AUTHOR BLOG: “Bird-in-the-middle”—a mid-elevation tropical species stuck in limbo

Fabio Berzaghi & John Bates

Linked paper: Comparative niche modeling of two bush-shrikes (Laniarius) and the conservation of mid-elevation Afromontane forests of the Albertine Rift by F. Berzaghi, J.E. Engel, A.J. Plumptre, H. Mugabe, D. Kujirakwinja, S. Ayebare, and J.M. Bates, The Condor: Ornithological Applications 120:4, October 2018.

Capture

A search through the tropical forest literature for “mid-elevation forests” reveals relatively few results compared to a search for high-elevation or lowland forests, and looking at a map of protected areas and land cover in mountainous tropical regions makes it clear why. For example, in the African Albertine Rift, most national parks tend to be in high elevation areas where slopes are steep and land conversion for human use is more difficult. As we move down the slopes, the habitat starts degrading until we arrive in the lowlands, where almost no intact habitat remains, particularly on the eastern side of the Rift.

In 2010, Voelker et al. described a new species of bush-strike, the Willard’s Sooty Boubou (Laniarius willardi), and noticed that this species occurs at lower elevations than its sister species, the Mountain Sooty Boubou (Lanarius poensis). We were thus wondering how much habitat was left for this mid-elevation species, knowing that in this region lower-elevation forests are degraded or have been converted to agriculture. Using niche modeling and land cover data, we discovered that these two species of birds reside at different elevations across a small portion of montane Africa, overlapping only in part. Unfortunately, the habitat for L. willardi has been greatly reduced, because mid-elevation forests are outside protected areas and national parks. L. willardi may not be able to move to higher elevations, as its preferred environmental conditions are between 1200 and 1900 meters; a large portion of its suitable habitat is found in the Democratic Republic of the Congo’s Itombwe Plateau, technically a protected area but problematic to protect.

The plight of L. willardi is probably similar to that of many other mid- and low-elevation species in the area. Even though our results are not such good news for birds and other mid-elevation species in the region, we also want to highlight the importance of scientific collaborations with local researchers and conservation units. These collaborations help us define habitats and species in need of attention. Importantly, the authors of our study are a combination of Africans and non-Africans, with a range of research foci including ornithology and conservation but also niche modeling and bioinformatics. The data used in our study are based on both museum specimens (historical and modern) and modern field observations, which were carried out by teams that always included African students and scientists from the countries where the data were collected. Conservation can only be successful in the long run if in-country capacity for conservation science is developed around the world.

The discovery of L. willardi and its description were made possible through modern scientific collection during collaborations between local Albertine Rift ornithologists and the Field Museum. Data from such modern collections will help clarify lingering concerns in the taxonomic community (particularly Birdlife International and the IUCN) in regards to the status of these two species relative to other black boubous occurring far to the west in the Cameroonian Highlands. Work like this has great value, because it allows highlighting issues of conservation concern at both regional and local scales. Each region of the Albertine Rift has its own history and ongoing issues with deforestation, instability and protection. There is no “one size fits all” solution to conservation in the Albertine Rift, but this paper helps emphasize that there is regional expertise in the form of researchers and conservation professionals who will make a difference. Opportunities to work with international colleagues to combine conservation and science, as in this paper, will be instrumental in building efforts to protect the incredible biota of this wonderful region.

AUTHOR BLOG: What time do baby birds leave home?

Christine Ribic

Linked paper: Diel fledging patterns among grassland passerines: Relative impacts of energetics and predation risk by C.A. Ribic, C.S. Ng, N. Koper, K. Ellison, P.J. Pietz, and D.J. Rugg, The Condor: Ornithological Applications 120:4, October 2018.

AUK-17-213 GRSP C Ribic-USGS

A Grasshopper Sparrow chick leaves its nest. Credit: C. Ribic, USGS

We know that human kids grow, mature, and gradually move towards a life that is independent of their parents’ home.  The same is true for baby birds: they also have to decide when the time is right to leave the nest and start on their journey to independence. This seems to involve a balancing act between making sure they are big and healthy enough to survive independently, while leaving the nest quickly to avoid predators. Nests are busy places where chicks beg for food and parents are constantly coming and going with food deliveries. All of this activity could easily draw predators to the nest! The timing of chicks leaving the nest (fledging) isn’t well understood, particularly for birds that live in grasslands, many of which are threatened or endangered due to habitat loss.

