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These little flying fellows seemed to have made themselves a small nest in the crevices of the roof of my house (I live in Poland). I don't know if this makes a difference, but I do live near a small park.

I'm wondering if this is a house sparrow or something else.

On one of the photos I could swear these look like common sparrows, but on another (the one where the wings are apart) it seems like a different species. It also seemed larger than a sparrow, but is hard to tell due to the distance at which I've seen the birds and the photos were taken. One other notable feature was that they seemed very loud…

Any help?

Based on your image I would rather identify it as an Eurasian Tree Sparrow. They are pretty similar to the House Sparrow, but have a distinct black spot below their eyes which is missing for the House Sparrows (image from the Wikipedia):

## House sparrows ruining my plants. How do i kill them?

Any idea on how to Permanently get rid of house sparrows? They've taken over the bird feeders we've set up for our pigeons. Plus, they destroying all my plants and creating a huge mess everyday. I've tried feeding them separately, setting up decoys, even have dogs but nothing seems to be working. They're just too many. We used to see alot of different bird species outside but now all we see are sparrows. I really want them gone and I'd go out and buy a pellet gun but everything's closed. I can't even buy bird poison. Is it possible to make poison at home using household products to all to their feed?

## Description

Unlike many other birds, House Wrens do not have brightly colored feathers or markings. Measuring 5 inches long with a plump body and a short tail.

The upperparts are unstreaked and grayish brown, the underparts are grayish white. Notice the faint or missing eye stripe that is common in other wrens.

The females and juveniles look the same as the adult male although recent fledglings are noticeably smaller.

The song of the young isn't as sure sounding as the adult males either. For the most part, they have no prominent field marks.

If you spend any time at all watching these birds you'll easily know the extent of its territory.

The male usually has three prominent perches from which he defends his territory of 1/2 - 3/4 acres.

## The Action of the Bird Matters

If the bird dies while inside the house, it's also indicative of a death in the near future. This means that you should never try to kill a bird that's made its way into your home.

Ironically, a bird defecating on the head of a person who lives inside the home will have good luck. Of course, it's easy not to think so at the time this happens.

Sometimes a bird keeps flying around, never settling into a single spot. This is said to indicate that there are spirits residing in the home.

If a black bird builds a nest in the home, it's said to be good luck. After all, the bird is trying to bring new life into the house.

A bird that taps against or hits your window might also be trying to tell you something. According to superstition, the bird might be trying to remind you of something. It could also tell you that you have a problem on the horizon that you need to solve even though there are many obstacles standing in the way.

Hi, About the "shortest incubation period record". House sparrows are comparable to other passerines in this respect, and theirs is not the shortest incubation period. According to a 2004 publication, equally short incubation periods (10 days) have been recorded for Carduelis flammea (common redpoll), Plectrophenax nivalis (snow bunting) and Calcarius lapponicus (lapland longspur), as well as a shorter period for Quelea quelea (red-billed quelea) at 9.6 days. The article reports an 8-day-record for the sparrow-larks of genus Eremopterix, from subtropical Africa. Source: Lloyd P. 2004. Eight- to ten-day incubation and nestling periods among Eremopterix sparrow-larks. Ibis 146: 347–350.

C. Morgan (10 May 2006) — Preceding unsigned comment added by 163.10.23.1 (talk) 16:44, 10 May 2006 (UTC)

## Sparrow Falling

Theories abound as to why house sparrows have declined. The answer likely lies in a combination of factors, all tied to rapid changes in both cities and farms. House sparrows may be highly adaptable, but that doesn’t mean they can thrive with every modification humans make to the environment.

The first house sparrow decline was actually reported in the 1920s, when automobiles began widely replacing horses. Sparrows feasted on the huge amount of spilled grain found in cities. When that food source was removed, sparrow populations decreased.

The Royal Society for the Protection of Birds and others note that changing agricultural practices likely play a significant role in the current sparrow decline. Once, farms were diverse, with crop fields and livestock barns scattered across the landscape. New, clean, intensified monocultures result in less spilled grain, and less cover around fields. In many parts of the world, other birds associated with farmland are also in decline.

Livestock is more frequently raised in confined operations, sometimes even indoors. All this results in fewer opportunities to feed on grain.

Similarly, city sanitary practices have improved, which may make finding meals more difficult for sparrows.

Research published in the journal *Frontiers in Ecology and Evolution* found that a combination of poor diet and air pollution induced physical stress on house sparrows, leading to reduced reproductive success.

The widely reported global insect decline may also be a significant factor. Many think of house sparrows as vegetarians, gobbling bird seed and grains. But, as with many birds, they rely on protein-rich insects to feed their young.

A house sparrow flock in Washington, DC. Photo © Mr.TinDC / Flickr

## Objective

Startup leaders and investors were influenced by these societal movements as much as by new research helping them understand how ESG can help advance business objective s in venture capital.

One of the UAE’s biggest objective s through the Emirates Mars Mission has been to spur a young generation of scientists and engineers to get into space systems development in order to help the UAE enter the space economy.

That’s right, not all content should be created with the objective of getting more conversions or even more traffic to your site.

The first was “where is the jar,” or an objective assessment based on the listener’s understanding.

