background-size: 140% # Thanks! --- class: center # Acknowledgements .pull-left[ Image Credits: ![](../image-library/sponsors/royalsociety.jpg) ![](../image-library/sponsors/noaa.png) Lizzie Wolkovich Henry Scharf ] .pull-right[ ![](../image-library/people/hastings.jpg) ![](../image-library/sponsors/nimbios.jpg) ] Code, slides, etc: <https://github.com/cboettig/decisions-vs-transients> --- # Traces for single time-series ![](index_files/figure-html/unnamed-chunk-12-1.png)<!-- --> --- # Traces for the ensemble fit ![](index_files/figure-html/unnamed-chunk-13-1.png)<!-- -->