Two times five, plus one

Article and photos by Joe Mish

What the eagle sees

I love math, as it reveals patterns of periodicity which lead to predictability and useful projection of the future and explanation of the past. Even chaos in nature follows mathematical formulas, as explained by Fibonacci’s sequence and the golden rule.

When a simple mathematical formula is applied to the pair of eagles that make their home on the South Branch of the Raritan River, an amazing picture is revealed.

Two times five plus one; Do the math and the answer is, eleven. It is this simple formula, with a single constant and two variables that summarize the efforts of one pair of eagles over a five-year period. It also theoretically predicts their future contribution to the greater eagle population.

The constant, two, is the single pair of eagles that have built and rebuilt their nest at a single riverside location on the South Branch.

Structures on the tongue to help stiffen it.

If any deserve to be called a constant, it is this dedicated pair of eagles. Though, over the years, argument between them has been has been loud and expressive. The larger female revealing her feelings in a series of threatening calls, directed at the male, beg for anthropomorphic interpretation. Dad proudly arrives with a large branch to improve the nest and mom decides its arrangement as if she was changing the furniture around. It is mom that spends the night on the nest. Food deliveries stop at dusk and by morning mom is hungry, needs to take a shower and stretch her wings. If dad is not there at first light, she becomes quite vocal, calling for him to take her place on the nest.

Every once in a while, dad would wander back a little late and get a real tongue lashing. Through the travails of their relationship, they persist as a dedicated pair. Their partnership is undeniable as they attend the needs of their offspring and each other. Both will bring food to the nest and share it with their partner. Though sometimes the fish provided has a few bites taken out.

The next variable, two, is the number of eggs this pair has laid and the number of chicks they have fledged every year for over five years.

To achieve one-hundred percent success on the number of eggs laid to eaglets fledged is quite an accomplishment. Not all eggs remain viable and not all hatched chicks survive. Some may fall out and be fatally injured or attacked by a predator. Of those that do successfully fledge, their fate is tenuous. This is one reason banding eagles can provide some data on survivability. If enough data is collected a statistical projection can be attempted by age group.

Any deviation from ‘two’ in our eagle formula is added or subtracted in the second variable. In this case it is plus one, which represents the fostering of an eaglet from a down stream nest that fell or was forced out by an attacker.

The aluminum band affixed to E82. This year both chicks were male.

Last year a female eaglet, assigned band number E68, was placed in the south branch nest during the scheduled banding session. The adult eagles and their two, six-week-old offspring, accepted the stranger. One can only imagine the endless thought bubbles appearing over each bird’s head to reveal their thoughts and words when two, magically became three. The adults had to work overtime to feed an extra hungry mouth and the established pair had to share the food provided. Consider the eagles at six weeks of age weighed almost seven pounds each.

Doing the math, our eagle pair can live thirty years or more. Subtract their immature years and in theory could produce, plus or minus, fifty offspring. Consider their first nestlings from the 2015 season are approaching maturity and the number of eagles of South Branch origin, keep growing. More impressive, today’s eagles may be seen by our grandchildren along the South Branch or several states away.

A four-year-old immature eagle captured in Quantico Virginia, March 15, 2018 as part of a study, was observed in South Jersey earlier this spring. A square solar panel on its back powers a transmitter and records a plot of its travels. Truly, the skies are the limit, to the world of an eagle and a lesson we might take to heart, literally and figuratively.

By year, this eagle pairs’ offspring have been banded with numbers…… 2015 – E14, E15,  2016 – E43, E44, 2017 – E57, E58, 2018 – E66, E67, E68 and 2019 – E82, E83.

Veterinarian with NJ fish and game endangered and non game species program, Erica Miller draws a blood sample while Kathy Clark assists in the process. Kathy is head of the endangered and non game species program.

Author Joe Mish has been running wild in New Jersey since childhood when he found ways to escape his mother’s watchful eyes. He continues to trek the swamps, rivers and thickets seeking to share, with the residents and visitors, all of the state’s natural beauty hidden within full view. To read more of his writing and view more of his gorgeous photographs visit Winter Bear Rising, his wordpress blog. Joe’s series “Nature on the Raritan, Hidden in Plain View” runs monthly as part of the LRWP “Voices of the Watershed” series. Writing and photos used with permission from the author. Contact See more articles and photos at