I suspect your objective , however, is to fix and flame your relationship.

All other issues—racial, feminine, even environmental—need to fit around this central objective .

Koenig has not been a sterile, objective narrator she has openly voiced her biases, concerns, and gut feelings all along.

Certainly that was the objective of the attack: The school is a private one run by the army for the children of soldiers.

Meeting an additional objective standard is necessary: can the vehicle safely transport you from one place to another?

Carles told me that MormonThink strives to be objective and impartial.

The two-thirds objective should be used as a finder, while the one-sixth is reserved for examining details.

They are easily seen with the one-sixth objective in the routine microscopic examination.

Search with a one-twelfth-inch objective , using very subdued light.

The embryos will collect in the water, and can be easily found with a two-thirds objective .

Once his one-track mind got to functioning on a certain objective it seldom digressed.

## Racist Bird Names Are Next on the Chopping Block

*(AP Photo/Fernando Llano)*

You would think that the Bachman’s sparrow and the Wallace’s fruit dove would be the least controversial creatures on earth. But it’s not the birds, it’s the people they were named after that’s generating the controversy. Alfred Russell Wallace actually has 4 other birds named in his honor — and each of them may be called something else before too long.

Wallace was a British naturalist, explorer, and anthropologist who is credited, along with Charles Darwin, of conceiving the theory of evolution through natural selection. But his writings are apparently filled with references to the “N” word. Despite his numerous accomplishments and contributions to science, he must be canceled for the sin of thinking like most other white people at the time.

“Conservation has been driven by white patriarchy,” said J. Drew Lanham, a black ornithologist. Has it been “driven” by “white patriarchy”? Or is it that whites organized most of humanity to protect the natural world when no one else did? It’s not “patriarchy.” It’s common sense.

Admittedly, whites went about the task of cataloging and studying the natural world like typical racists of the 17th, 18th, and 19th centuries. That’s when most of the nomenclature for animal species was applied. Some pretty despicable people have lent their names to the lexicon and perhaps the issue deserves serious study.

What the issue doesn’t need is the hysterical caterwauling of those who claim injury from a bird name.

“I am deeply troubled by the racist actions of John James Audubon and recognize how painful that legacy is for Black, Indigenous and people of color who are part of our staff, volunteers, donors and members,” [Audubon Society] interim chief executive Elizabeth Gray said in a statement in May. “Although we have begun to address this part of our history, we have a lot more to unpack.”

For [black ornithologist Corina] Newsome, community engagement manager for Georgia Audubon, the pain is real. When she first wore her organization’s work shirt, “I felt like I was wearing the name of an oppressor,” she said, “the name of someone who enslaved my ancestors.”…

Indeed, White explorers, conservationists and scientists who crossed the world conveniently ignored the fact that birds had been discovered, named and observed by native people for centuries before their arrival.

To the Cherokee, eagles are the awâ’hili and crows are kâgû. The English common name for the chickadee is a butchered translation of the Cherokee name, tsïkïlïlï. Similar-sounding names for other birds that English speakers renamed or mispronounced are scattered throughout East Coast tribes.

The explorers didn’t “conveniently ignore” anything. Many times, as in the chickadee name, whites couldn’t pronounce or tried to phonetically spell a place or animal name. A famous example is the city of “Chicago.” In the Algonquin language, the place where the city was built was called “shikaakwa,” meaning “striped skunk” or “onion.”

But since native Americans and native Africans had no written language, how were white people supposed to get it right? Naturalists in the field had to try and put a name to an animal they had never seen using a language with which they were mostly unfamiliar. As the chickadee example shows, they made an effort to use native language in naming species but usually fell short.

“A whole lot of Native people, in thinking about birds, don’t open a book of science. Their book of science is in the knowledge possessed by people in generations before them, the elders,” said Shepard Krech III, a professor emeritus at Brown University.

Bird lovers have agitated to change eponyms linked to racists for several years but have encountered resistance.

It would cause confusion in the profession and among casual birders, opponents said. Books and ledgers would have to be revised, and people would have to learn new names. Only twice have such objections been overcome and the American Ornithological Society approved a switch. The first was for the oldsquaw, a species of waterfowl now known as the long-tailed duck. And last summer, the McCown’s longspur became the thick-billed longspur — the first time a name with a Confederate past was dropped.

Whatever happened to viewing the totality of someone’s life before condemning them to the ash heap of history? Race and racism should not and cannot define an entire person’s existence. That’s seriously flawed logic.

## BiologyBase

Each spring about 600,000 Sandhill Cranes migrate north from the southern U.S. to central Canada where they breed. During the migration, these 4ft tall birds spend a few weeks resting and feeding along the middle reaches of the Platte River in central Nebraska.

While there, the birds spend their days in small flocks wandering the post-harvest corn fields eating weed-shoots, snails and worms. At night, they gather in the wide, shallow river away from predators. These overnight gatherings can number in the tens of thousands of birds in one small area of the river.

This is the largest gathering of cranes on the planet, and a spectacle well worth experiencing first hand.

This year, along a short stretch of the river just east of Kearney, Nebraska, about 70,000 birds gathered. The Rowe Audubon Sanctuary there hosts morning and evening trips to their blinds to watch the birds either gathering or leaving the river. Yesterday I visited them and had a great time standing in a blind watching a few thousand cranes being cranes.

