Why and how we should join the shift from significance testing to estimation.

A paradigm shift away from null hypothesis significance testing seems in progress. Based on simulations, we illustrate some of the underlying motivations. First, p-values vary strongly from study to study, hence dichotomous inference using significance thresholds is usually unjustified. Second, 'statistically significant' results have overestimated effect sizes, a bias declining with increasing statistical power. Third, 'statistically non-significant' results have underestimated effect sizes, and this bias gets stronger with higher statistical power. Fourth, the tested statistical hypotheses usually lack biological justification and are often uninformative. Despite these problems, a screen of 48 papers from the 2020 volume of the Journal of Evolutionary Biology exemplifies that significance testing is still used almost universally in evolutionary biology. All screened studies tested default null hypotheses of zero effect with the default significance threshold of p = 0.05, none presented a pre-specified alternative hypothesis, pre-study power calculation and the probability of 'false negatives' (beta error rate). The results sections of the papers presented 49 significance tests on average (median 23, range 0-390). Of 41 studies that contained verbal descriptions of a 'statistically non-significant' result, 26 (63%) falsely claimed the absence of an effect. We conclude that studies in ecology and evolutionary biology are mostly exploratory and descriptive. We should thus shift from claiming to 'test' specific hypotheses statistically to describing and discussing many hypotheses (possible true effect sizes) that are most compatible with our data, given our statistical model. We already have the means for doing so, because we routinely present compatibility ('confidence') intervals covering these hypotheses.

Negative effects of nitrogen deposition on Swiss butterflies.

Nitrogen (N) deposition from agriculture and combustion of fossil fuels is a major threat to plant diversity, but its effects on organisms at higher trophic levels are unclear. We investigated how N deposition may affect species richness and abundance (number of individuals per species) in butterflies. We reviewed the peer-reviewed literature on variables used to explain spatial variation in butterfly species richness and found that vegetation variables appeared to be as important as climate and habitat variables in explaining butterfly species richness. It thus seemed likely that increased N deposition could indirectly affect butterfly communities via its influence on plant communities. To test this prediction, we analyzed data from the Swiss biodiversity monitoring program for vascular plants and butterflies in 383 study sites of 1 km2 that are evenly distributed throughout Switzerland. The area has a modeled N deposition gradient of 2-44 kg N ha-1 year-1 . We used traditional linear models and structural equation models to infer the drivers of the spatial variation in butterfly species richness across Switzerland. High N deposition was consistently linked to low butterfly diversity, suggesting a net loss of butterfly diversity through increased N deposition. We hypothesize that at low elevations, N deposition may contribute to a reduction in butterfly species richness via microclimatic cooling due to increased plant biomass. At higher elevations, negative effects of N deposition on butterfly species richness may also be mediated by reduced plant species richness. In most butterfly species, abundance was negatively related to N deposition, but the strongest negative effects were found for species of conservation concern. We conclude that in addition to factors such as intensified agriculture, habitat fragmentation, and climate change, N deposition is likely to play a key role in negatively affecting butterfly diversity and abundance.

