presentation.Rmd

---
title: "A computational Cultural Transmission model of Bronze Age burial rites in Central, Northern and North-western Europe"
subtitle: Observations on spatial and cultural distance
author: "Clemens Schmid"
date: "27/09/2018"
institute: Institute of Pre- and Protohistoric Archaeology, Kiel University
fontsize: 9pt
output:
  beamer_presentation:
    includes: 
      in_header: preamble.tex
    keep_tex: true
fig_caption: yes
editor_options: 
  chunk_output_type: console
---

```{r, echo = FALSE}
# https://stackoverflow.com/questions/25646333/code-chunk-font-size-in-rmarkdown-with-knitr-and-latex
def.chunk.hook  <- knitr::knit_hooks$get("chunk")
knitr::knit_hooks$set(chunk = function(x, options) {
  x <- def.chunk.hook(x, options)
  ifelse(options$size != "normalsize", paste0("\\", options$size,"\n\n", x, "\n\n \\normalsize"), x)
})
knitr::opts_chunk$set(echo = TRUE, cache = TRUE)
```

## TOC

\textblockcolour{mDarkTeal}

\huge

- Introduction to the data

- Cultural Distance

- Cultural and Spatial Distance

- Simulation


# Introduction

## Data

![Radon-B ^14^C dates of graves 2200-800 calBC (Albers Equal Area Conic).](figures/general_map.jpeg){ height=85% }

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  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
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      \textbf{Radon-B:} Database of \textsuperscript{14}C dates for the european Bronze Age
    \end{minipage}}%
\end{textblock*}

\begin{textblock*}{65pt}(5pt,100pt)
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  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
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      \textsuperscript{14}C dating is an important absolute dating method: One date equals a \textbf{fuzzy point in space and time with context information}
    \end{minipage}}%
\end{textblock*}

\begin{textblock*}{65pt}(295pt,40pt)
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  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
      \raggedright\footnotesize\color{white}
      Context for dates from graves: \textbf{burial type} \& \textbf{burial construction}
    \end{minipage}}%
\end{textblock*}

\begin{textblock*}{65pt}(295pt,100pt)
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  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
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      Heterogeneous \textbf{information density} in space and time
    \end{minipage}}%
\end{textblock*}

## Research Area and Regions

![Artificial Regions: 400km distance, 240km radius, >= 70 dates.](figures/general_map_research_area_regions.jpeg){ height=85% }

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      Divide and Conquer: Separation into eight \textbf{artificial regions} within the area of the highest data density
    \end{minipage}}%
\end{textblock*}

## Development -- Absolute Numbers

\begin{columns}
  \begin{column}{0.48\textwidth}  
    \begin{figure}
      \includegraphics{figures/development_amount_regions_burial_type.jpeg}
      \caption{\textbf{burial type} development: Sum of \textsuperscript{14}C dates whose $2\sigma$ range cover the respective year.}
    \end{figure}
  \end{column}
  \begin{column}{0.35\textwidth}
    \begin{figure}
      \includegraphics{figures/development_amount_regions_burial_construction.jpeg}
      \caption{\textbf{burial construction}}
      \vspace{1.8cm}
    \end{figure}
  \end{column}
\end{columns}

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  \setlength\fboxrule{2pt}%
  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
      \raggedright\footnotesize\color{white}
      Data structure transformation: Individual \textsuperscript{14}C dates to region wise \textbf{time series} of burial rite \textbf{presence}
    \end{minipage}}%
\end{textblock*}

## Development -- Proportions

\begin{columns}
  \begin{column}{0.48\textwidth}
    \begin{figure}
      \includegraphics{figures/development_proportions_regions_burial_type.jpeg}
      \caption{\textbf{burial type} development: Year wise proportions of dates. \textit{unknown} is filtered out.}
    \end{figure}
  \end{column}
  \begin{column}{0.35\textwidth}
    \begin{figure}
      \includegraphics{figures/development_proportions_regions_burial_construction.jpeg}
      \caption{\textbf{burial construction}}
      \vspace{1.8cm}
    \end{figure}
  \end{column}
\end{columns}

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  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
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      Data structure transformation: Time series of absolute appearances to \textbf{time series} of burial rite \textbf{proportions} -- \textbf{burial rite proxy}
    \end{minipage}}%
\end{textblock*}

# Cultural Distance

## Squared Euclidian Distance (SED)

**Question:** How do the developments in these regions for **burial type** and **burial construction** relate to each other? Which regions behave alike?

\usebeamertemplate*{title separator}

The **Squared Euclidian Distance** is a a simple **measure of between-group similarity** that can be applied to the **burial rite proxy** data.

