Motivating biology and datasets

Thus, from the war of nature, from famine and death, the most exalted object which we are capable of conceiving, namely, the production of the higher animals Clarkia flower, directly follows. There is grandeur in this view of life, with its several powers, having been originally breathed by the Creator into a few forms or into one; and that, whilst this planet has gone circling on according to the fixed law of gravity, from so simple a beginning endless forms most beautiful and most wonderful have been, and are being evolved.

— Charles Darwin,
On the Origin of Species (1859)

Earth’s vast biological diversity has been (and is being) created by the gradual splitting of one species into two, a process repeated countless times throughout history. For this reason, evolutionary biologists are fascinated by speciation. A crucial moment in speciation occurs when two populations, once separated, come back into contact. In many cases, they can still produce hybrids—but these hybrids are often unfit in one way or another.

Wouldn’t it be cool if, at this stage, the populations could evolve a mechanism to preferentially mate with their own kind? The adaptive evolution of avoiding mating with a closely related species—a process known as reinforcement—does just that. However, the evolution of reinforcement is complex and has only been conclusively documented in a handful of cases.

Dave Moeller and colleagues (including me) have been investigating one potential case of reinforcement. Clarkia xantiana subspecies parviflora (hereafter parviflora) is an annual flowering plant native to California. Unlike its outcrossing sister subspecies, Clarkia xantiana subspecies xantiana (hereafter xantiana), parviflora predominantly reproduces through self-pollination.

Figure 1: parviflora petals tend to be larger as populations get further away from xantiana.

Not all populations of parviflora self-fertilize at the same frequency. Dave has observed that populations sympatric with (i.e., occurring in the same area as) xantiana appear more likely to self-fertilize than allopatric populations (Figure 1). Over the past few years, we have conducted numerous studies to evaluate the hypothesis that this increased rate of self-fertilization has evolved via reinforcement as a mechanism to avoid hybridizing with xantiana.

Throughout this book, I will use data related to the topic of divergence, speciation, and reinforcement between Clarkia subspecies as a path through biostatistics. I hope that this approach allows you to engage with the statistics while not having to keep pace with a bunch of different biological examples. Below, I introduce the major datasets that we will explore.

RILs between sympatric and allopatric parviflora

Figure 2: Making a RIL population: A cross between individuals from two populations is followed by multiple generations of self-fertilization. As a result, each “line” becomes a mosaic of ancestry blocks inherited from either initial parent of the RIL. The figure above (from Behrouzi & Wit (2017)) illustrates this process, with the original parental chromosome segments depicted in green and red.

To investigate which traits, if any, help parviflora populations sympatric with xantiana avoid hybridization, Dave generated Recombinant Inbred Lines (RILs). To do so, he crossed a parviflora plant from “Sawmill Road”—a population sympatric with xantiana—with a parviflora plant from “Long Valley,” far from any xantiana populations. After this initial cross, lines were self-fertilized for eight generations. This process breaks up and shuffles genetic variation from the two parental populations while ensuring each line is genetically stable.

By setting these RILs out in the field and observing how many pollinators visited each line, we hope to identify which traits influence pollinator visitation and ultimately hybridization. Because parviflora plants often self-pollinate and because pollinators effectively transfer pollen from the plentiful xantiana plants to parviflora, we assume that greater pollinator visitation corresponds to higher hybrid seed set. However, we will test this assumption!!!

RIL Data

Below is the RIL dataset. You can learn about the columns (in the Data dictionary tab) and browse the data (in the Data set tab). The full data are available at
this link. Aside from pollinator visitation and hybrid seed set, all phenotypes measured come not from the plants in the field, but means from replicates of the genotype grown in the greenhouse.

RIL variation

Figure 3: An illustration o the variabiltiy in the recombinant inbred lines. Pictures by Taz Mueller and arranged by Brooke Kern.

Data Dictionary

Variable_Name	Data_Type	Description
ril	Categorical (Factor/String)	Identifier for Recombinant Inbred Line (RIL). This is the 'genotype'.
location	Categorical (Factor/String)	Field site where the plant was grown.
prop_hybrid	Numeric (discrete)	Proportion of genotyped seeds that were hybrids (see num_hybrid and offspring_genotyped for more information).
mean_visits	Numeric	Average number of pollinator visits per plant over a 15-minute observation.
growth_rate	Numeric	Growth rate of the plant.
petal_color	Categorical (Binary)	Petal color phenotype (in this case 'pink' or 'white').
petal_area_mm	Numeric	Date when the first flower opened (in Julian days, i.e., days since New Year's).
date_first_flw	Date	Node position of the first flower on the stem.
node_first_flw	Numeric	Petal area measured in square millimeters (mm²).
petal_perim_mm	Numeric	Petal perimeter measured in millimeters (mm).
asd_mm	Numeric	The Anther-Stigma Distance (ASD) is the linear distance between the closest anther (the floral part that releases pollen) and the stigma (the floral part that accepts pollen) in a flower, measured in millimeters (mm). The smaller this distance, the more opportunity for self-fertilization.
protandry	Numeric	Degree of protandry (e.g., time difference between male and female phase) measured in days. More protandry means more outcrossing.
stem_dia_mm	Numeric	Stem diameter measured in millimeters (mm).
lwc	Numeric	Leaf water content (LWC).
crossDir	Categorical (Binary)	Cross direction
num_hybrid	Numeric (discrete)	The number ofseeds that where hybrid.
offspring_genotyped	Numeric (discrete)	The number of seeds genotyped.

Data set

RIL Hybridization Data

Below is the hybridization dataset. For each plant in the field we genotyped eight seeds at species-specific markers to identify if they were the product of hybridization with xantiana. The phenotypes belong to the genotype of the maternal plant (i.e. they are the same as those in the pollinator visitation data set). I include data at both the level of the seed and a summary at the level of the maternal plant.

RIL Combined Data

Behrouzi, P., & Wit, E. (2017). Detecting epistatic selection with partially observed genotype data using copula graphical models. Journal of the Royal Statistical Society: Series C (Applied Statistics), 68. https://doi.org/10.1111/rssc.12287