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https://github.com/gottacatchenall/thesis_proposal

its the thesis proposal
https://github.com/gottacatchenall/thesis_proposal

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its the thesis proposal

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# Introduction



Within the last several hundred years, human activity has induced

rapid changes in Earth's atmosphere, oceans, and surface. Greenhouse

gas emissions have caused an increase in the temperature of both

Earth's terrain and oceans, and both agricultural and urban

development has rapidly reshaped Earth's land cover. The bulk of this

change has occurred within the last several hundred years, a

geological instant, inducing a sudden shift in conditions to Earth's

climate and biosphere. As a result _ecological forecasting_---modeling

how ecosystems and their services will change in the future---and then

using these forecasts to make decisions to mitigate the negative

consequences of this change on ecosystems, their functioning, and the

services they provide to humans has emerged as an imperative for

ecology and environmental science [@Dietze2017PreEco]. However, robust

prediction of ecological processes is, to say the least, quite

difficult [@Beckage2011LimPre; @Petchey2015EcoFor]. This difficultly

is compounded by a few factors, the first being that sampling

ecosystems is not easy. Ecological data is often biased, noisey, and

sparse in both space and time. The current paucity of ecological data

has resulted in much interest in developing global systems for

_ecosystem monitoring_ [@Makiola2020KeyQue], which would systematize

the collection of biodiversity data in a manner that makes detecting

and predicting change more possible than at the moment

[@Urban2021CodLif].



The second major challenge in ecological forecasting is that the

underlying dynamics of ecological processes are unknown and instead

must be inferred from this (sparse) data. Much of the history of

quantitatively modeling ecosystems have been done in the language of

dynamical systems, describing how the value of an observable state of

the system, represented by a vector of numbers $[x_1, x_2, \dots,

x_n]^T = \vec{x}$ changes over time, yielding models in the form of

differential equations in continuous-time settings, $\frac{dx}{dt} =

f(x)$, or difference equations in discrete-time settings, $x_t =

f(x_{t-1})$, where $f:\mathbb{R}^n \to \mathbb{R}^n$ is an arbitrary

function describing how the system changes on a moment-to-moment basis

(e.g. in the context of communities, $f$ could be Lotka-Volterra,

Holling-Type-II or DeAngelis-Beddington functional response). The form

of this functional response in real systems, and whether it is

meaningfully non-zero for a given species interaction, is effectively

unknown and must be predicted [@Strydom2021RoaPre], and some forms of

these dynamics are inherently more "forecastable" than others

[@Chen2019RevCom; @Pennekamp2019IntPre; @Beckage2011LimPre]. The

initial success of these forms of models can be traced back to the

larger program of ontological reductionism, which became the default

approach to modeling in the sciences after its early success in

physics, which, by the time ecology was becoming a quantitative

science (sometime in the 20th century, depending on who you ask),

became the foundation for mathematical models in ecology.



However, we run into many problems when aiming to apply this type of

model to empirical ecological data. Ecosystems are perhaps the

quintessential example of system that cannot be understood by

iterative reduction of its components into constituent

parts---ecological phenomena are emergent: the product of different

mechanisms operating at different spatial, temporal, and

organizational scales [@Levin1992ProPat].  Further this analytical

approach to modeling explicitly ignores known realities: ecological

dynamics not deterministic and many analytic models in ecology assume

long-run equilibrium. Finally, perhaps the biggest challenge in using

these models to describe ecological processes is ecosystems consist of

more dimensions than the tools of analytic models are suited for. As

the number of variables in a model increases, so does the ability of

the scientist to discern clear relationships between them given a

fixed amount of data, the so-called "curse" of dimensionality.



But these problems are not solely unique to ecology. The term

_ecological forecasting_ implicitly creates an analogy with weather

forecasting. Although it has become a trite joke to complain about the

weather forecast being wrong, over the last 50 years the field of

numerical weather prediction (NWP) has dramatically improved our

ability to predict weather across the board [@Bauer2015QuiRev]. The

success of NWP, and the Earth observation systems that support it

[@Hill2004ArcEar], should serve as a template for development of a

system for monitoring Earth's biodiversity. Much like ecology, NWP is

faced with high-dimensional systems that are governed by different

mechanisms at different scales. The success of NWP is that, rather

than, say, attempt to forecast the weather in Québec by applying

Navier-Stokes to entire province, to instead use simulation models

which describe known mechanisms at different scales, and use the

availability to increasing computational power to directly simulate

many batches of dynamics which directly incorporate stochasticity and

uncertainty in parameter estimates via random number generation.