There are several other places along the river that provide similar experiences. This is just the one I picked, but I can recommend visit.

During the day, you can find cranes along any roadway, feeding in the open fields. A large number can be seen from the Interstate (I-80) as well, so even if you’re just driving through, it’s something to watch for.

Rowe Sanctuary also have a live “crane cam” that I highly recommend watching – check it out at dawn or dusk local time (about 7 am/pm) for the maximum number of birds. Make sure you have your sound turned on, you can hear them.

My own small compilation video of what I saw is presented here below. Enjoy!

Yesterday I ventured back to Omaha’s Henry Doorly Zoo and had a very nice time. I took quite a lot of video. Here’s a little video production on endangered Lake Victoria Cichlid fishes which the zoo breeds.

(note the sound track is entirely optional, as it is background music)

One of my Christmas presents this year is a membership for Omaha’s Henry Doorly Zoo. Since they only have calendar year memberships, it starts today (1/1/10) and wishing to take full advantage of it, I went.

I’ve been to the Omaha Zoo once before, about 18 months ago in the summer of 2009. Not much has changed in that time, except the weather. Where it was sweltering with occasional showers when I went then, it was freezing with occasional flurries today. I think there’s about a 90 degree (F) difference in the air temperature between the two days.

It was, as expected, a pleasant visit today. Very few people were there so it was easy to get around. The animals were not sleeping in their dens to get out of the heat, which is often a problem with summer zoo visits.

Unfortunately, until we stopped at the restaurant at the end of our visit, there was no sign anywhere that most of the zoo was closed due to the snow and ice. All the hoofed stock, the aviary and all the larger enclosures were closed. This is not to be unexpected, but disappointing to not find this out until two hours in to the visit (no sign at the front desk!).

Wayfinding at this zoo is notedly lacking. Though there are a few signs here and there, it was very difficult to figure out, even with map in hand, where things are. There are lots of meandering intersections with no signage whatever. Also not good.

We began this visit at the aquarium. It’s a nice enough aquarium, and better than some I’ve been to. I’m not sure if it has a focus, but it has some really nifty animals.

A highlight for me was the Tufted Puffin exhibit. I’ve not seen them on display anywhere else, though I know some other places have them. Seeing several penguin species was also a treat. Other highlights were the Pacific Giant Octopus, which was not hiding as they usually do, and the Leafy Sea Dragon.

I’m also a sucker for Amazonian fishes, and they have a nice Amazon river exhibit, though while the size of the individual fishes they have is impressive, it’s a very limited collection for an exhibit next to one of the great river systems in the world.

We also visited the primate buildings, and were able to see the youngest Gorilla in the collection, a young male about 4 months hold. They have a nice sign explaining that while his mother was taking care of him, he became injured and they had to make the decision to separate & human-raise him.

His mother, I’d like to point out, was the first test-tube baby Gorilla, and having her reproduce is a great mark. It might be nice for some signage about that – I had to put it together through several different signs.

The Orangutan and Gorilla buildings are quite nice, though like the outside, there’s no wayfinding aids to speak of. Especially in the Gorilla area where many of the outdoor enclosures can be seen from inside, it would be nice to have at least one sign noting “this way to the winter enclosures” or something like that.

We had, for some reason, difficulty in getting to the Big Cat house. Though the entrance is only a few feet away from the Gorilla and Orangutan buildings, there’s no wayfinding aid until you happen by an ordinary door with a small sign that kinda tells you it’s the winter entrance. And finding that door was a long trek down and around a snowy hill. But the cats are nice, and many of them were enjoying a day of limited visitorship and were perched near the front glass of their winter quarters. Of course it was very nice to see the Siberian Tigers with outdoor access and lying in the snow.

There was a strange sign on the lion enclosure, stating that the lions had access to the indoor enclosure. Um. They were indoors and so were we. Did someone not read?

I was also disappointed in not seeing a clouded leopard. They’re one of my favorite cats, and their listed as in the collection of the Big Cat House by the zoo’s website (which is not exactly informative). But the Snow and Snow Leopards were nice to see.

For today, the aviary was the only other part of the zoo we wanted to see, but of course that was closed. We’ll be going regularly through the rest of the year to make sure I get to see everything thoroughly.

Our final stop was the zoo’s restaurant, where we had a very pleasant meal. It is, as such places go neither spectacular nor bad. However, having a zoo department staff meeting in that public space was not a good thing. There was some minor procedural and personnel talk that probably shouldn’t have been aired in public spaces.

In any event, it was a pleasant visit and I did get to see some great things. I would definitely recommend the zoo, and I’m happy to be a member and will be returning. There were just some things I would like to see done better.

And as they point out – even in weather like today (7F), they have 6 acres of enclosed exhibit space to keep warm.

For more information, the website of Omaha’s Henry Doorly Zoo is http://www.omahazoo.com/

In honor of todays 150th anniversary of the publication of Charles Darwin’s “On the Origin of Species” I thought I might try to address a simple question. What is a species?

Simple? Not quite. Like some other things, many biologists have to fall back on “I know a species when I see one.” It’s a slightly slippery concept, this species thing. The problem is, primarily, that nothing in biology is an absolute – including this sentiment.