Our new research focused on a variety of grassland songbirds, such as meadowlarks, sparrows, and longspurs. We found that the time baby birds leave the nest has more to do with having enough food (energetics) than avoiding predators. This is surprising because research on birds nesting in shrubs says that risk of predation is the most important thing affecting when chicks leave the nest. This suggests that nests in grasslands (hidden on the ground with protective cover from surrounding grasses and a few low shrubs) face different risks than nests placed in shrubs.

We found that grassland chicks can start to leave anytime throughout the day and when they leave depends on what species they are. Some chicks, like Clay-colored Sparrow and Grasshopper Sparrow, usually left the nest in the early morning, while Eastern Meadowlark and Chestnut-collared Longspur left closer to mid-morning. But sometimes chicks delayed leaving until the afternoon, with their siblings waiting until the next day to depart. The time it takes for all the chicks to leave a nest can be several hours to more than a day! Maybe some chicks are taking advantage of their siblings’ early departures to get more food and attention from mom and dad before they finally leave, too.

Measuring fledging time can be tricky because chicks run in and out of the nest multiple times before leaving for good. We don’t know why they do this; maybe they are exploring their world and gaining confidence before leaving to brave the world outside their home. Remember these birds have only been alive for a week and a half or so!  Regardless, it’s a bit like kids going off for college but returning for school breaks … nestlings may leave and return repeatedly before fully fledging. Fledging is not nearly as simple as people think it is!

Understanding the fledging process allows us to better understand the biology of grassland birds. Learning about the pressures they face in their daily lives lets us understand what threats they face and how those threats may change as people alter grasslands. Grassland birds are declining more than birds of any other habitat type across North America. Research like this is part of understanding why they are declining and what we can do to help them recover.

AUTHOR BLOG: Count me in! I am available for detection at 6 AM on May 26th

Péter Sólymos

Linked paper: Evaluating time-removal models for estimating availability of boreal birds during point count surveys: Sample size requirements and model complexity by P.  Sólymos, S.M. Matsuoka, S.G. Cumming, D. Stralberg, P. Fontaine, F.K.A. Schmiegelow, S.J. Song, and E.M. Bayne, The Condor: Ornithological Applications 120:3, August 2018.

Point count survey duration rarely changes within projects but varies greatly among projects. As more and more large-scale studies are compiling and analyzing point count data from disparate sources, standardization becomes critical, because count duration greatly affects observations. The Boreal Avian Modelling (BAM, www.borealbirds.ca) project aims to further continental scale avian conservation through the integration and analysis of point count data collected across northern North America. In order to estimate population density and population size for landbird species, data integration became a real issue for us.

Two of the main sources of variation in the observed counts have nothing to do with ecological variables of interest, such as land cover and climate, but rather are considered nuisance variables. These are point count radius and point count duration. Recognizing that most studies do not follow survey protocol recommendations aimed to facilitate data integration (see e.g. Matsuoka et al. 2014), we opted to use model-based techniques to place our variable data on a common footing.

We first tackled standardizing for varying point count radii through distance sampling (Matsuoka et al. 2012) and eventually combined this with a removal model-based correction for varying point count duration. We named the method QPAD, referring to terms of our statistical notation: probability of detection (q), probability of availability (p), area surveyed (A) and population density (D) (Solymos et al. 2013). In the present paper we assessed different ways of controlling for point count duration. As the title indicates, we performed a cost-benefit analysis to make recommendations about when to use different types of the removal model.

We evaluated a conventional removal model and a finite mixture removal model, with and without covariates, for 152 bird species. We found that the probabilities of predicted availability under conventional and finite mixture models were very similar with respect to the range of probability values and the shape of the response curves to predictor variables. However, finite mixture models were better supported for the large majority of species. We also found overwhelming support for time-varying models irrespective of the parametrization.

So what is a finite mixture model? In our case, it splits the population of birds present at a location into frequent and infrequent singers. In previous parametrizations, researchers assumed that the singing rate of the infrequent group varies with date and time, whereas frequent singers remain frequent singers independent of time of year or time of day. We compared this to an alternate parametrization that assumes that individuals change behaviour over time and switch from frequent to infrequent singing behaviour—so it is the proportion of the two groups that varies. We found that the latter assumption was favoured.