Efectos Negativos del Depósito de Nitrógeno sobre las Mariposas Suizas Resumen El depósito de nitrógeno (N) proveniente de la agricultura y la quema de combustibles fósiles es una gran amenaza para la diversidad botánica, pero sus efectos sobre organismos que se encuentran en niveles tróficos más altos no están claros. Investigamos cómo el depósito de N puede afectar a la riqueza y abundancia (número de individuos por especie) de especies de mariposas. Analizamos la literatura revisada por pares sobre las variables usadas para explicar la variación espacial en la riqueza de especies de mariposas y descubrimos que las variables de vegetación resultaron ser tan importantes como las variables climáticas y de hábitat para explicar la riqueza de especies de mariposas. Por lo tanto, parece probable que el incremento en el depósito de N podría afectar indirectamente a las comunidades de mariposas por medio de su influencia sobre las comunidades botánicas. Para probar esta predicción analizamos datos del programa de monitoreo de biodiversidad suiza de plantas vasculares y mariposas en 383 sitios de estudio de 1 km2 que están distribuidos uniformemente por toda Suiza. El área tiene un gradiente modelado de depósito de N de 2-44 kg N ha−1 año−1 . Usamos modelos lineales tradicionales y modelos de ecuación estructural para inferir los determinantes de la variación espacial en la riqueza de especies de mariposas en Suiza. El nivel elevado de depósito de N estuvo vinculado consistentemente con la diversidad baja de mariposas, lo que sugiere una pérdida neta de diversidad de mariposas causada por el incremento en el depósito de N. Nuestra hipótesis establece que, a elevaciones bajas, el depósito de N puede contribuir a la reducción en la riqueza de especies de mariposas por medio del enfriamiento microclimático debido al incremento en la biomasa de las plantas. A elevaciones más altas, los efectos negativos del depósito de N sobre la riqueza de especies de mariposas también podrían ser mediados por la riqueza reducida de especies de plantas. En la mayoría de las especies de mariposas, la abundancia tuvo una relación negativa con el depósito de N, pero el efecto negativo más fuerte se halló para las especies de importancia para la conservación. Concluimos que además de los factores como la agricultura intensificada, la fragmentación del hábitat y el cambio climático, el depósito de N probablemente tenga un papel importante en los efectos negativos sobre la diversidad y abundancia de mariposas.

Estimating Effects of Species Interactions on Populations of Endangered Species.

Global change causes community composition to change considerably through time, with ever-new combinations of interacting species. To study the consequences of newly established species interactions, one available source of data could be observational surveys from biodiversity monitoring. However, approaches using observational data would need to account for niche differences between species and for imperfect detection of individuals. To estimate population sizes of interacting species, we extended N-mixture models that were developed to estimate true population sizes in single species. Simulations revealed that our model is able to disentangle direct effects of dominant on subordinate species from indirect effects of dominant species on detection probability of subordinate species. For illustration, we applied our model to data from a Swiss amphibian monitoring program and showed that sizes of expanding water frog populations were negatively related to population sizes of endangered yellow-bellied toads and common midwife toads and partly of natterjack toads. Unlike other studies that analyzed presence and absence of species, our model suggests that the spread of water frogs in Central Europe is one of the reasons for the decline of endangered toad species. Thus, studying population impacts of dominant species on population sizes of endangered species using data from biodiversity monitoring programs should help to inform conservation policy and to decide whether competing species should be subject to population management.

Estimating unbiased phenological trends by adapting site-occupancy models.

As a response to climate warming, many animals and plants have been found to shift phenologies, such as appearance in spring or timing of reproduction. However, traditional measures for shifts in phenology that are based on observational data likely are biased due to a large influence of population size, observational effort, starting date of a survey, or other causes that may affect the probability of detecting a species. Understanding phenological responses of species to climate change, however, requires a robust measure that could be compared among studies and study years. Here, we developed a new method for estimating arrival and departure dates based on site-occupancy models. Using simulated data, we show that our method provided virtually unbiased estimates of phenological events even if detection probability or the number of sites occupied by the species is changing over time. To illustrate the flexibility of our method, we analyzed spring arrival of two long-distance migrant songbirds and the length of the flight period of two butterfly species, using data from a long-term biodiversity monitoring program in Switzerland. In contrast to many birds that migrate short distances, the two long-distance migrant songbirds tended to postpone average spring arrival by -0.5 days per year between 1995 and 2012. Furthermore, the flight period of the short-distance-flying butterfly species apparently became even shorter over the study period, while the flight period of the longer-distance-flying butterfly species remained relatively stable. Our method could be applied to temporally and spatially extensive data from a wide range of monitoring programs and citizen science projects, to help unravel how species and communities respond to global warming.

Natural grazing by horses and cattle promotes bird diversity in a restored European alluvial grassland.