Biology is a science full of exceptions. It’s very very rarely a cut and dried science, especially around the edges. What a species is is one of those edges.

The most common definition of a species is the “biological species concept”. Basically this states that a species is any population of organisms that has the potential under natural conditions to mate and produce fertile offspring (a group that can get together and have babies that can grow up to have babies).

This works pretty much for most vetebrates (animals with backbones like mammals & birds). Perhaps the most important word in the definition is “potential”. This is included because, obviously, males and males can’t get together to produce offspring, but any male should be able to mate with any female, and their female offspring should be able to mate with any other male.

It also accounts for geography and time – two individuals may live in different places or different times, but if they did live together and mated, then they could produce offspring. A cheetah living in the 1850s is the same species as one living in the 1950s because if they were brought together, they could reproduce. The same is true of cheetahs living today in an Australian zoo and on the African veldt. They could reproduce if they got together.

Another part of this species concept is the “under natural conditions” provision. It covers populations that would never get together unless “forced”. For instance, in captivity, lions and tigers will produce offspring. Most of the offspring are not able to reproduce, but some are. But in the wild, the two species would never mate. Tigers and lions are more apt to kill each other in the wild when they meet than settle down to raise a family.

The final component of the biological species concept is that the kids of any such mating needs to be able to have kids of their own. Lions and tigers when they mate rarely produce fertile offspring. The same is true of most organisms that mate across the species boundary – their kids are sterile and can’t have kids.

There are several other species definitions, and I’ll cover many of those in the near future. Meantime, pick up a copy of The Origin Of Species

and take a read. It’s the most important book in biology. Really.

Part of my move to the Missouri River Valley included the acquisition of three cats. Or should I say the acquisition BY three cats. They belong to my host here and they’re wonderful.

The cats all love to play with water if it’s moving. They’ll spend long minutes staring and batting at a dripping faucet. Like most cats they’ll also play with just about anything that moves.

Cats’ vision is actually different than our own. They do not see a static environment very well, but they are immediately attracted to and able to clearly see any movement against a background.

Their prey in the wild (and sometimes around the house), of course, is mostly small creatures. Often these creatures are well camouflaged. The one thing they can’t camouflage is their movement and cat vision takes advantage of that.

A dripping faucet, bouncing light or rolling cat toy are attractive to cats because their instinct is to chase small moving prey. And their vision is tuned to seeing it better.

In fact, a cats’ eyes are so keenly adapted to see motion more clearly (and so comparably poor at seeing non-moving things) that if you look very very closely into a cat’s eyes, you’ll see they vibrate! Just a little, but this vibration puts the whole world into motion. This way the cats can see things much more clearly.

This adaptation also helps them to see in the dark – cats are, really, nocturnal animals after all. In dim light their eyes can see the motion against a background, even if they can’t see the background details.

So if you want to attract the attention of a cat, move!

With my migration to the center of the country came an opportunity to put out a bird feeder. I’ve had it up for a little over a week now and there are birds coming regularly now.

It often takes a week or more for birds to discover a new feeder. Birds establish daily patterns of movement to make the most out of local resources (food and water) and it can take some time for them to break out of those patterns.

Actually, some birds, like House Sparrows (*Passer domesticus*) are better at breaking out of those patterns than others. In the case of the House Sparrow, they’re very good at it. This often means they’re the first ones to a new feeder.

Once one bird, such as a House Sparrow, has found the feeder, other birds start to notice. Birds are always watching out for what’s going on around them, even with other species of birds.

Some species are more alert to predators and some (like the House Sparrows) are more alert to new feeding opportunities. This way all the birds in an area benefit from taking advantage of the strengths of others.

This also happens, of course, within a species. Birds that flock pay attention to the birds around them. As different species have their strengths, some individuals are more alert to predators or food sources than others. All the birds in the flock benefit from watching the others.

And rarely is the same bird the one who always spots a danger or opportunity. Different birds in a flock and different species in an area will notice things at different times. Sometimes the House Sparrows will lead and sometimes the Jays will lead.

This same type of behavior is common to all animals that collect in groups. A herd of antelope is better than watching for a lion than a single antelope simply because there are more eyes pointed in more directions. A school of fish is more likely to notice a patch of food than a single fish.

We humans do it too. A group of people is more likely to see an oncoming car when crossing a road, or notice the sign of the restaurant they’re looking for.

In some neighborhoods too, there is a flocking behavior among humans. Once one person starts feeding birds and showing enjoyment, often some of their neighbors start doing it too.

It’s that time of year in the Northern Hemisphere when the hours of daylight are getting shorter and temperatures in most places are getting cooler.

But at this same time, the Southern Hemisphere is starting to warm up. The hours of daylight are getting longer and while many may still it Fall (or Autumn), the season’s heading for summer.

The change has to do with the tilt in the axis of the Earth in relation to the sun. The planet’s rotation axis (the imaginary line through the earth between the north pole and the south pole) is tilted at about a 45 degree angle. As the planet takes its trip around the sun (which takes about 365 days), for about half that trip the north pole is closer to the sun than the south pole. For the other half of the trip, the south pole is closer.

