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Using an 18-year dataset of arrival dates of 65 species of Maine migratory breeding birds, I take a deeper view of the data to ask questions about the shapes of the distribution. For each year, most species show a consistent right-skewed pattern of distribution, suggesting that selection is stronger against individuals that arrive too early compared to those that arrive later. Distributions are consistently leptokurtic, indicating a narrow window of optimal arrival dates. Species that arrive earlier in the spring show higher skewness and kurtosis values. Nectarivorous species showed more pronounced skewness. Wintering area did not explain patterns of skewness or kurtosis. Deviations from average temperatures and the North Atlantic Oscillation index explained little variation in skewness and kurtosis. When arrival date distributions are broken down into different medians (e.g., 5% median and 75% median), stronger correlations emerge for portions of the distribution that are adjacent, suggesting species fine-tune the progress of their migration. Interspecific correlations for birds arriving around the same time are stronger for earliest migrants (the 25% median) compared to the true median and the 75% median.

Abundant evidence for global climate change exists in monotonic increases in carbon dioxide concentrations, melting of polar ice caps with concomitant sea level rise, and record hot temperatures around the world [

Over the past 18 years, I have been coordinating a citizen-science effort to document the first arrival dates of Maine migratory breeding birds across the state [

In this contribution, I take a longer view of the data. Rather than concentrating on the impact of various climatic variables on arrival dates, I explore the statistical distribution of arrival dates reported by all observers. As argued by [

I also break down the distributions to see if the dates of arrivals of the earliest arriving individuals of a species can predict the arrival of the later arriving birds. I examine the interannual correlations of arrivals for 65 species of birds. With this deeper view, I am less focused on the responses of particular birds and more focused on discovering patterns by examining elements of the distributions of arrival dates.

The data for this study come from the 18 years (1994–2011) of data on arrival dates of Maine migratory breeding birds [

Map of Biophysical Regions of Maine, based on [

Birds were categorized into one of nine foraging types (

Foraging types, skewness, kurtosis and major migration period of the 65 species used in this study. The skewness and kurtosis values are the mean of the 18 yearly values. An asterisk after particular skewness or kurtosis values indicates that the value is significantly different from zero in Wilcoxon rank tests using the Bonferroni correction to insure an experiment-wise

Species | Foraging Type | Skewness | Kurtosis | Migration Period |
---|---|---|---|---|