Finite mixture models provide some really nice insight into how singing behaviour changes over time and, due to having more parameters, they provide a better fit and thus minimize bias in population size estimates. But all this improvement comes with a price: Sample size requirements (or more precisely, the number of detections required) are really high. To have all the benefits with reduced variance, one needs about 1000 non-zero observations to fit finite mixture models—20 times more than needed to reliably fit conventional removal models. This is much higher than previously suggested minimum sample sizes.

All of our findings indicate that lengthening the count duration from 3 minutes to 5-10 minutes is an important consideration when designing field surveys to increase the accuracy and precision of population estimates. Well-informed survey design, combined with various forms of removal sampling, is useful in accounting for availability bias in point counts, thereby improving population estimates and allowing for better integration of disparate studies at larger spatial scales. To this end, we provide our removal model estimates as part of the QPAD R package and the R functions required to fit all the above outlined removal models as part of the detect R package. We at the BAM project and our collaborators are already utilizing the removal model estimates to correct for availability bias in our continental and regional projects to inform better management and conservation of bird populations. Read more about these projects in our annual report.

AUTHOR BLOG: The real story behind murres’ pear-shaped eggs

Tim Birkhead

Linked paper: The pyriform egg of the Common Murre (Uria aalge) is more stable on sloping surfaces by T.R. Birkhead, J.E. Thompson, and R. Montgomerie, The Auk: Ornithological Advances 135:4, October 2018.

murre eggFor the past six years, Jamie Thompson, Bob Montgomerie, and I have tried to understand why murres produce a pear-shaped (pyriform) egg.

It started one evening in 2012 when I watched a well-known TV presenter take a murre’s egg from a tray of birds’ eggs in a museum. “The reason it is this shape,” he said, “is so that if it is knocked, it will spin on its axis rather than rolling off the cliff ledge.” He demonstrated this by spinning the egg.

I was appalled. That idea was nonsense and had been dismissed over a century earlier. Yes, if you take an empty eggshell you can indeed lie it on its side and spin it like a top on its side. But a murre egg full of yolk, albumen, and a developing embryo will not spin like that without undue force.

Having offered to send the presenter the papers pointing out why the spinning-like-a-top idea was wrong, I had a sudden crisis of confidence, and decided I had better re-read those papers myself.

I soon realized that the more widely accepted view — that a pyriform egg rolls in an arc and thereby minimizes the risk that it will fall off the breeding ledge — was not very convincing either. The rolling-in-an-arc idea gained support initially by some experiments in the 1960s using model eggs (made from plaster of Paris). But it was later found that model eggs simply do not roll like real eggs. Subsequent experiments with real murre eggs provided no convincing evidence for the rolling-in-an-arc idea, either.

What’s more, incubating murres invariably orient their egg with its blunt end directed up the slope, in towards the cliff, so that if the egg does roll, it will roll out to the edge. If the purpose of the pyriform egg was to prevent it from rolling off the ledge, then it would more sensible for the parent to orientate the egg the other way.

We decided to re-investigate, thinking explicitly about the selection pressures that might influence the shape of a murre’s egg.

We had two ideas. First, murres are poor flyers that breed at high density. As a result, crash landings onto incubating birds are common, so perhaps a pyriform shape confers greater strength and resilience against impacts. That proved to be a difficult idea to test.

Our second idea rested on the observation that murre ledges are filthy with excrement. Perhaps the pyriform shape enables an egg to keep its blunt end clean such that the pores for air exchange do not become blocked. We found that the density of pores on the blunt end of the egg was relatively high and, if you look at the distribution of dirt on murre eggs, most of it is on the pointed end. These results are consistent with the dirt hypothesis. However, it wasn’t clear whether avoiding dirt or avoiding damage from impacts were sufficiently strong selection pressures to have produced the shape.

Then, while climbing on murre ledges in 2017, I had a sudden thought. Perhaps the pyriform shape allows a murre’s egg to rest stably on the sloping ledges that murres often breed on. I had fresh murre eggs and Razorbill eggs (which are much less pointed and more elliptical in shape) to hand, and I tried placing them on a 30o rock slope. The murre egg rested there immediately, the Razorbill egg rolled off (into my hand, of course), and, indeed, there was no way I could position the Razorbill egg stably on that slope.