But forecasting is only half the story---if indeed "[ecologists] have

hitherto only interpreted the world in various ways; the point is to

change it", then once we have a forecast about how an ecosystem will

change in the future, what if this forecast predicts a critical

ecosystem service will deteriorate? We are still left with the

question, what do we do in the time being to mitigate the potentially

negative consequences a forecast predicts? In this framing, mitigating

the consequences of anthropogenic change on ecosystems becomes an

optimization problem: given a forecast of the future state of the

system, and some "goal" state for the future, the problem is then to

optimize our intervention into the system to maximize the probability

the system approaches our "goal" state. This dissertation aims to

provide a framework for ecosystem monitoring and forecasting

(@fig:thesis, left), and each chapter addresses some aspect of this

pipeline to data from a monitoring network to forecasts to mitigation

strategy (@fig:thesis, right).



![Left: a framework for ecosystem monitoring, forecasting, and

mitigation. From the top, a set of biodiversity observatories which

form a monitoring network. Each collect various biodiversity data

products. From this raw data, we derive essential biodiversity

variables (EBVs), and forecast how they change over time. Based on

this forecast, we wish to choose the best possible mitigation strategy

to maximize the chance the realized future outcomes of the EBV

approaches the target state. Right: Each panel represents a chapter of

the thesis, which follows the flow of the framework on the left.

](./figures/thesisconcept.png){#fig:thesis}



The primary research challenges this thesis addresses are: how do we

design ecological samples to detect change? How do we build the software

infrastructure to assimilate data from a variety of sources? And how

do we propagate uncertainty from data to forecasts? The flow of

chapters follows the flow in @fig:thesis (left), from data collection

via a monitoring network, to forecasting an essential biodiversity

variable (EBV), to optimizing mitigation strategy based on

constraints. In chapter one, we discuss how simulation can aid in the

design of ecological samples and monitoring network design. In chapter

two we use data to forecast the uncoupling of a plant-pollinator

network. In chapter three, we apply simulation methods in landscape

ecology to optimize corridor placement to maximize the

time-until-extinction of a metapopulation. The fourth and final

chapter is the software (_MetacommunityDynamics.jl_) which enables the

rest of the dissertation.



# Chapter One: Optimizing spatial sampling of species interactions



## Context



Ecosystems are composed of interactions between species, yet this

remains one of the greatest shortfalls of data in biodiversity science

[@Strydom2021RoaPre]. This is, in no small part, because species

interactions are considerably more difficult to sample than

single-species processes. However, understanding and predicting

species interactions, and how anthropogenic change is affecting them,

is one of the grand challenges faced by modern ecologists

[@Jordano2016ChaEco]. Further, co-occurrence is often used as a proxy

for species interaction when this is not necessary always a valid

assumption [@Blanchet2020CooNot].



## Objective



The goal of this chapter is to use simulation models to investigate

the relationship between species relative abundance, sampling effort,

and probability of observing an interaction between species in order

to aid in the design of samples of ecological interactions across

space, and to provide a null expectation of the false-negative

probability for a dataset of a given size. Further, it then proposes a

method for optimizing the spatial sampling locations to maximize the

probability of detecting an interaction between two species given a

fixed number of total of observations and the distributions of each

species. This addresses the optimization of monitoring network part of

the flow from data to mitigation at the top of @fig:thesis, left.



![A taxonomy of occurrence, co-occurrence, and interaction false negatives in data](./figures/ch2.png){#fig:fnrtaxonomy}



## Methods



We begin by proposing a method to compute a null expectation of the

probability of an interaction false-negative as a function number of

total observations of individuals of _all species in the species

pool_. This is done by simulating the process of observation, where

the probability that an observation is of a given species is that

species' relative abundance. We show that the realized false-negative

rate can be quite high, simply as a byproduct of the distribution of

relative abundance in communities. We use a log-normal distribution of

relative abundance [@Hubbell2001UniNeu] and simulating the process of

observation on food-webs generated using the niche model

[@Williams2000SimRul] with connectance parameterized by the

flexible-links model [@MacDonald2020RevLin]. An example of this

relation for networks with varying species richness is shown in

@fig:fnr.



