Migration Ruleset Decisions

Introduction

In this markdown file, I attempt to explain my decisions behind why I chose certain rules for this migration ruleset. Defining migration to eastern mallards is not easy, but I believe this ruleset does an impressive job at categorizing migration for these birds. Please feel free to email me any comments or concerns.

This file will be organized into broader “steps”, with each broad step containing more specific information surrounding the rules.

Filtering steps
Finding migratory movements and molt
Assigning migratory status
Migratory bird ruleset
Assigning resident seasons
Partial migrants

Filtering Steps

Remove birds with gaps during migration

So as to not assign migrations incorrectly, I removed birds with gaps during migration. Specifically, I removed birds that had gaps of greater than 10 days. This removed this many bird year combinations from the analysis.

Some of these individuals maybe have had a complete spring migration or complete fall migration, yet summer/winter would still not be able to be defined. Not sure if it was worth it to still somehow include these in the analysis.

If I didn’t remove these birds, spring and fall migration may not be categorized (because they’re missing the large migratory jumps) or categorized incorrectly. For instance, a bird could take two large jumps yet doesn’t take data until the second jump. The first jump could be 15 days prior, but since there was no information, the ruleset would assume that migration happened at the second jump.

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Finding migratory movements and molt

Step lengths

Following Beatty et al., 2014; Kohl et al., 2022; and Highway et al., 2024, I graphed the natural log of hourly step lengths. This is to see generally what mallard movement looks like. If the step length was greater than 1 hour and 6 minutes (I gave it a buffer as sometimes they don’t take exactly every hour), then the Haversine distance was calculated, the angular distance between two points on the surface of a sphere. Then, those distances were natural logged and graphed. I visually assessed the graph and tried to find when breaks happened. To me, I saw breaks at 0.4 and 35 km. That means that distances greater than 35 are migratory movements and breaks < 0.4 are wetland movements. The papers mentioned above have similar assessments.

Finding molt movements

I decided to quickly look and find instances of molting to help determine if movements in August later on are molting movements are early fall migration. To do this, following Beatty et al., 2014 and Kohl et al., 2022, I took the average hourly step length of each day. Then, I looked for a period of 20-60 days where the mallard had an average below 0.4 km of movement. This period needed to be between July 15th and Nov 1st.

This produced the following bird year combinations. As you can see, I wasn’t able to parse out molting for more than half of the mallards.

## # A tibble: 389 × 6
##      bandnum  year run_id start_date end_date   duration
##        <int> <int>  <int> <date>     <date>        <dbl>
##  1 208764918  2024      1 2024-08-01 2024-09-26       57
##  2 208764924  2024      3 2024-08-17 2024-09-14       29
##  3 208764929  2024      1 2024-08-01 2024-09-12       43
##  4 208764967  2024      1 2024-08-01 2024-09-20       51
##  5 213720083  2024      9 2024-09-19 2024-11-01       44
##  6 213720085  2024      3 2024-08-20 2024-10-13       55
##  7 213720093  2024      1 2024-08-01 2024-08-24       24
##  8 213720102  2022      1 2022-08-01 2022-08-25       25
##  9 213720104  2023      3 2023-08-10 2023-09-30       52
## 10 213720138  2023      5 2023-09-05 2023-10-30       56
## # ℹ 379 more rows

Calculating daily displacement

For all bird year combinations, I calculated daily displacement when the hourly gap was less than 72 hours. If the gap was more, daily displacement was just not calculated. This is to prevent assigning migration incorrectly. This will be used to figure out when migration is happening. I assume migration to be happening if the daily displacement is greater than 35 km, the value found in the figure above.

Assigning migratory status

Before beginning the real ruleset, I need to first parse out migratory and resident birds. This is because only migratory birds will need to have seasons defined. To do this, I employ the following calculations.

Look at all times in a bird year and see if the bird moved more than 35 km
Calculate the displacement between the second day of the bird’s “banding life” and july 1st (or death date if before). Sometimes birds make a jump right after banding so I wanted to avoid this. I’m calling this the mid net displacement
Calculate the last observation of the year
Calculate if the bird had a jump > 35 km July - Sept

Migratory bird

A migratory bird is a bird that moved more than 35 km at least once before July 1st and had a mid net displacement of more than 75 km. I’m assuming that the largest homerange size of a resident bird would be 75 km (35 x 2 = 70, give or take a few). This might be a bit excessive, but during data exploration, some of these resident birds do move around a lot.

Resident bird

A resident bird was either one of two things. 1) The bird had a daily displacement < 35 km for their whole life. 2) They took a 35 km jump at some point, yet their mid net displacement was less than 75 km.

