Evolution in fluctuating environments

Reaction norms for larval viability in Drosophila pseudoobscura

Mon, 07 Nov 2011 22:43:30 GMT

Reaction norms for larval viability in a natural population of Drosophila pseudoobscura. Each line is the reaction norm for the relative larval viability at three different temperatures for a fourth chromosome homozygote. Most genotypes have a variable phenotype with qualitatively different environmental sensitivities and substantial genotype-by-environment interaction. For example, six out of the 23 genotypes show no significant environmental sensitivity (grey). Other genotypes exhibit poor viability for all temperature regimes (AA 1005) while genotypes have a high viability at low temperatures but deteriorate with increasing temperature (AA 1035). In contrast, genotype AA 1052 exhibits the highest viability at intermediate temperatures while PA 851 shows the opposite trend with higher viability for marginal temperatures. Data from Dobzhansky and Spassky 1944, Genetics 29:270-290.

Based on Pineda-Krch (2011).

Results

Mon, 07 Nov 2011 22:43:15 GMT

No results so far, but event the vanilla model (i.e. no genetic constraints, linear y_0(x(t)), etc.) could potentially give very interesting results.

From Svanbäck et al. (2009)

LRG lab meeting (November 7, 2011)

Mon, 07 Nov 2011 22:42:30 GMT

The purpose of this lab meeting is to give a brief whirlwind tour of the historical, political, theoretical and empirical background of phenotypic plasticity. I will discuss some recent theoretical results from the literature on the role of phenotypic plasticity in adaptive evolution and brainstorm around possible questions and directions of this project.

I will start off by briefly outline the scientific methodology (Open Notebook Science) I am using in this research project.

This project has two (very different) overarching aims:

Explore how variable environments influence evolutionary adaptations, specifically how the rate and amplitude of environmental fluctuations influence evolutionary adaptation to a fixed phenotype or evolution of increased potential for phenotypic plasticity.
Explore how theoretical research can benefit by being conducted in a completelly transparent way

Her are the "slides":

Open Notebook Science

Evolution in fluctuating environments

Genotype-by-environment interaction figure

Mon, 07 Nov 2011 22:41:00 GMT

Effects of genotype and environment on the distribution of phenotypes in a series of hypothetical reaction norms. A continuous environmental gradient, e.g. temperature, is shown on the horizontal axis with the distribution of environments experienced by a population indicated (x, y and z). The blue and red lines represent the reaction norms of different genotypes with the resulting distribution of phenotypes given on the y-axis, e.g. f_1(x) is the distribution of phenotypes for genotype 1 in the environmental distribution x. (A) In the absence of genotype-by-environment interaction the reaction are parallel and, although different in phenotype (f_1(x) \neq f_2(x)) respond similarly to differences in the environment. Note how the variance of the phenotypic distributions differ from the variance of the environmental distribution. (B) In the presence of genotype-by-environment interaction, manifested by the reaction norms having different slopes, the two genotypes respond differently to the environment. Note how the variance of f_1(x) now is different from the variance of f_2(x). In both (A) and (B) the distribution of phenotypes is bimodal and most of the variation is genetic because the genotypes differ substantially in their phenotypes. (C) Crossing reaction norms are an especially strong case of genotype-by-environment interaction. Around the crossing point of the norms, the genotypes are indistinguishable in the phenotypic mixture, i.e. f_1(y) \approx f_2(y), giving an appearance of less genetic diversity than what is actually present in the population. Away from the crossing point the individual genotypes can be identified in the bimodal phenotypic distribution but with a reversed ranking on either side of the crossing point. For example, while genotype 1 is superior in environment x, f_1(x) > f_2(x), genotype 2 is ranked higher in environment z, i.e. f_1(z) < f_2(z).

Based on Pineda-Krch (2011).

Model

Mon, 07 Nov 2011 22:39:33 GMT

The aim is to devise a simple quantitative genetic simulation model

Key parameters

x(t) = the environment at time t
y_0 = optimal phenotype, where y_0(x(t)) = a function
y_m = ecological genotype, i.e. phenotype in the absence of phenotypic plasticity
k = plasticity genotype, i.e. slope of linear reaction norm

Key quantities

Realized ecological pheotype assuming a linear reaction norm: y = k x(t) + y_m
Deviation from optimal phenotype: y_\Delta = y-y_m
Amount of phenotypic plasticity expressed: |y-y_m|
Realized carrying capacity: K = K_0 \times \mathcal{N}(y_\Delta, \sigma_K) where K_0 is the maximal carrying capacity and \mathcal{N} = \exp \left[ \frac{y_\Delta^2}{2\sigma_K^2} \right]
Hence K=K_0 if y_\Delta=0 and K \ll K_0 if y_\Delta \ll 0 or y_\Delta \gg 0.