My colleague Jamie was climbing with me, so I called him over, said “Watch this!”, and demonstrated again. Same result. Then, together with Bob Montgomerie, we devised a series of tests to establish just how stable murre and Razorbill eggs are across a range of egg shapes on slopes of different steepness. We quantified egg shape using a new approach (Biggins et al. 2018). We then conducted two experiments, one using a moving slope and the other using three static slopes at 20o, 30 o and 40 o. We tested to see at what angle each egg would begin to roll on the moving slope and how successful we were at stably positioning each egg on the static slopes.

The results are clear. The more pyriform the egg, the more stable and less likely to roll out of place it is. Our results are NOT about how an egg will roll when it becomes unstable, but about whether it begins to roll in the first place, either when knocked or during changeovers. Our results indicate that the stability of a pyriform egg also makes it easier and safer for murres to manipulate (with their beak, wings and feet) their eggs during incubation and changeovers.

STABILITYinfographicV4

 

Links:

I started studying Common Murres (common guillemots in the UK) Uria aalge in 1972, on Skomer Island, off the coast of Wales, UK.  I have kept that study — whose main thrust is population monitoring — going ever since: www.justgiving.com/guillemotsskomer

The video describing our murre egg study is here:  https://youtu.be/e-189LIYa0Y

Tim Birkhead academic website: https://www.sheffield.ac.uk/aps/staff-and-students/acadstaff/birkhead

 

Other relevant papers:

Biggins, J. D., Thompson, J. E. & Birkhead, T. R. 2018. Accurately quantifying the shape of birds’ eggs. Ecology and Evolution 8: in press.

Birkhead, T. R. 2017. Vulgar errors — the point of a Guillemot’s egg. British Birds 110: 456-467.

Birkhead, T.R., Thompson, & J. E., Biggins, J. D. 2017. The point of a guillemor’s egg. Ibis 159: 255-265.

Birkhead, T. R., Thompson, J. E. & Biggins, J. D. 2017.  Egg shape in the common guillemot Uria aalge and Brunnich’s guillemot U. lomvia: not a rolling matter? Journal of Ornithology 158: 679-685.

Birkhead, T.R., Thompson, J. E., Biggins, J. D. & Montgomerie, R. 2018.  The evolution of egg shape in birds: selection during the incubation period. Ibis, in press.

AUTHOR BLOG: Newly discovered crossbill species numbers few

Craig W. Benkman

Linked paper: Habitat associations and abundance of a range-restricted specialist, the Cassia Crossbill (Loxia sinesciuris) by N.J. Behl and C.W. Benkman, The Condor: Ornithological Applications 120:3, August 2018.

Untitled

A female Cassia Crossbill.

Based on the size and structure of the lodgepole pine cones and the abundance of crossbills in the South Hills and Albion Mountains, Idaho, that I observed on the way to a joint AOU and COS meeting in Boise in 1996, I told several colleagues at the meeting that I might have discovered a new form of crossbill. Although they were skeptical, over the years my students and I have found that this crossbill is engaged in a coevolutionary arms race with the pine, favoring an increase in seed defenses directed at the crossbills. This has caused the crossbill to diverge and speciate into what we now call the Cassia Crossbill (Loxia sinesciuris).

Restricted to the lodgepole pine atop two small ranges on the northeast edge of the Great Basin Desert, this bird was of clear conservation concern, especially given the forecasts of lodgepole pine disappearing from the region late in this century. This became all the more troubling as we watched the Cassia Crossbill population plummet by over 80% between 2003 and 2011. The decline was related to an increase in hot summer days (>32°C or 90°F; 8 days in 2003, 3 in 2005, 4 in 2006, and 4 in 2007) that caused many of the normally closed cones of lodgepole pine to open and shed their seeds, much like they would if there was a stand-replacing fire. Such seeds are lost to Cassia Crossbills, which rely on seeds in the older, closed cones as they weather and gradually become available throughout the year. Fortunately, hot summer days have been few since 2007, allowing the crossbill population to rebound. However, given its restricted range, apparent small population size, and vulnerability to higher temperatures, we needed an estimate of their global population size and habitat preferences to inform and guide us. Nate Behl did just that work for his master’s thesis, and it appears in the article “Habitat associations and abundance of a range-restricted specialist, the Cassia Crossbill (Loxia sinesciuris)” in The Condor: Ornithological Applications.