The change-over happens on the days we call the “solstice”. Starting at the winter solstice (December 21st or 22nd), the north pole gradually points more an more toward the sun. At the summer solstice (June 21st or 22nd) the north pole starts pointing away from the sun.

These days are also known as the shortest and longest days of the year. The daylight in the northern hemisphere is longest on the summer solstice, and shortest in the southern hemisphere.

There are also two “equinox” days – around September 21 and March 20th. These are the “flip days” where the daylight and night time are of equal length. The north and south poles are, at those times, changing between pointing toward and away from the sun.

The length of daylight also affects the temperature. Less daylight means there’s less time for the sun to heat the earth (rocks, dirt, water), so the overall temperature drops.

Okay, what has all this got to do with biology? Lots.

Many plants and animals react to the length of daylight or to the change in temperature. Sometimes it’s difficult to figure out whether the organism is responding to light or heat.

But, as day length gets shorter (and temperature drops), some animals begin to migrate toward the hemisphere that’s getting more daylight. Some start eating more so they can put on weight for hibernation. Many plants set seed or flower as days get shorter.

As daylight gets longer, many animals get ready to breed. Many plants start their growth season and put out their flowers for pollination.

These changes in animal and plant behavior are, of course, more pronounced the farther north and south the organisms live. Near the equator the changes are not nearly as dramatic.

The Amazon and Congo Rainforests, for instance, don’t have as much daylight change as here in the north-central Great Plains of North America. The sun is always nearly overhead for them. So, temperatures there (except in the highlands) rarely get really cold. While here, we’re expecting snow already this weekend, just about three weeks after the equinox.

So, all those changes in the world around you – trees budding or losing their leaves, animals migrating, flowers blooming, are responses to the way the Earth is tilted in space.

Happy southern summer and northern winter.

About a week ago I hung up a bird feeder in my new backyard. It’s a tube feeder filled with safflower seeds.

Here in the Missouri River Valley, that’s apparently a good seed to put out to attract birds other than grackles (which come to the yard anyway).

Today I got the first birds to visit! The first I saw was a House Sparrow, which is introduced and nothing special. But it was quickly followed by a White-breasted Nuthatch. Also nothing special to me, as they come to feeders where ever they’re found.

The third bird, though! It was a Black-capped Chickadee. Of course that’s not too surprising, since they’re a common bird at feeders, but it’s the first one I’ve ever had at a feeder.

I’ve fed birds in Mississippi and in California, two places where you’re not likely to get Black-capped Chickadee.

In Mississippi I would get Carolina Chickadees, which do hybridize with the Black-capped, and are difficult to tell apart except for song (at least at first glance). In California the Chestnut-backed Chickadee was the feeder chickadee. Mountain Chickadees also occur in California, but not in the lowland areas I lived.

Chickadees are some of my favorite birds. They belong to the family Paridae that includes the chickadees, tits and titmice. They are some of the most intelligent of birds, and individuals of several species have learned extremely complex behaviors. All are small, generally much smaller than blackbirds.

So. I’m going to enjoy my bird feeders and watching those chickadees.

Dinosaurs may have weighed less than previously thought.

According to Scientific American, a paper published in the Jun 21, 2009 issue of the Journal of Zoology, (http://www.wiley.com/bw/journal.asp?ref=0952-8369) has reexamined the calculations upon which our understanding of the weights of non-avian dinosaurs.

The old calculations, used for several decades, apparently are full of flaws and end up estimating weight at about twice the actual weight. The authors of the paper have proposed new calculations that are much more accurate. In estimating an elephant’s weight from a single femur, the new calculations were only seven pounds off the actual recorded weight of the elephant (1300 actual, 1307 estimated). The old calculation estimated the elephant’s weight at over 20,000 pounds.

As the Scientific American article says, this has the potential to change much of what we think we know about dinosaurs. *Tyrannosaurus rex*, for instance, goes from a six ton to a three ton carnivore. Still a mighty beast, not something you want to meet on a dark night in a jungle.

However, a three ton (6000 pound) carnivore could require much less food. New estimates of weights for the large dinosaurs should help solve several apparent riddles about how such creatures could find enough food to sustain themselves.

There are many more exciting potential ramifications for this change in calculation. Look for new insights to be coming out of paleontology – and not just for dinosaurs. There are lots of mammals that will need their weight recalculated.

According to the BBC, a Gyrfalcon (*Falco rusticolus*) nest in Greenland has been identified that is over 2,500 years old. It is currently in use. There are apparently also three nests about 1,000 years old. At least one of them appears to be in current use.

Gyrfalcons nest on ledges on cliffs, so it make much sense that if a suitable ledge remains available, it would remain used. That a bird would use a spot for such a long time is not so unusual. Many ground and cliff nesting birds might use the same place for a very long time. In the case of ground nesters, it’d be less likely that a particular spot would be used continuously for that long, but the general area – a beach, an area of tundra or some similar place might be used for thousands of years.

The trick, of course, is that in order to be used constantly, the spot needs to remain suitable for that amount of time so the bird will continue to find it. When nest sites are numerous (on a basically flat beach, they’re pretty much everywhere) the birds don’t need to return to the same exact spot each year.