Ecological model: No cost of plasticity

\frac{dN(y_m,k,t)}{dt} = r N(y_m,k,t) \left( 1- \frac{N(y_m,k,t)}{K_0 \times \mathcal{N}(y_\Delta, \sigma_K)} \right)

Ecological model: Cost of plasticity

If r=b-d(k) then

\frac{dN(y_m,k,t)}{dt} = (b-d(y,y_m)) N(y_m,k,t) \left( 1- \frac{N(y_m,k,t)}{K_0 \times \mathcal{N}(y_\Delta, \sigma_K)} \right)

where d(y,y_m) = d_0(1+|y-y_m|) where d_0 is background mortality (in the absence of plasticity).

Evolution

In this model two uncorrelated traits are under evolution, the ecological genotype y_m and the plasticity genotype k.

Woltereck

Mon, 07 Nov 2011 19:28:16 GMT

The response curves obtained by Woltereck when rearing three pure lines (A, B and C) of a freshwater daphnia (Hyalodaphnia cucullata) on different levels of resources. Horizontal axis: resource level (poor, intermediate, and enriched) and vertical axis: relative head hight. Although Woltereck expected the phenotypic response of the different lines to vary with resources availability he did not expect, however, that the phenotypic response of each genotype under the same environmental conditions would be different. Of the three lines examined for helmet height, one was nearly indifferent to changes in resources (C), another responded to a change from intermediate to abundant resources (B), whereas the third responded to a change from poor to intermediate resources (A). Figure from Woltereck 1909, Verhandlungen der Deutschen Zoologischen Gesellschaft 19:110-173.

Based on Pineda-Krch (2011).

Introduction

Mon, 07 Nov 2011 19:08:06 GMT

Evolution unfolds against a backdrop of environmental variability taking place on different time scales, from rapid climate shifts occuring at a decadal time scale, to climatic changes occurring over a few millennial, regular glacial-interglacial transitions with cycles of roughly a hundred thousand years, to long-term warming or cooling trends over hundreds of thousands to millions of years. Our aim here is to develop a simple eco-evolutionary model aimed at exploring how the time scale of climate change influence evolutionary dynamics.

There are an increasing number of studies showing that adaptive evolution can unfold over timescales spanning several order of magnitude. For example, while organisms with short generation times, e.g. microorganisms and invertebrates, have the potential for rapid adaptations to changes in their environment, organisms with long generation times, e.g. megafauna and long lived trees, are respond over a much longer time scale.

A few real world examples: pesticide resistance in insects (DDT and mosquitoes) and drug resistance in pathogens (antibiotic resistance in bacteria), ...

Several factors determine the rate of evolutionary adaptation, many which are species specific, including the mutation rate, generation rate, nature of selection (strength, direction), genetic constraints (Hellmann & Pineda-Krch (2007)), etc. In a changing environment, e.g. under global warming, all populations face the same rate of environmental change.

The aim of this study is to explore how variable environments influence evolutionary adaptations, specifically how the rate and amplitude of environmental fluctuations influence evolutionary adaptation to a fixed phenotype or evolution of increased potential for phenotypic plasticity. This work builds on the work by Svanbäck et al. (2009) addressing how a fluctuating environment promotes the evolution of increased phenotypic plasticity but with the key difference that in this study my goal is to also quantify the time scales over which adaptation to a fixed phenotype or evolution of increased potential for phenotypic plasticity takes place. In contrast to Svanbäck et al. I am here using a simpler model of a siongle population experiencing an exogeneously driven variable environment (similarly to Hellmann & Pineda-Krch (2007)).

The success of a plastic response largely depend on the predictability of the environment. Lags in the response to environmental changes or unpredictable environmental changes can impose significant ecological costs compared with that experienced by fixed genotypes. Using theoretical models it has been shown that an increased ability for plastic responses is less likely to evolve in stable environments while plastic phenotypes tend to be selectively favoured in environments that are intrinsically variable in space and time, e.g. due to species interactions and in fluctuating environments (Svanbäck et al. (2009). The time scale over which the environment is changing relative to the average life span of individuals in the population is one important aspect determining the evolutionary outcome. For example, if the duration of an environmental regime is less than the average generation time of individuals, the population cannot easily respond by adaptation in a fixed (non-plastic) genotype. Under this scenario individuals having genetic variation for phenotypic plasticity are expected to be favoured. Whether the population will adapt by increasing its capacity for phenotypic plasticity ultimately depends on the costs and physiological limits associated with the plastic phenotype.