\huge $$d_{ij}^2 = \sum_{k = 1}^{n} (p_{ik} - p_{jk})^2$$ \normalsize

- $d_{ij}^2$: Squared Euclidean Distance between two groups $i$ and $j$
- $k$: Variant counter
- $n$: Total amount of variants in a population
- $p_{ik}$: Relative frequency of the $k$'th variant in population $i$
- $p_{jk}$: Relative frequency of the $k$'th variant in population $j$

## Region-Region Distance Matrix

![**burial type**: SED for each region relationship. Approximated with LOESS.](figures/regions_regions_squared_euclidian_distance_burial_type.jpeg){ height=85% }

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      The \textbf{SED} can be calculated for every year of every one of the $8*8=64$ region relationships
    \end{minipage}}%
\end{textblock*}

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  \noindent\fbox{%
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      Low distance at the start and end due to the \textbf{universal shift from inhumation to cremation} with rise of the \textbf{Urnfield culture}
    \end{minipage}}%
\end{textblock*}

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  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
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      The different \textbf{adoption rates} are visible as \textbf{peaks of cultural distance}
    \end{minipage}}%
\end{textblock*}

<!--

## Mean Region-Region Distance Matrix

![**burial type**: Mean SED for each region relationship. The lower, the closer.](figures/regions_regions_mean_squared_euclidian_distance_burial_type.jpeg){ height=85% }

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  \setlength\fboxrule{2pt}%
  \noindent\fbox{%
    \begin{minipage}{\linewidth - 2\fboxsep - 2\fboxrule}%
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      Central European Cluster?
    \end{minipage}}%
\end{textblock*}

## Mean Region Distance Matrix

![**burial construction**: Mean SED for each region relationship.](figures/regions_regions_mean_squared_euclidian_distance_burial_construction.jpeg){ height=85% }

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      Northwestern European Cluster?
    \end{minipage}}%
\end{textblock*}

-->

## Parallel Developments?

\begin{columns}
  \begin{column}{0.48\textwidth}
    \begin{figure}
      \includegraphics{figures/regions_squared_euclidian_distance_burial_type.jpeg}
      \caption{\textbf{burial type} Development of SED to all the others for each region.}
    \end{figure}
  \end{column}
  \begin{column}{0.48\textwidth}
    \begin{figure}
      \includegraphics{figures/regions_squared_euclidian_distance_burial_construction.jpeg}
      \caption{\textbf{burial construction}\newline}
    \end{figure}
  \end{column}
\end{columns}

## Correlation of **Burial Type** and **Burial Construction** Distance

\begin{adjustwidth}{-3em}{-3em}
  \begin{figure}
    \includegraphics{figures/squared_euclidian_distance_burial_type_vs_burial_construction.jpeg}
    \caption{Correlation of \textbf{burial type} and \textbf{burial construction} mean SED in time slices of 200 years. \newline Each double point represents one region-region relationship.}
  \end{figure}
\end{adjustwidth}

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  \noindent\fbox{%
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      The distances of \textbf{burial type} and \textbf{construction} do \textbf{not correlate} -- except maybe in the late Early Bronze Age
    \end{minipage}}%
\end{textblock*}



# Cultural and Spatial Distance

## Spatial Distance Classes

![Spatial distance network and definition of distance classes](figures/general_map_distance_network.jpeg){ height=85% }

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      The definition of artificial regions as units of analysis makes distance measures difficult. \textbf{Ordinally scaled distance classes} are the only valid option here.
    \end{minipage}}%
\end{textblock*}

## Correlation of **Burial Type** and **Spatial** Distance

\begin{adjustwidth}{-3em}{-3em}
  \begin{figure}
    \includegraphics{figures/squared_euclidian_distance_vs_spatial_distance_burial_type.jpeg}
    \caption{\textbf{burial type}: Correlation of mean SED and spatial distance in timeslices of 200 years.}
  \end{figure}
\end{adjustwidth}

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      Spatial distance is only relevant \textbf{before} the widespread transformation in the Middle Bronze Age starts
    \end{minipage}}%
\end{textblock*}

## Correlation of **burial construction** and **spatial** distance

\begin{adjustwidth}{-3em}{-3em}
  \begin{figure}
    \includegraphics{figures/squared_euclidian_distance_vs_spatial_distance_burial_construction.jpeg}
    \caption{\textbf{burial construction}: Correlation of mean SED and spatial distance in timeslices of 200 years.}
  \end{figure}
\end{adjustwidth}

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      Spatial distance is overall \textbf{more relevant} and again in the late Early Bronze Age significant
    \end{minipage}}%
\end{textblock*}

# Simulation

## Preliminary Considerations

Funeral rituals are **behaviour/ideas/cultural traits** and spread in space and time. They exist in **social space** and their spread depends on social relationships.