![Relationship between total number of observed interactions negatives (x-axis) and the probability that an interaction is a true-negative as a function of different realized false-negative rates (colors), assuming each observed negative is independent---the same as the negative-Bernoulli distribution.](./figures/negativebinomial.png)



We then go on to test some assumptions of this neutral model with

empirical data. Primarily we analytically show that our neutral model,

if anything, underestimates the probability of false-negatives if

there are positive associations between species co-occurrence, and we

show these positive associations exist in two sets of spatially

replicated samples of interaction networks [@Hadfield2014TalTwo;

@Thompson2000ResSol; @fig:posassoc]---further I'm planning to add the

field data from chapter two into this analysis once available. Finally

this chapter proposes a simulated annealing method to optimize the a

set of $n$ points in space to maximize the probability of detecting an

interaction between two species $a$ and $b$ with _known_ distributions

$D_a$, $D_b$.



## Results



The first major result is using the simulation of the observation

process described above to generate expectations of interaction

false-negative rate (FNR) as a function of total number of

observations, with the goal being for this estimate to be used as

correction for detection  error when fitting an interaction prediction

model. This relationship varies with the total richness of the

metaweb (see @fig:fnr).



![The realized false-negative-rate of interaction detection (y-axis) as a function of the total number of observations of all species in the species pool (different richnesses in different colors). Each point is the mean of 50 replicates, with one standard-deviation in the first shade, and two standard deviations in the second shade.](./figures/ch2_fnr.png){#fig:fnr}



The second major result is that we analytically show that the this

simulated observation model, by assuming that there is no association

between observing two species given that they interact, actually under

predicts the realized false-negative interaction rate. We then

demonstrate that this positive association association exists in two

empirical systems [@fig:posassoc].  



![Demonstrates positive associations in co-occurrence. Left: the product of the marginal probability of observing two species (A and B) in a sample (x-axis) agaianst the computed joint probability of observing these species together (y-axis). Dashed line indicates $y=x$, meaning no association between the two. Each point is an observed interaction between two species. Right: the distribution of the difference between these joint and marginal probabilities. Both are non-zero with $p < 10^-50$ via a t-test.](./figures/positiveassociations.png){#fig:posassoc}



## Progress



This chapter is mostly complete. The only remaining work is the

implementation of simulated annealing optimization process. This will

be done by using a proposal function which takes a set of coordinates

in space and proposes a new location for each point based on a

distance-decaying kernel.



# Chapter Two: Forecasting the spatial uncoupling of a plant-pollinator network



## Context



Interactions between plants and pollinators form networks which

together structure the "architecture of biodiversity"

[@Bascompte2007PlaMut]. The functioning and stability of ecosystems

emerge from these interactions, but anthropogenic change threatens to

unravel and "rewire" these interaction networks

[@CaraDonna2017IntRew], jeopardizing the persistence of these systems.

Plant-pollinator networks face two possible forms of rewiring in

response to anthropogenic environmental change: spatial and temporal.

Range shifts could cause interacting species to no longer overlap in

space, and shifts in phenology could cause interacting species to no

longer occur at the same time of year.



## Objective



This chapter uses several years of data on bumblebee-flower phenology

and interactions across several field sites, each consisting of

several plots across an elevational gradient, combined with spatial

records of species occurrence via GBIF to forecast the uncoupling of

the plant-pollinator metaweb of Colorado.



![Chapter two conceptual figure. Left: the sources of data and how

they can be combined. Right: The flow from data to interaction

prediction using a few different interaction prediction

models.](./figures/ch1.png)



## Methods



The data for this chapter is derived from multiple sources that can be

split into four categories. (1) Field data from three different field

sites across Colorado, each with multiple plots across an elevational

gradient, for seven, seven, and three years respectively. This data

was collected by Paul CaraDonna and Jane Oglevie (from the Rocky

Mountain Biological Laboratory; RMBL) and Julian Resasco (CU Boulder).