When the birds are tree or bush nesting, they can’t be quite that faithful to a nest spot – any given year a fire or other incident might take the previous year’s home away. They have to be flexible enough to use a different place for their nest.

In the case of the Gyrfalcons, they have found stable ledges, where ledges are uncommon and the birds have used them – partly because they have no or almost no choice if they’re going to breed. So the same sites get used year after year. It makes perfect sense, but it’s cool to have the idea proven.

Doing the “paleontology” of these nest has given much new information to the scientists doing the study. They have found new information about the diet and other habits of the Gyrfalcon over the last 2,500 years by studying the remains found in the nests.

Similar work is done with woodrat (*Neotoma* spp) nests found in the American desert southwest. While woodrats may not use the nests quite as long as the falcons, the large nests can become preserved. Also known as packrats, the woodrats collect things from the area around their nests, which may include just about anything.

Excavating the nests has yielded some important information about the past climates in the area.

## Curvilinear regression

Use curvilinear regression when you have graphed two measurement variables and you want to fit an equation for a curved line to the points on the graph.

### When to use it

Sometimes, when you analyze data with correlation and linear regression, you notice that the relationship between the independent (*X*) variable and dependent (*Y*) variable looks like it follows a curved line, not a straight line. In that case, the linear regression line will not be very good for describing and predicting the relationship, and the *P* value may not be an accurate test of the null hypothesis that the variables are not associated.

You have three choices in this situation. If you only want to know whether there is an association between the two variables, and you're not interested in the line that fits the points, you can use the *P* value from linear regression and correlation. This could be acceptable if the line is just slightly curved if your biological question is "Does more *X* cause more *Y*?", you may not care whether a straight line or a curved line fits the relationship between *X* and *Y* better. However, it will look strange if you use linear regression and correlation on a relationship that is strongly curved, and some curved relationships, such as a U-shape, can give a non-significant *P* value even when the fit to a U-shaped curve is quite good. And if you want to use the regression equation for prediction or you're interested in the strength of the relationship (*r* 2 ), you should definitely not use linear regression and correlation when the relationship is curved.

A second option is to do a data transformation of one or both of the measurement variables, then do a linear regression and correlation of the transformed data. There are an infinite number of possible transformations, but the common ones (log, square root, square) will make a lot of curved relationships fit a straight line pretty well. This is a simple and straightforward solution, and if people in your field commonly use a particular transformation for your kind of data, you should probably go ahead and use it. If you're using the regression equation for prediction, be aware that fitting a straight line to transformed data will give different results than fitting a curved line to the untransformed data.

Your third option is curvilinear regression: finding an equation that produces a curved line that fits your points. There are a lot of equations that will produce curved lines, including exponential (involving *b X* , where *b* is a constant), power (involving *X b* ), logarithmic (involving log(*X*)), and trigonometric (involving sine, cosine, or other trigonometric functions). For any particular form of equation involving such terms, you can find the equation for the curved line that best fits the data points, and compare the fit of the more complicated equation to that of a simpler equation (such as the equation for a straight line).

Here I will use polynomial regression as one example of curvilinear regression, then briefly mention a few other equations that are commonly used in biology. A polynomial equation is any equation that has *X* raised to integer powers such as *X* 2 and *X* 3 . One polynomial equation is a quadratic equation, which has the form *Y*̂=*a*+*b _{1}X*+

*b*, where

_{2}X 2*a*is the

*y*&ndashintercept and

*b*

_{1}and

*b*

_{2}are constants. It produces a parabola. A cubic equation has the form

*Y*̂=

*a*+

*b*+

_{1}X*b*+

_{2}X 2*b*and produces an S-shaped curve, while a quartic equation has the form

_{3}X 3*Y*̂=

*a*+

*b*+

_{1}X*b*+

_{2}X 2*b*+

_{3}X 3*b*and can produce M or W shaped curves. You can fit higher-order polynomial equations, but it is very unlikely that you would want to use anything more than the cubic in biology.

_{4}X 4### Null hypotheses

One null hypothesis you can test when doing curvilinear regression is that there is no relationship between the *X* and *Y* variables in other words, that knowing the value of *X* would not help you predict the value of *Y*. This is analogous to testing the null hypothesis that the slope is 0 in a linear regression.

You measure the fit of an equation to the data with *R* 2 , analogous to the *r* 2 of linear regression. As you add more parameters to an equation, it will always fit the data better for example, a quadratic equation of the form *Y*̂=*a*+*b _{1}X*+

*b*will always be closer to the points than a linear equation of the form

_{2}X 2*Y*̂=

*a*+

*b*, so the quadratic equation will always have a higher

_{1}X*R*2 than the linear. A cubic equation will always have a higher

*R*2 than quadratic, and so on. The second null hypothesis of curvilinear regression is that the increase in

*R*2 is only as large as you would expect by chance.

### Assumptions

If you are testing the null hypothesis that there is no association between the two measurement variables, curvilinear regression assumes that the *Y* variable is normally distributed and homoscedastic for each value of *X*. Since linear regression is robust to these assumptions (violating them doesn't increase your chance of a false positive very much), I'm guessing that curvilinear regression may not be sensitive to violations of normality or homoscedasticity either. I'm not aware of any simulation studies on this, however.