Questions needing answers

Mon, 07 Nov 2011 18:42:21 GMT

Should plasticity itself carry a cost (similarly to Svanbäck et al. (2009))? This means that there would be two costs, i) due to plasticity and ii) due to deviations from the optimal phenotype.
- Pros of plasticity cost: more "realistic"
- Cons of plasticity cost: more complicated model, at least one more parameter

What should functional form for y_0(x(t)) be? Arbitrary? Does the functional form matter? Could it be of interest to explore different functional forms?
- Pros of exploring different functional forms: Results potentially more broadly applicable, we might be able to generalize
- Cons of exploring different functional forms: Simulations and analysis much more time consuming

Linear reaction norms are simple but probably unrealistic. Should I explore more complex reaction norms, e.g. non-linear reaction norms and/or piece-wise reaction norms (see e.g. Reaction norms for larval viability in Drosophila pseudoobscura)
- Pros of linear y_0(x(t)): nice and simple
- Cons of linear y_0(x(t)): too simple? Arbitrary choise of functional form. Non-linear functional forms could potentially give very different results.

Should we wxplore constraints between y_m and k (see e.g. Hellmann & Pineda-Krch (2007))?
- Pros of constraints: potentially more interesting results, more "realistic"
- Cons of constraints: more complex model, introduces arbitrary stuff (unless we can find studies backing things up)

Do we need sex?
- Pros of sex: more "realistic"
- Cons of sex: makes life more complicated

Daphnia

Mon, 07 Nov 2011 18:40:47 GMT

Two genetically identical individuals of the water flea Daphnia lumholtzi. The individual on the left was exposed to chemical cues from a predatory fish and the individual to the right was not. The pointed anterior prolongation, or helmet, on the head and the extended tail spine provide protection predators locating its prey by sight. The development of the helmeted phenotype confers a higher metabolic costs than the smaller rounded head resulting in smaller brood volumes. The two phenotypes were initially believed to be a separate species. Scanning electron micrograph courtesy of C. Laforsch and R. Tollrian.

Based on Pineda-Krch (2011).

About

Mon, 07 Nov 2011 18:07:55 GMT

This is my personal research notebook for the Evolution in fluctuating environments project.

This notebook and all the associated data, code and results is publicly available in as close to real-time as possible. This research notebook is primarily a tool for me to organize and record results, ideas, and progress with the aim of being intelligible to me in the future. For someone with a graduate studies background in evolutionary biology, ecology and math, some of what is here might be accessible, and perhaps even be of interest.

If you want to (re)use any content look at the license first. If you want to cite the notebook look at the citation guideline first.

Why an ONS project?

There are many and reasons why people decide to embark on ONS (Open Notebook Science). Here is an incomplete list of some of the reasons for why I decided to conduct this research project in the spirit of Open Notebook Science? There is no particular order to the list. The entries are numbered to simplify cross-referencing.

It's your tax dollars at work.
Much more better use of public money (and of resources in general) by allowing others to reuse and/or build on ideas/code/data... (http://figshare.com/)
Greatest benefit to society (scientific discoveries disseminated as they happen, not years later when it appears in traditional journals)
May give rise to collaborations with others in the field
May give rise to collaborations with others outside of the field which could take the projects in unexpected directions and give rise to new inter/trans-disciplinary research directions and projects.
More brain power (leverages the collective wet ware of the social web). Combining the ideas of many minds make hard scientific problems easier to solve (http://michaelnielsen.org/blog/open-science-2/). Expand our ability to solve the most challening scientific problems, think of it as parallelized science (computers have done it for decades). As a result this the range of scientific problems we can hope to solve expands.
Avoid getting scooped, specifically
1. The good:If it has already been published others can draw your attention to this early on. Better than being told by a referee after submitting your paper.
2. The bad: If someone else is working on it at the same time they could let you know and allow the two of you to ensure that no-one gets scooped (or they could of course just try to speed things up and get it out before you). Basic principle: treat colleagues the way you want them to treat you, in other words, while I don't want to get scooped I also have no interest to scoop some one else. It is in everyone's interest to avoid accidental scooping. The person you scoop may be on your next search/tenure/promotion/grant committee and or the next faculty that your department hires and puts in the office next to you. And vice versa.
3. The ugly: Someone stealing your idea/data and publishing it. Will not work since there is a public record that it is yours (case in point, it would be like stealing the Mona Lisa and putting it on displayed in another museum). Isn't stealing a public project/data/idea an oxymoron anyway?
Reproducibility. Although the number of irreproducible results are increasing perhaps the most famous example is Fermat's Last Theorem which remained irreproducible for hundreds of years.
Accountability and fraud prevention
Increase public understanding of how science works and how scientific progress comes about
Of historical interest. Case in point, we are still studying the notebooks of <name of favorite famous dead scientist>, e.g. Darwin, Einstein, etc. (Not that I am suggesting anyone will ever study my notebook)
Improving the scientific process by encouraging others to embrace more transparent (and reproducible) research practices and contribute to dispelling myths about all the bad stuff people think will happens if you do science in the nude.
Providing a view into the daily life of a scientist may inspire young people to pursue a career in science (of course it could also dissuade them) (http://stargrads.net/blogs/davinci/2009/06/an-essay-on-open-notebook-science/)
Increasing exposure and citations (now that people actually can reproduce and/or access the data and result)
Help others solve problems by allowing them to use and/or modify my code and (perhaps more importantly) letting others learn from your mistakes and dead ends.
Others can (re)use my data (e.g. for us in projects addressing different/alternative/complementary questions)
Improve the scientific work environment by increasing trust, respect and openness between researchers and research groups.
To attract students and postdocs to your research group.