(2) GBIF spatial occurrence records of each of these species across

Colorado, including a metaweb of interactions across all of Colorado

taken from GBIF. (3) Remotely sensed data consisting of current and

forecasted bioclimatic variables from CHELSA. (4) Phylogenies for

both bee and flower species derived from NCBI GenBank barcodes for

mitochondrial COI (bumblebees) and chloroplast rbcL (flowers).



As the data we have is spatially sparse and likely to contain many

interaction false-negatives, we begin by predicting a metaweb of

interactions across Colorado as they exist _in the present_. We do

this using a set of candidate interaction prediction models: relative

abundance only, phylogenetic embedding only (a la @Strydom2021FooWeb),

niche embedding only (encompassing both phenology and environmental

niche, similar to @Gravel2019BriElt), and all pairwise combinations of

those constituent models. After validating and selecting the best

performing model, we then predict how these distributions of each of

these species will change under the CMIP6 consensus climate forecast

[@Karger2017CliHig], and then finally quantify the reduction in

spatial overlap between species for which there is a predicted interaction.



## Results



The in-progress results are the prerequisites for the

analysis outlined above: phylogenies for both plant and bee species

(appendix figure one) and species distribution models for all species (an

example shown in appendix figure two).



## Progress



At the moment, we have derived phylogenies and SDMs for all the

species present in the Colorado GBIF metaweb (appendix figures one and

two). I've also been exploring the data available from Julian Resasco.

The primary constraint on further progress is that we are waiting on

the finalization of a data sharing agreement with RMBL.



# Chapter Three: Optimizing corridor placement against ecological dynamics



## Context



As land-use change has caused many habitats to become fragmented and

patchy, promoting landscape connectivity has become of significant

interest to mitigate the effects of this change on Earth's

biodiversity [@Resasco2019MetDec]. However, the practical realities of

conservation mean that there is a limitation on how much we can modify

landscapes in order to do this.



## Objective



What is the best place to put a corridor given a constraint on how

much surface-area you can change in a landscape? This is the question

this chapter seeks to answer. Models for inferring corridor locations

have been developed, but are limited in that are not developed around

promoting some element of ecosystem function, but instead by trying to

find the path of least resistance in an existing landscape from a

derived resistance surface [e.g. @Peterman2018ResRP]. This chapter

proposes a general algorithm for optimizing spatial restoration effort

to move a measurement of ecological dynamics toward a target state.



## Methods



![A conceptual example of how we go from a map of landcover with a set of points where occurrence of a species has been recorded (top left), to the set of all possible landscape modifications (green box, where each point in the green box is a unique landscape modification, with three examples shown as pink, red and orange dots), to computing resistance surfaces based on proposed landscape modifications (center) and then simulate the distribution of extinction times for a metapopulation in this new landscape (right).](./figures/ch3.png){#fig:ch3}



We propose various landscape modifications that alter the cover of a

landscape, represented as a raster. We then compute a new resistance

surface based on the proposed landscape modification using

Circuitscape [@McRae2008UsiCir], and based on the values of resistance

to dispersal between pair of locations we simulate spatially-explicit

metapopulation dynamics [@Ovaskainen2002MetMod;

@Hanski2000MetCap] to estimate a distribution of time-until-extinction

for each landscape modification. The largest challenge in implementing

this algorithm is the space of potential modifications grows as

$O((nm)!)$ for an $n$ by $m$ raster. For most actual landscapes to which

we wish to apply this method, the set of possible modifications becomes

uncomputably large, so we use simulated annealing to explore the

search space of possible modifications to estimate the modification

that maximizes the time-until extinction of simulated metapopulation

dynamics under that hypothetical modified landscape.



The biggest challenge in implementing simulated annealing in this

context is defining a proposal function for landscape modifications.

At the moment this is done by computing the minimum-spanning-tree

(MST) of the spatial nodes (locations where occurrence has been

observed), and then proposing corridors that only connect nodes that

are already connected in the MST. The primary reason for doing this is

to the cut down the size of the search space to enable quicker

convergence, although the final software that implements this

algorithm will enable alternative methods of proposing modifications.



The goal output of this chapter is not only to provide a set of

discrete corridor options, but also to rank the cells in the raster by

priority based on how many times they are included in the distribution

of "good" corridors after simulated annealing has converged. Further,

the final component of this chapter is measuring the effect of

land-use change on the robustness of the optimized corridor by

simulating various neutral models of urban and agricultural sprawl,

and determining if the proposed modifications still maximize

time-until-extinction when the landcover in the landscape is not

static.