Curvilinear regression also assumes that the data points are independent, just as linear regression does. You shouldn't test the null hypothesis of no association for non-independent data, such as many time series. However, there are many experiments where you already know there's an association between the *X* and *Y* variables, and your goal is not hypothesis testing, but estimating the equation that fits the line. For example, a common practice in microbiology is to grow bacteria in a medium with abundant resources, measure the abundance of the bacteria at different times, and fit an exponential equation to the growth curve. The amount of bacteria after 30 minutes is not independent of the amount of bacteria after 20 minutes if there are more at 20 minutes, there are bound to be more at 30 minutes. However, the goal of such an experiment would not be to see whether bacteria increase in abundance over time (duh, of course they do) the goal would be to estimate how fast they grow, by fitting an exponential equation to the data. For this purpose, it doesn't matter that the data points are not independent.

Just as linear regression assumes that the relationship you are fitting a straight line to is linear, curvilinear regression assumes that you are fitting the appropriate kind of curve to your data. If you are fitting a quadratic equation, the assumption is that your data are quadratic if you are fitting an exponential curve, the assumption is that your data are exponential. Violating this assumption&mdashfitting a quadratic equation to an exponential curve, for example&mdashcan give you an equation that doesn't fit your data very well.

In some cases, you can pick the kind of equation to use based on a theoretical understanding of the biology of your experiment. If you are growing bacteria for a short period of time with abundant resources, you expect their growth to follow an exponential curve if they grow for long enough that resources start to limit their growth, you expect the growth to fit a logistic curve. Other times, there may not be a clear theoretical reason for a particular equation, but other people in your field have found one that fits your kind of data well. And in other cases, you just need to try a variety of equations until you find one that works well for your data.

### How the test works

In polynomial regression, you add different powers of the *X* variable (*X*, *X* 2 , *X* 3 &hellip) to an equation to see whether they increase the *R* 2 significantly. First you do a linear regression, fitting an equation of the form *Y*̂=*a*+*b _{1}X* to the data. Then you fit an equation of the form

*Y*̂=

*a*+

*b*+

_{1}X*b*, which produces a parabola, to the data. The

_{2}X 2*R*2 will always increase when you add a higher-order term, but the question is whether the increase in

*R*2 is significantly greater than expected due to chance. Next, you fit an equation of the form

*Y*̂=

*a*+

*b*+

_{1}X*b*+

_{2}X 2*b*, which produces an S-shaped line, and you test the increase in

_{3}X 3*R*2 . You can keep doing this until adding another term does not increase

*R*2 significantly, although in most cases it is hard to imagine a biological meaning for exponents greater than 3. Once you find the best-fitting equation, you test it to see whether it fits the data significantly better than an equation of the form

*Y*=

*a*in other words, a horizontal line.

Even though the usual procedure is to test the linear regression first, then the quadratic, then the cubic, you don't need to stop if one of these is not significant. For example, if the graph looks U-shaped, the linear regression may not be significant, but the quadratic could be.

### Examples

Fernandez-Juricic et al. (2003) examined the effect of human disturbance on the nesting of house sparrows (*Passer domesticus*). They counted breeding sparrows per hectare in 18 parks in Madrid, Spain, and also counted the number of people per minute walking through each park (both measurement variables).

Graph of sparrow abundance vs. human disturbance with linear regression line.

The linear regression is not significant (*r* 2 =0.174, 16 d.f., *P*=0.08).

Graph of sparrow abundance vs. human disturbance with quadratic regression line.

The quadratic regression is significant (*R* 2 =0.372, 15 d.f., *P*=0.03), and it is significantly better than the linear regression (*P*=0.03). This seems biologically plausible the data suggest that there is some intermediate level of human traffic that is best for house sparrows. Perhaps areas with too many humans scare the sparrows away, while areas with too few humans favor other birds that outcompete the sparrows for nest sites or something.

Graph of sparrow abundance vs. human disturbance with cubic regression line.

The cubic graph is significant (*R* 2 =0.765, 14 d.f., *P*=0.0001), and the increase in *R* 2 between the cubic and the quadratic equation is highly significant (*P*=1×10 &minus5 ). The cubic equation is *Y*̂=&minus87.765+50.601*X*&minus2.916*X* 2 +0.0443*X* 3 .

The quartic equation does not fit significantly better than the cubic equation (*P*=0.80). Even though the cubic equation fits significantly better than the quadratic, it's more difficult to imagine a plausible biological explanation for this. I'd want to see more samples from areas with more than 35 people per hectare per minute before I accepted that the sparrow abundance really starts to increase again above that level of pedestrian traffic.

Ashton et al. (2007) measured the carapace length (in mm) of 18 female gopher tortoises (*Gopherus polyphemus*) in Okeeheelee County Park, Florida, and X-rayed them to count the number of eggs in each. The data are shown below in the SAS example. The linear regression is not significant (*r* 2 =0.015, 16 d.f., *P*=0.63), but the quadratic is significant (*R* 2 =0.43, 15 d.f., *P*=0.014). The increase in *R* 2 from linear to quadratic is significant (*P*= 0.001). The best-fit quadratic equation is *Y*̂=&minus899.9+5.857*X*&minus0.009425*X* 2 . Adding the cubic and quartic terms does not significantly increase the *R* 2 .