\usebeamertemplate*{title separator}

Simulation concept: 

- Ideas are **entities** with simple behaviour: **greedy expansion**

- Ideas life in a configurable, diachronic **population network**

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Funeral rituals are a special category of ideas: They have a relatively low interaction with the human-environment system and can be treated as **selectively neutral**. [Dunnell 1978]

The main mechanisms of diffusion of neutral variants are **innovation**, **drift** and **flow**. [Neiman 1995]

- **Drift:** Individual traits will dominate due to stochastic processes

- **Flow:** Information transfer causes synchronization across group boundaries

## Population Graph Creation

![Example Population Graph. Arranged with the Fruchterman & Reingold algorithm.](figures/population_graph_connection_001_time_arrow.png){ height=85% }

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      \textbf{R Package} to create undirected population networks with configurable \textbf{population size development}, \textbf{number of groups}, \textbf{degree of intra- and intergroup transmission}, etc.
    \end{minipage}}%
\end{textblock*}

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      Every individual's position in social space and time is defined by their \textbf{vertical and horizontal} connections
    \end{minipage}}%
\end{textblock*}

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      Groups have a \textbf{high degree of internal} and a \textbf{low degree of external} interaction
    \end{minipage}}%
\end{textblock*}

## Idea Expansion Simulation

```{cpp eval = FALSE, size = 'footnotesize'}
...
// make random decision to convert or ignore a node based on the edge weight
  std::vector<std::pair<int, bool>> success_per_neighbor(neighbors.size());
  for (auto& i : all_neighbors_information) {
    // make decision
    // if the node is already occupied, it's more difficult
    // if more than one contact, then there's a convincing bonus
    std::pair<int, bool> success;
    if (std::get<3>(i)) {
      success = std::make_pair(
        std::get<0>(i), 
        std::get<1>(i) * log2(std::get<2>(i) + 1) >= randunifrange(75, 100)
      );
    } else {
      success = std::make_pair(
        std::get<0>(i), 
        std::get<1>(i) * log2(std::get<2>(i) + 1) >= randunifrange(0, 100)
      );
    }
    success_per_neighbor.push_back(success);
  }
...
```

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  \noindent\fbox{%
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      \textbf{C++ CLI program} to simulate idea expansion within the population network
    \end{minipage}}%
\end{textblock*}

## Simulation Application: Correlation of Spatial and Cultural Distance

![Correlation of cultural and spatial distance over time for **real world observations**.](figures/sed_simulation_step_1.jpeg){ height=88% }  

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      Can correlation of spatial and cultural distance \textbf{be ruled out?}
    \end{minipage}}%
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## Simulation Application: Correlation of Spatial and Cultural Distance

![**+** Correlation development for **100 simulation runs** with **equal intergroup distance**.](figures/sed_simulation_step_2.jpeg){ height=88%  }

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      Can correlation of spatial and cultural distance \textbf{be ruled out?}
    \end{minipage}}%
\end{textblock*}

## Simulation Application: Correlation of Spatial and Cultural Distance

![**+** Diagnostic **boxplots** for simulation runs.](figures/sed_simulation_step_3.jpeg){ height=88%  }

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      Can correlation of spatial and cultural distance \textbf{be ruled out?}
    \end{minipage}}%
\end{textblock*}

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      \textbf{Equal intergroup distance}: Unlikely development in the Early Bronze Age   
    \end{minipage}}%
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## Simulation Application: Correlation of Spatial and Cultural Distance

![**+** Diagnostic **dotplots** indicating mantel test results.](figures/sed_simulation_step_4.jpeg){ height=88%  }

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      Can correlation of spatial and cultural distance \textbf{be ruled out?}
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      \textbf{Equal intergroup distance}: Unlikely development in the Early Bronze Age
    \end{minipage}}%
\end{textblock*}

## Simulation Application: Correlation of Spatial and Cultural Distance

![Same plot, but simulations now with **spatial intergroup distance**.](figures/high_spatial_interaction.jpeg){ height=88%  }

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      Can correlation of spatial and cultural distance \textbf{be ruled out?}
    \end{minipage}}%
\end{textblock*}

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      \textbf{Equal intergroup distance}: Unlikely development in the Early Bronze Age   
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      \textbf{Spatial intergroup distance}: Unlikely development in the Late Bronze Age  
    \end{minipage}}%
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      \textbf{burial type} behaves \textbf{highly atypical} if we assume spatial correlation
    \end{minipage}}%
\end{textblock*}

# Conclusion

## Observations and Hypotheses

- The diffusion of the **cremation funeral tradition** and **traditions of flat vs. mound graves** are **independent**.

- Both processes are **mostly independent** of **spatial distance**: Not a simple diffusion process!

- **Other interaction networks** could yield better predictions: Elite Networks, Religious superstructures, ...

\usebeamertemplate*{title separator}

- **Sociocultural complexity** in the Bronze Age is generally **increasing**. Still the **homogeneity & heterogeneity** of certain cultural traits **vary greatly**.

##

\titlepage