Partial Migrant bird

A partial migrant was the following 1) The bird had a daily displacement > 35 during June, July, August, or Sept, but still had a mid net displacement of less than 75 km (because displacement was calculated between the beginning of the year and july 1st). This means that the bird was a resident, yet took a molt migration. These birds are going to be classified as partial migrants.

Unknown bird

Unknown birds are birds that were banded and died before April 24st without taking a spring migration. I can’t confirm if they were a migrant or resident. April 24th came from the 95% quantile of the start of all spring migrations. As I need to have migrant, resident, or partial resident delinations, I made this category so later I can filter these birds out.

Migratory bird ruleset

Birds that were determined to be migratory were then fit through the following ruleset. First, all daily displacement instances of more than 35 km were “flagged” as potential migratory instances. See the distribution of those below.

## Warning: Using `size` aesthetic for lines was deprecated in ggplot2 3.4.0.
## ℹ Please use `linewidth` instead.
## This warning is displayed once every 8 hours.
## Call `lifecycle::last_lifecycle_warnings()` to see where this warning was
## generated.

Now, just because a movement was more than 35 km does not necessarily make it a migratory movement. The following rules go through what can’t be a migratory movement.

Winter movement rules

All Jan movements were suppressed as these were likely winter movements or getting pushed farther south (Nichols et al., 1983; Sauter et al., 2010). Both papers show that mallards make a lot of cold related movements during the winter.
From Feb 1 - March 10th, if a mallard moves north less than 100 km it is not considered migration. In all honesty, I can’t find any literature to back this up. All I know is it seems common for some mallards to move in Feb and not migrate till April. If stopovers can’t be long, then I don’t want this first movement to be categorized as migration and the second one not.

Spring and fall rules

All movements that don’t fall into the above categories are considered migration potentials. If movement is in the months of Feb - June, this ruleset happens: If two bouts of spring migration are less than 21 days apart, then the inbetween stopover will be considered migration as well. If more than 21 days apart, only the first jump is considered migration.
All movements that don’t fall into the above categories are considered migration potentials. If movement is in the months of Aug - Dec, this ruleset happens: If two bouts of fall migration are less than 35 days apart, then the inbetween stopover will be considered migration as well. If more than 35 days apart, only the first jump is considered migration (O’Neal et al., 2012 says fall was 28 +- 12 days; Hagy et al., 2014 says average of 34.7 days; Krementz et al., 2012 says 15).

Migration bout filtering

We now have potential migration bouts for each bird year. We’re not done filtering yet though…

Getting rid of forays: The net displacement of each migratory bout was calculated (distance from start of migratory bout to end of migratory bout). If the net displacement was less than 50 km, then this is not a migration, just a foray.
molt migration: If a migratory movement in summer/fall came BEFORE the molting period that was calculated earlier, then it will become a molt migration/summer movement but only if there are two migratory movements. It seems as if many mallards are molting after fall migration. For instance, they hop down 300 km, then molt, and never move again. To clarify, here are two examples of this happening

Example One - Two migratory movements

In this example, the mallard migrates south and THEN molts. After molt, the individual jumps down again. The second jump is considered migration. Note that molting will not be a season in this analysis, in fact, molt will just be considered part of summer. You need to zoom in to see the molt.

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Example Two - One migratory movement

In this case, my molting analysis found that the bird molting in Sept, after a huge migratory movement south. She then stayed there for the winter. In this case, I’m defining the movement as fall migration, not part of summer like I did above.

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What about birds where molting wasn’t parsed out?

For those that did not have a molt migration that was parsed out, yet still had a movement in these dates, a migratory bout was only called fall migration if it moved north more than 50 km or if it moved south less than 300 km. If the southern distance was more than 300 km, I called that the start of fall migration.

At this instance, each bird now has one spring movement and one fall movement.

Assigning resident seasons

Next, I looked at the distribution of migratory movements for spring and fall for all migratory birds. I extracted the 10% and 90% quantile per year per season and used that to assign resident birds their seasons.

If you’re concerned about some of the movements in the graph below (why is a bird migrating end of June), please scroll to the bottom of the markdown file where I will have some maps made.

Partial migrants

Lastly, some individuals migrated north for spring migration but never returned in the fall. These are also going to be considered partial migrants. They became “residents” on their spring breeding grounds. To be a partial migrant they did not have a fall migration that year, but only if they made it till Dec 28th, as the last known bird in migration was Dec 27th.

A partial migrant is a resident bird that makes a molt migration, or a “migratory” bird that becomes a resident on the breeding grounds.

Here’s an example of one…you can see that it doesn’t have a fall migration assigned.

We either keep summer to be that long…or insert the 80% quantile of migratory birds.

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