## Progress



Currently I have an algorithm for proposing landscape modifications

and a simple implementation of simulated annealing. The only gap left

is implementing Circuitscape estimation of resistance surfaces and

running benchmarking tests for the resulting chapter.



# Chapter Four: MetacommunityDynamics.jl: a virtual laboratory for community ecology



## Context



Building models for ecological forecasting is an imperative

[@Dietze2018IteNea], but before applying forecasting methods to actual

data, we need a way to determine the efficacy of different forecasting

methods. We need a software library to generate synthetic

data from a _known_ set of mechanisms and parameters to test our

methods for parameter inference and forecasting on a system with

_known_ ground-truth dynamics to assess the effectiveness of these

inference and forecasting methods.



## Objective



The final chapter consists of a collection of modules in the `Julia`

language for different aspects of community ecology, including most of

the code used for the preceding chapters. Indeed

`MetacommunityDynamics.jl` (MCD.jl) is at the center of this set of

tools, but due to the nature of the Julia language, MCD.jl is

inter-operable with several existing packages within the `EcoJulia`

organization, including several to which I have contributed.



![The structure of the software libraries used as part of MCD.jl](./figures/ch4.png){#fig:software}



## Methods



A diagram showing the relation between these packages is shown in

@fig:software. `MetacommunityDynamics.jl` is built on

`DynamicGrids.jl`, a library for high-performance gridded simulations

in the `Julia` language, and Dispersal.jl [@Maino2021PreGlo], and

extension of `DynamicGrids.jl` specifically for modeling organism

dispersal. It also contains integrations with `EcologicalNetworks.jl`

[@Poisot2019EcoJl] to generate metawebs, or can use empirical networks

from Mangal.jl [@Banville2021ManJl]. It implements the general

framework for community dynamics proposed by @Vellend2010ConSyn, where

all community processes can divided into four categories: selection,

dispersal, drift, and speciation.



## Results



In @fig:foodwebtraj we see a sample output of simulated food-web

dynamics for a metaweb of 100 species generated using the

minimum-potential-niche model [@Allesina2008GenMod] with connectance

$C=0.05$ and forbidden-link probability of $0.5$. The dynamics change

according to a Lotka-Volterra functional response, dispersal with

distance inversely proportional to trophic-level, linear mortality,

and logistic growth for any species at the producer trophic-level.



![Sample output of simulated food web dynamics from MetacommunityDynamics.jl. Timestep (x-axis), and biomass of each species (y-axis). ](./figures/foodwebtraj.png){#fig:foodwebtraj}



## Progress



The software as it exists is capable of simulating the biomass

dynamics of arbitrarily large food-webs using Lotka-Volterra, Holling

Type-II, or Holling Type-III functional responses. It currently has

methods to implement Gaussian drift, and various forms of dispersal

via `Dispersal.jl`. Also functional are occupancy dynamics for Levins

metapopulations [@Levins1969DemGen], and spatially explicit

Hanski-Ovaskainen metapopulations [@Hanski2000MetCap;

@Ovaskainen2002MetMod]. This is most of what needs to exist for the

preceding chapters. In-progress functionality includes selection

(which affects growth-rate) on arbitrary environmental variables in

progress, as well as traits.



# Discussion



Developing a system for global biodiversity monitoring is an

imperative to mitigate biodiversity loss and its impacts on humanity.

In my thesis I hope to provide a template for the digital

infrastructure that enables the pipeline from data collection, to

forecast, to actionable information, both through software that can be

used to solve these problems (chapters one, three, four), and

vignettes of how these software can be applied (chapters one, two).



Biodiversity science would be wise to use the success of

numerical-weather prediction and the Earth monitoring system that

supports it as a template. Further, we should embrace methodological

advances in computational statistics that can enable more robust

prediction of the dynamics of complex systems than is possible using

the tools of analytic models---not just because they can provide more

efficacious predictions, but also because they enable a more direct

representation of uncertainty, which is crucial for developing

ecological forecasting models which provide actionable information to

stakeholders, and to find a way for humans to live sustainably on

Earth, the only planet on which life has ever been known to occur.



# References