Cassia Crossbills occupy about 70 km2 of lodgepole pine forest and number only ~5,800 birds. Thus, at the population nadir in 2011 there were probably about 1,500 Cassia Crossbills. That is worrisome, especially given the forecasts for more extreme temperatures later in this century. Nate also found that Cassia Crossbills occur more commonly in larger, mature stands of lodgepole pine on the cooler north-facing slopes where large numbers of seeds can accumulate in closed cones. This makes sense, but the outlook for the continued accumulation of seeds in closed cones in the canopy is bleak. More hot summer days are projected, along with increasing fire frequency, preventing pine from reaching the ages most productive for the Cassia Crossbill.

AUTHOR BLOG: Ancient Fossil Bones of a Recently Extinct Cormorant

Junya Watanabe

Linked paper: Pleistocene fossils from Japan show that the recently extinct Spectacled Cormorant (Phalacrocorax perspicillatus) was a relict by J. Watanabe, H. Matsuoka, and Y. Hasegawa, The Auk: Ornithological Advances 135:4, October 2018.

The new and heretofore unfigured species of the birds of North America

Live reconstruction of the Spectacled Cormorant from study skins. Artwork by Joseph Wolf, from Elliott (1869), The New and Heretofore Unfigured Species of the Birds of North America, Volume 2.

Numerous extinction events have taken place in geologically recent time, caused to varying degrees by human activity. Although relatively much is known about how humans have given “final blows” to animal species in recent history, little is known about the long-term biogeographic and evolutionary history of extinct animals. This is where archaeological and fossil records play crucial roles. One of the most (in)famous examples of historic extinctions is the case of the Great Auk, which was once widespread in the North Atlantic Ocean but was driven to extinction in the mid-19th century due to hunting by humans. There is one potential parallel, though less widely known, in the North Pacific Ocean; a large seabird species called Spectacled Cormorant (Phalacrocorax perspicillatus) was driven to extinction almost contemporaneously. This species was first discovered in the 18th century on Bering Island, part of the Commander Islands, by German explorer Georg Steller, who became the only naturalist to observe the birds in life. Following the colonization of the island by humans in the early 19th century, this species was hunted by humans, and it was driven to extinction in the 1850s. As there has been no record of the species outside Bering Island, it is considered to have been restricted to the island throughout its existence. Our new study in The Auk: Ornithological Advances, however, reports the first definitive record of the cormorant species outside Bering Island, demonstrating that the species was in fact not restricted to the island in the past.

Through our study of Japanese fossil birds, my colleagues and I identified 13 fossil bones of the Spectacled Cormorant from upper Pleistocene deposits (dated ~120,000 years ago) in Japan. The fossil bones were recovered from Shiriya, northeastern Japan, through excavations led by my co-author Yoshikazu Hasegawa of the Gunma Museum of Natural History. Through detailed examination of the bird fossils from the site, it became evident that a cormorant species much larger than any of the four native cormorant species in present-day Japan was represented in the material. At first, we suspected the presence of a new species, but this turned out not to be the case. Through a literature survey, I came across a 19th-century paper by American ornithologists Leonhard Stejneger and Frederic Lucas that described bones of the Spectacled Cormorant collected on Bering Island. The dimensions and illustrations given in the paper were strikingly similar to the Japanese fossils. I decided to visit the Smithsonian Institution’s National Museum of Natural History in Washington, D.C., where the bones described by Stejneger and Lucas are stored. After careful examination, the Japanese fossils turned out to agree in every detail with bones of the Spectacled Cormorant from Bering Island, rather than with any other species compared, to the extent that I was convinced that the Japanese fossils belong to the same species as the Bering Island bones.

The occurrence of the Spectacled Cormorant from Japan is the first definitive record of this species outside Bering Island and indicates that the species underwent a drastic range contraction or shift since the Pleistocene. In other words, the population of this species on Bering Island discovered by Steller was in fact a relict, with most of the species’ past distribution already lost. Changes in oceanographic conditions might be responsible for the local disappearance of the species in Japan; paleoclimate studies have shown that the oceanic productivity around Shiriya dropped drastically in the Last Glacial Maximum (~20,000 years ago), which would have seriously affected the population of the species. Although it might be possible that hunting of that species by humans took place in prehistoric Japan, no archaeological evidence for that is known so far. The entire picture of the recent extinction event of the Spectacled Cormorant might be more complex than previously thought, as is becoming evident for some other extinct seabirds in other parts of the world.