Ring-necked Duck ( |
Aquatic | 0.240 | 3.354 * | April |

Great Blue Heron ( |
Aquatic | 0.620 * | 4.667 * | April |

Turkey Vulture ( |
Scavenger | 0.509 * | 3.757 * | March/April |

Osprey ( |
Raptor | 0.699 * | 4.687 * | April |

Broad-winged Hawk ( |
Raptor | −0.390 | 4.249 * | April |

American Kestrel ( |
Raptor | 0.449 * | 4.001 * | April |

Killdeer ( |
Ground predator | 0.873 * | 4.392 * | March/April |

Spotted Sandpiper ( |
Ground predator | 0.161 | 2.965 * | May |

Wilson's Snipe ( |
Ground predator | 0.476 * | 2.861 * | April |

American Woodcock ( |
Ground predator | 1.231 * | 5.490 * | March/April |

Chimney Swift ( |
Aerial | 0.523 | 3.863 * | May |

Ruby-throated Hummingbird ( |
Nectarivore | 0.108 | 6.901 * | May |

Belted Kingfisher ( |
Aquatic | −0.636 | 5.357 * | April |

Yellow-bellied Sapsucker ( |
Scansorial | 1.479 * | 3.578 * | April |

Northern Flicker ( |
Scansorial | −0.783 | 7.253 * | April |

Eastern Wood-Pewee ( |
Aerial | −0.729 | 6.373 * | May |

Least Flycatcher ( |
Aerial | 0.283 | 3.745 * | May |

Eastern Phoebe ( |
Aerial | 1.907 * | 5.463 * | March/April |

Great Crested Flycatcher ( |
Aerial | 0.582 | 4.525 * | May |

Eastern Kingbird ( |
Aerial | −0.518 | 6.045 * | May |

Blue-headed Vireo ( |
Leaf-gleaner | 0.478 | 3.832 * | April/May |

Warbling Vireo ( |
Leaf-gleaner | 0.533 * | 2.883 * | May |

Red-eyed Vireo ( |
Leaf-gleaner | 0.335 | 5.247 * | May |

Tree Swallow ( |
Aerial | 0.945 * | 4.166 * | April |

Barn Swallow ( |
Aerial | 0.173 | 3.037 * | May |

House Wren ( |
Ground predator | 0.277 | 3.239 * | May |

Winter Wren ( |
Ground predator | 0.627* | 2.792* | April |

Ruby-crowned Kinglet ( |
Leaf-gleaner | 0.454 | 3.725 * | April/May |

Eastern Bluebird ( |
Ground predator | 0.225 | 3.708 * | April |

Veery ( |
Ground predator | −0.181 | 3.808 * | May |

Hermit Thrush ( |
Ground predator | 0.301 | 4.693 * | May |

Wood Thrush ( |
Ground predator | 0.175 | 3.891 * | May |

Gray Catbird ( |
Ground predator | −0.637 | 8.439 * | May |

Brown Thrasher ( |
Ground predator | 0.217 | 3.579 * | May |

Ovenbird ( |
Leaf-gleaner | 0.216 | 5.452 * | May |

Northern Waterthrush ( |
Leaf-gleaner | 0.367 | 3.585 * | May |

Black-and-white Warbler ( |
Leaf-gleaner | 0.653 | 3.838 * | April/May |

Nashville Warbler ( |
Leaf-gleaner | 0.804 * | 4.546 * | May |

Common Yellowthroat ( |
Leaf-gleaner | 0.928 * | 5.056 * | May |

American Redstart ( |
Leaf-gleaner | 0.448 | 5.434 * | May |

Northern Parula ( |
Leaf-gleaner | 0.098 | 5.056 * | May |

Magnolia Warbler ( |
Leaf-gleaner | 0.262 | 3.562 * | May |

Blackburnian Warbler ( |
Leaf-gleaner | 0.628 | 4.514 * | May |

Yellow Warbler ( |
Leaf-gleaner | 0.470 | 4.187 * | May |

Chestnut-sided Warbler |
Leaf-gleaner | 0.629 | 4.823 * | May |

Black-throated Blue Warbler ( |
Leaf-gleaner | 0.652 * | 3.838 * | May |

Palm Warbler ( |
Leaf-gleaner | 0.579 | 3.824 * | April |

Pine Warbler( |
Leaf-gleaner | 0.651 | 4.208 * | April |

Yellow-rumped Warbler ( |
Leaf-gleaner | −0.835 | 8.506 * | April/May |

Black-throated Green Warbler ( |
Leaf-gleaner | 0.667 * | 4.061 * | May |

Canada Warbler ( |
Leaf-gleaner | 0.320 | 3.429 * | May |

Chipping Sparrow ( |
Granivore | −0.254 | 4.446 * | April |

Savannah Sparrow ( |
Granivore | 0.014 | 3.676 * | April |

Song Sparrow ( |
Granivore | −0.792 | 8.560 * | Mar/April |

Swamp Sparrow ( |
Granivore | 0.094 | 3.426 * | April |

White-throated Sparrow ( |
Granivore | −1.986 * | 7.842 * | April |

Scarlet Tanager ( |
Leaf-gleaner | 0.651 * | 3.746 * | May |

Rose-breasted Grosbeak ( |
Granivore | 0.764 | 6.092 * | May |

Indigo Bunting ( |
Granivore | 0.157 | 3.026 * | May |

Bobolink ( |
Ground predator | 0.605 | 7.210 * | May |

Red-winged Blackbird ( |
Ground predator | 1.483 * | 6.222 * | Mar |

Eastern Meadowlark ( |
Ground predator | 1.992 | 2.583 * | April |

Common Grackle ( |
Ground predator | 1.426 * | 7.179 * | Mar |

Baltimore Oriole ( |
Leaf-gleaner | 0.010 | 7.857 * | May |

I classified each of the 65 species according to its major wintering area: South America, Central America, Caribbean, or southeastern United States. Central and South America along with Caribbean were combined into a Long category for the long-distance migration those birds undertake. Long contrasts with Short, referring to those birds wintering in the United States with a less arduous migration.

For each species-year combination, I used Stata 12 statistical software to calculate the skewness and kurtosis [

For the distribution of each species-year combination, I calculated five metrics: the 5% median, the 10% median, the 25% median, the true median (50% median) and the 75% median. I used Pearson product-moment correlations to evaluate the pair-wise relationship between each type of median across the 18 years of the study.

Using the values of the 25% median, 50% median and 75% median, I used Pearson correlation tests to test for significant relationships between pairs of species that were migrating in the same time interval. Thus, I developed one table of all possible combinations of species arriving in a particular month. This analysis tests for the independence of migration schedules among the species in the study.

The quantity of arrival data for each Biophysical Region (

Distribution of first arrival dates for American Woodcock for 1994. The distribution is right-skewed with some leptokurtosis (more pronounced peak and thinner tails than seen in a normal distribution).

Wilcoxon signed-rank tests indicate every species has a significant positive kurtosis (a value of zero is expected for a normal distribution). The positive kurtosis is termed leptokurtosis, indicating a pronounced peak in the middle of the distribution with thinner than expected tails to the distribution.

I used a Kruskal-Wallis rank test to determine if foraging type (^{2} = 21.81, ^{2} = 65.64,

Relationship of foraging type on kurtosis. A Kruskal-Wallis rank test indicated significant differences among feeding types.