Sounds to good to be true? Others with more ONS experience may have a better feeling for whether these reasons are actually true or just wishful thinking. For me it is an experiment (aka [beta]).

What is beta?

beta aka 'experimental feature'
experimental feature aka buggy, unreliable, non-permanent, 'testing the waters'
buggy aka errors
unreliable aka errors
non-permanent aka 'I can change my mind any minute'
'testing the waters' aka 'I can change my mind any minute'

Contact information

Physical home

Centre for Mathematical Biology
632 Central Academic Building
University of Alberta
Edmonton, AB T6H 2G1, Canada

Web home

http://pineda-krch.com

Email

mpineda at math dot ualberta dot ca

What is beta?

Mon, 07 Nov 2011 06:37:48 GMT

beta aka 'experimental feature'
experimental feature aka buggy, unreliable, non-permanent, 'testing the waters'
buggy aka errors
unreliable aka errors
non-permanent aka 'I can change my mind any minute'
'testing the waters' aka 'I can change my mind any minute'

Todo

Mon, 07 Nov 2011 06:31:36 GMT

What is this?: This is a list of stuff that needs to be done, some of it is important and some of it not.
Who will do it?: Me or you. If you want to contribute this is the place to start.
If you wish to contribute: Email me and let me know what you have in mind.

search

Identify relevant key references and add them to a reference folder (probably needs to be password protected)
Write simulation code

Why an ONS project?

Mon, 07 Nov 2011 06:28:09 GMT

It's your tax dollars at work.
Much more better use of public money (and of resources in general) by allowing others to reuse and/or build on ideas/code/data... (http://figshare.com/)
Greatest benefit to society (scientific discoveries disseminated as they happen, not years later when it appears in traditional journals)
May give rise to collaborations with others in the field
May give rise to collaborations with others outside of the field which could take the projects in unexpected directions and give rise to new inter/trans-disciplinary research directions and projects.
More brain power (leverages the collective wet ware of the social web). Combining the ideas of many minds make hard scientific problems easier to solve (http://michaelnielsen.org/blog/open-science-2/). Expand our ability to solve the most challening scientific problems, think of it as parallelized science (computers have done it for decades). As a result this the range of scientific problems we can hope to solve expands.
Avoid getting scooped, specifically
1. The good:If it has already been published others can draw your attention to this early on. Better than being told by a referee after submitting your paper.
2. The bad: If someone else is working on it at the same time they could let you know and allow the two of you to ensure that no-one gets scooped (or they could of course just try to speed things up and get it out before you). Basic principle: treat colleagues the way you want them to treat you, in other words, while I don't want to get scooped I also have no interest to scoop some one else. It is in everyone's interest to avoid accidental scooping. The person you scoop may be on your next search/tenure/promotion/grant committee and or the next faculty that your department hires and puts in the office next to you. And vice versa.
3. The ugly: Someone stealing your idea/data and publishing it. Will not work since there is a public record that it is yours (case in point, it would be like stealing the Mona Lisa and putting it on displayed in another museum). Isn't stealing a public project/data/idea an oxymoron anyway?
Reproducibility. Although the number of irreproducible results are increasing perhaps the most famous example is Fermat's Last Theorem which remained irreproducible for hundreds of years.
Accountability and fraud prevention
Increase public understanding of how science works and how scientific progress comes about
Of historical interest. Case in point, we are still studying the notebooks of <name of favorite famous dead scientist>, e.g. Darwin, Einstein, etc. (Not that I am suggesting anyone will ever study my notebook)
Improving the scientific process by encouraging others to embrace more transparent (and reproducible) research practices and contribute to dispelling myths about all the bad stuff people think will happens if you do science in the nude.
Providing a view into the daily life of a scientist may inspire young people to pursue a career in science (of course it could also dissuade them) (http://stargrads.net/blogs/davinci/2009/06/an-essay-on-open-notebook-science/)
Increasing exposure and citations (now that people actually can reproduce and/or access the data and result)
Help others solve problems by allowing them to use and/or modify my code and (perhaps more importantly) letting others learn from your mistakes and dead ends.
Others can (re)use my data (e.g. for us in projects addressing different/alternative/complementary questions)
Improve the scientific work environment by increasing trust, respect and openness between researchers and research groups.
To attract students and postdocs to your research group.