Further reading

Fuller, E. (2001). Extinct Birds, revised edition. Cornell University Press, New York, NY.

Hume, J. P. (2017). Extinct Birds, 2nd edn. Bloomsbury Natural History, London.

AUTHOR BLOG: Are All Eggs Created Equal? Saltmarsh Sparrows Support Gender Equality

Bri Benvenuti and Adrienne Kovach

Linked paper: Annual variation in the offspring sex ratio of Saltmarsh Sparrows supports Fisher’s hypothesis by B. Benvenuti, J. Walsh, K.M. O’Brien, M.J. Ducey, and A.I. Kovach, The Auk: Ornithological Advances 135:2, April 2018.

blog photo

Three Saltmarsh Sparrow chicks banded as part of a study on offspring sex ratios. Photo: B. Benvenuti

In birds, females have the ability to control the sex of individual eggs; therefore, a mother may be able to choose whether she prefers each egg laid to be a male or female. This means that offspring sex ratios are not usually left to chance. From an evolutionary standpoint, this can be very beneficial, as different circumstances may favor the success of sons versus daughters.

But how does one know if it would be better to have more sons or daughters? Evolutionary theory suggests that if the potential benefits of raising one sex over the other vary in relation to environmental or maternal conditions, then females should favor the production of that sex. Typically, high quality sons are more beneficial to mothers, because they have the potential to produce far more grandchildren than daughters can (males can mate many times, but females are limited by how many eggs they can produce, incubate, and raise to fledging). More grandchildren = greater lifelong success.  Still, there is a risk to biasing offspring production toward sons; if the son is low quality (competitively inferior), he may not reproduce at all.  On the other hand, daughters tend to be “cheaper” to raise than sons. They need less resources to reach maturity, and if they survive, they almost always reproduce. With this in mind, one could logically say that producing daughters represents the “safe bet”—you might get a smaller payout (in terms of numbers of grandchildren), but you know you’ll get something.

Armed with this information, we chose to investigate whether Saltmarsh Sparrows manipulate the sex of their offspring based on environmental or maternal conditions as we would expect based on evolutionary theory. These tidal marsh specialist birds live a stressful life—they build nests in the marsh grasses just inches above the marsh surface that is regularly subjected to tidal flooding. Nests are more likely to escape these flooding events and successfully fledge offspring if they are timed to fledge within the 28 day lunar tidal cycle. Saltmarsh Sparrows are also one of the world’s most promiscuous birds, with almost every egg in a nest having a different father thanks to the scramble of competition among males for access to females. These characteristics provide interesting hypotheses in the context of evolutionary theory, so we asked, would Saltmarsh Sparrow mothers produce more sons, who would be larger and a) more likely to survive a nest flooding event and b) have the ability to produce more offspring through multiple matings? Or would they take the “safe bet” and produce more females?

To test our hypotheses, we collected nesting data from Saltmarsh Sparrow breeding locations in New England marshes over five years. We used DNA analysis to determine the sex of Saltmarsh Sparrow chicks and calculated the offspring sex ratio for our four study sites and across the whole study population. We then used a modeling approach to determine if there was an influence of environmental conditions (year, tidal flooding, precipitation), temporal effects (nest initiation in relation to flood tides, timing within the breeding season), or maternal condition on offspring sex ratios.

Surprisingly, we found an even offspring sex ratio of 1.03:1 (males to females) across all years and sites, and offspring sex ratios did not vary as a function of the environment, tidal flooding risk, or female condition. What we did find was an interesting pattern of annual variation between male and female bias that mirrored the adult sex ratio in the preceding year.

While numerous studies have provided evidence that female birds may have the ability to adjust offspring sex ratios in an adaptive way, we found no evidence for adaptive sex ratio manipulation in Saltmarsh Sparrows in relation to our hypotheses. Instead, the observed time-lagged relationship between offspring and adult sex ratio meets expectations of frequency-dependent selection, whereby females respond to higher frequencies of one sex by increasing production of the rarer sex, which would have a temporary fitness advantage. Our findings overall show support for balanced offspring sex ratios at a population level over time.