Foraging type | Skewness | Kurtosis |
---|---|---|

Aerial insectivore | 0.38 | 4.65 |

Aquatic feeder | 0.35 | 3.09 |

Gleaner | 0.45 | 4.59 |

Granivore | 0.32 | 5.48 |

Ground predator | 0.31 | 4.41 |

Nectarivore | 0.06 | 7.38 |

Piscivore | 0.22 | 4.13 |

Raptor | 0.03 | 4.90 |

Scansorial predator | 0.35 | 5.42 |

Scavenger | 0.51 | 3.76 |

A Kruskal-Wallis rank test was used to test the statistical effect of migration month on skewness and kurtosis (^{2} = 49.70, ^{2} = 30.43,

The relationship of migration period on skewness and kurtosis. Means are provided. Migration period had significant effects on both measurements in Kruskal-Wallis rank tests.

Migration period | Skewness | Kurtosis |
---|---|---|

March | 1.45 | 6.73 |

March/April | 0.57 | 4.65 |

April | 0.26 | 4.38 |

April/May | 0.24 | 4.57 |

May | −0.29 | 4.83 |

Kruskal-Wallis rank tests failed to show an effect of wintering area (and hence migratory distance) on skewness (^{2} = 7.34, ^{2} = 3.32, ^{2} = 0.37, ^{2} = 0.21,

To examine the statistical effect of TempDep on skewness, I used regression analyses. With the Bonferroni correction, no significant relationship was found any of the 65 species (all

No significant relationship of NAO index with skewness was detected by regression analysis for all 65 species. Regression analyses also failed to find a relationship between NAO index and kurtosis. None of these 130 regressions yielded a p-value below the Bonferroni-corrected value of

Percentage of species whose various medians show a significant Pearson correlation (

March–April (10 species)

5% | 10% | 25% | 50% | |
---|---|---|---|---|

10% | 100 | |||

25% | 50 | 80 | ||

50% | 20 | 50 | 10 | |

75% | 20 | 30 | 40 | 100 |

April (16 species)

5% | 10% | 25% | 50% | |
---|---|---|---|---|

10% | 88 | |||

25% | 38 | 81 | ||

50% | 25% | 43 | 88 | |

75% | 25 | 31 | 44 | 69 |

April–May (6 species)

5% | 10% | 25% | 50% | |
---|---|---|---|---|

10% | 83 | |||

25% | 50 | 67 | ||

50% | 17 | 17 | 83 | |

75% | 0 | 0 | 17 | 67 |

May (31 species)

5% | 10% | 25% | 50% | |
---|---|---|---|---|

10% | 87 | |||

25% | 58 | 84 | ||

50% | 26 | 55 | 77 | |

75% | 6 | 16 | 32 | 94 |

Box plots showing the percentage of interspecific significant correlations (

To seek effects of climate change on bird migration, ornithologists have used two sorts of data. A few studies have been conducted where the arrival of all members of a local population of a few species are recorded through a banding program or intensive censusing of territorial males [

The second approach was used in this study. The analysis in this contribution was designed to seek patterns of deviation from the normal distribution in the shape of the arrival date curves. Studies using arrival dates of migratory birds to seek evidence of global climate change have concentrated on the mean or median dates [

The first result from this analysis is that the distributions of arrival dates have third (skewness) and fourth (kurtosis) moments that differ from a normal distribution. In the majority of cases, the distribution shows a right skew (

I believe these patterns of skewness and kurtosis are informative in relation to the selective pressures on arrival date. The piling up of values on the left side of the distribution implies that the pressure to delay migration until food resources are available is stronger than the pressure to arrive early to procure a favorable territory. The leptokurtic distribution suggests that the median arrival dates are even more advantageous than one would expect if the data were normally distributed.

Foraging type of birds had an impact on the skewness of yearly arrival date distributions (

The month of arrival was correlated with skewness and kurtosis values. Arrivals in March are more perilous than later arrivals because of the fickle nature of the Maine spring. One predicts more of a right-skewed and leptokurtic distribution for early arrivals. That pattern was observed with the two earliest migrants, Red-winged Blackbird and Common Grackle, showing highest skewness and kurtosis [

For all species, the skewness of yearly distributions of arrival dates was not related to the deviation of springtime temperatures from the long-time average. Temperature patterns occur on a broad-scale from Delaware north through Maine [

The larger scale driver of weather, the North Atlantic Oscillation, is related to the timing of bird migration [

We have abundant evidence now that both photoperiod and weather patterns influence the timing of avian migration [

In this paper, I have taken a longer, exploratory view of an 18-year dataset of arrival dates for 65 species of migratory birds that nest in Maine. Right-skewed arrival dates (

I am grateful to the more than 200 volunteers across the state of Maine who have contributed arrival data to this project. Liam O’Brien provided helpful statistical advice. Financial support for this project came from the Division of Natural Sciences at Colby and from the dedicated research funds associated with the Leslie Brainerd Arey Chair in the Biosciences at Colby College.