Sounds to good to be true? Others with more ONS experience may have a better feeling for whether these reasons are actually true or just wishful thinking. For me it is an experiment (aka [beta]).

Pineda-Krch (2011)

Mon, 07 Nov 2011 06:25:00 GMT

Pineda-Krch M. Phenotypic plasticity. Chapter in The Sourcebook in Theoretical Ecology (Alan Hastings and Louis Gross, eds.). University of California Press. To appear.

Literature review

Mon, 07 Nov 2011 06:21:00 GMT

The current study builds upon the work of Svanbäck et al. (2009) and Hellmann & Pineda-Krch (2007). This is how the current study differs,

Exogeneously generated fluctuations
More realistic costs to phenotypic plasticity
...

Examples of phenotypic plasticity

Mon, 07 Nov 2011 06:21:00 GMT

Put some cool pictures here...

Aims

Mon, 07 Nov 2011 06:21:00 GMT

The aims of this study are to,

Explore evolutionary dynamics in exogeneously driven fluctuating environments.
Consider alternative, and more relastic, costs to plasticity, specifically delay in plastic response and irreversible plasticity.
Determine the temporal scales of climatic change that accelerate evolutionary adaptation while others accelerate the evolution of phenotypic plasticity?

Workflow for ONS

Mon, 07 Nov 2011 06:19:00 GMT

Dealing with non-electronic resources, type in handwritten notes and scribbles. Pros. looks good and searchable. Cons. time consuming to enter. Scan. Pros: fast Cons: not searchable

Solution: do something inbetween. Scan or photograph the original notes and include them in the notebook as a figure. Then ad a caption where the contens of the figure is summarized using appropriate shorthand keywords and brief summary.

Dealing with copyrighted material, specifically with journal articles. Obviously one would get in trouble fast if one were to post journal articles online. Possible solution, keep journal articles in a password protected folder (access only granted on an individual basis) but incorporate highlighted text, annotations, and clips of figures into notebook. WOuld this raise the hackles of

Dealing with people. How would one deal with people who would not want their comments published online? Anonymize their comments should make them happy but makes it harder for me to manage and use the notebook.

Svanbäck et al. (2009)

Mon, 07 Nov 2011 06:19:00 GMT

@ARTICLE{svanback.etal09,
  author = {Svanbäck, R. and Pineda-Krch, M. and Doebeli, M.},
  title = {Fluctuating population dynamics promotes the evolution of phenotypic plasticity},
  journal = {The American Naturalist},
  year = {2009},
  volume = {174},
  pages = {176-189},
  file = {svanback.etal09.pdf:svanback.etal09.pdf:PDF}
}

http://www.math.ualberta.ca/~mpineda/public/svanback.etal09.pdf

Hellmann & Pineda-Krch (2007)

Mon, 07 Nov 2011 06:19:00 GMT

@ARTICLE{hellmann.pineda-krch07,
  author = {Hellmann, J. and Pineda-Krch, M.},
  title = {Constraints and Reinforcement on Adaptation Under Climate Change: Selection of Genetically Correlated Traits},
  journal = {Biological Conservation},
  year = {2007},
  volume = {137},
  pages = {599-609},
  note = {Authors in alphabetical order},
  file = {hellmann.pineda-krch07.pdf:hellmann.pineda-krch07.pdf:PDF}
}

http://www.math.ualberta.ca/~mpineda/public/hellmann.pineda-krch07.pdf