The first part of the graph is not surprising it's easy to imagine why bigger tortoises would have more eggs. The decline in egg number above 310 mm carapace length is the interesting result it suggests that egg production declines in these tortoises as they get old and big.

X-ray of a tortoise, showing eggs. Graph of clutch size (number of eggs) vs. carapace length, with best-fit quadratic line.

### Graphing the results

As shown above, you graph a curvilinear regression the same way you would a linear regression, a scattergraph with the independent variable on the *X* axis and the dependent variable on the *Y* axis. In general, you shouldn't show the regression line for values outside the range of observed *X* values, as extrapolation with polynomial regression is even more likely than linear regression to yield ridiculous results. For example, extrapolating the quadratic equation relating tortoise carapace length and number of eggs predicts that tortoises with carapace length less than 279 mm or greater than 343 mm would have negative numbers of eggs.

### Similar tests

Before performing a curvilinear regression, you should try different transformations when faced with an obviously curved relationship between an *X* and a *Y* variable. A linear equation relating transformed variables is simpler and more elegant than a curvilinear equation relating untransformed variables. You should also remind yourself of your reason for doing a regression. If your purpose is prediction of unknown values of *Y* corresponding to known values of *X*, then you need an equation that fits the data points well, and a polynomial regression may be appropriate if transformations do not work. However, if your purpose is testing the null hypothesis that there is no relationship between *X* and *Y*, and a linear regression gives a significant result, you may want to stick with the linear regression even if curvilinear gives a significantly better fit. Using a less-familiar technique that yields a more-complicated equation may cause your readers to be a bit suspicious of your results they may feel you went fishing around for a statistical test that supported your hypothesis, especially if there's no obvious biological reason for an equation with terms containing exponents.

Spearman rank correlation is a nonparametric test of the association between two variables. It will work well if there is a steady increase or decrease in *Y* as *X* increases, but not if *Y* goes up and then goes down.

Polynomial regression is a form of multiple regression. In multiple regression, there is one dependent (*Y*) variable and multiple independent (*X*) variables, and the *X* variables (*X*_{1}, *X*_{2}, *X*_{3}. ) are added to the equation to see whether they increase the *R* 2 significantly. In polynomial regression, the independent "variables" are just *X*, *X* 2 , *X* 3 , etc.

### How to do the test

#### Spreadsheet

I have prepared a spreadsheet that will help you perform a polynomial regression. It tests equations up to quartic, and it will handle up to 1000 observations.

#### Web pages

There is a very powerful web page that will fit just about any equation you can think of to your data (not just polynomial).

Salvatore Mangiafico's *R Companion* has sample R programs for polynomial regression and other forms of regression that I don't discuss here (B-spline regression and other forms of nonlinear regression).

To do polynomial regression in SAS, you create a data set containing the square of the independent variable, the cube, etc. You then use PROC REG for models containing the higher-order variables. It's possible to do this as a multiple regression, but I think it's less confusing to use multiple model statements, adding one term to each model. There doesn't seem to be an easy way to test the significance of the increase in *R* 2 in SAS, so you'll have to do that by hand. If *R* 2 _{i} is the *R* 2 for the *i*_{th} order, and *R* 2 _{j} is the *R* 2 for the next higher order, and d.f._{j} is the degrees of freedom for the higher-order equation, the F-statistic is d.f._{j}×(*R* 2 _{j}&minus*R* 2 _{i})/(1&minus*R* 2 _{j}). It has *j* degrees of freedom in the numerator and d.f._{j}=*n*&minus*j*&minus1 degrees of freedom in the denominator.

Here's an example, using the data on tortoise carapace length and clutch size from Ashton et al. (2007).

In the output, first look for the *R* 2 values under each model:

For this example, *n*=18. The F-statistic for the increase in *R* 2 from linear to quadratic is 15×(0.4338&minus0.0148)/(1&minus0.4338)=11.10 with d.f.=2, 15. Using a spreadsheet (enter =FDIST(11.10, 2, 15)), this gives a *P* value of 0.0011. So the quadratic equation fits the data significantly better than the linear equation.

Once you've figured out which equation is best (the quadratic, for our example, since the cubic and quartic equations do not significantly increase the *R* 2 ), look for the parameters in the output:

This tells you that the equation for the best-fit quadratic curve is *Y*̂=&minus899.9+5.857*X*&minus0.009425*X* 2 .

### References

Ashton, K.G., R.L. Burke, and J.N. Layne. 2007. Geographic variation in body and clutch size of gopher tortoises. Copeia 2007: 355-363.

Fernandez-Juricic, E., A. Sallent, R. Sanz, and I. Rodriguez-Prieto. 2003. Testing the risk-disturbance hypothesis in a fragmented landscape: non-linear responses of house sparrows to humans. Condor 105: 316-326.

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This page was last revised July 20, 2015. Its address is http://www.biostathandbook.com/curvilinearregression.html. It may be cited as:

McDonald, J.H. 2014. Handbook of Biological Statistics (3rd ed.). Sparky House Publishing, Baltimore, Maryland. This web page contains the content of pages 213-219 in the printed version.

©2014 by John H. McDonald. You can probably do what you want with this content see the permissions page for details.