Context: A challenge in grassland conservation is to maintain both the openness and the heterogeneity of the habitat to support the diversity of their animal communities, including birds-a taxon that is known to be sensitive to disturbance. An increasingly used management tool in European grassland conservation, especially in rewilding projects, is grazing by large herbivores such as horses and cattle. These grazers are believed to create and maintain patchy landscapes that promote diversity and richness of other species, but their influence on birds is often debated by conservationists, who raise concerns about the impact of disturbance by the grazers. Objectives: Our aim was to examine the relationship between the abundance and species richness of birds across four foraging guilds and the area utilization patterns of Highland cattle and Konik horses in an alluvial grassland in France. We also aimed to examine the influence of land cover and season on the spatial distribution, including abundance and species richness, of different bird guilds present in the grazed area. Methods: We used GPS-collars on all grazers and recorded their positions on an hourly basis over a study period of 1.5 years, assessing patterns of area usage. We counted birds weekly along three transects to describe their distribution within the grazed area and carried out land-cover surveys to describe the habitat. To assess how species richness and abundance of birds of different guilds were related to grazer density, season, and habitat characteristics, we used GAMM models in a spatially explicit framework. We also compared bird numbers at our main study site with a nearby non-grazed control area. Results: The number of birds in the grazed area was about twice the number in the non-grazed control area. Within the grazed area, the abundance of open-area foraging birds increased with increasing grazer density. The number of woodland-foraging birds was also positively correlated with grazer density but less so than open-area foraging birds. The number of individuals in the aerial and wetland bird guilds was not correlated with the density of grazers. Most bird species and individuals were observed on open landscapes scattered with woody patches and waterbodies, and on areas with moderate grazer density. Conclusions: Low-intensity grazing represents a potentially important management tool in creating heterogeneity in alluvial grasslands, thereby promoting suitable habitat for a diverse assemblage of bird species.

Alpine songbirds at higher elevations are only raised with a slight delay and therefore under harsher environmental conditions.

The breeding phenology of birds is often timed to coincide with a peak in food availability. However, the shortening of the vegetation period with increasing elevation may force bird species at high elevations to breed earlier in relation to optimal environmental conditions due to time constraints. We investigated differences in fledging dates in five Alpine woodland songbird species along an elevational gradient from 1500 to 2200 m in Switzerland. We estimated fledging dates from a nationwide citizen science bird monitoring dataset and used the date when the proportion of observations of 'fledged young' reached 50% among all observations indicating breeding behaviour. This measure had the advantage that we could estimate average timing of the broods across a wide geographic range and over many years without the need to search for individual nests. We then compared differences in timing of the broods with climatic conditions and larch budburst across different elevational bands. The daily mean air temperature of 10-15°C was reached 34-38 days later at 2200 m compared to 1500 m, which is a similar delay as found in previous reports on snow melt-out date. The average delay in larch budburst was 19.2 days at 2200 m compared to 1500 m. In comparison, the average timing of the birds' broods was only 5.4 days later in coal tits and 0.5 days later in Alpine tits at 2200 compared to 1500 m (the two species for which we had the narrowest interval estimates). Also, the estimated delay at higher elevations in the broods of song thrushes, mistle thrushes and Eurasian chaffinches was relatively small. Rather than postponing breeding dates to better environmental conditions later in the season that would match the earlier conditions at low elevation, songbirds breeding at higher elevations may thus have evolved adaptations to cope with the harsher conditions.

Strong migratory connectivity and seasonally shifting isotopic niches in geographically separated populations of a long-distance migrating songbird.

Whether migratory animals use similar resources during continental-scale movements that characterize their annual cycles is highly relevant to both individual performances and population dynamics. Direct knowledge of the locations and resources used by migrants during non-breeding is generally scarce. Our goal was to estimate migratory connectivity of a small Palaearctic long-distance migrant, the common nightingale Luscinia megarhynchos, and to compare resources used in non-breeding areas with resources used at the breeding grounds. We tracked individuals of three geographically separated populations and characterised their stable isotope niches during breeding and non-breeding over 2 years. Individuals spent the non-breeding period in population-specific clusters from west to central Africa, indicating strong migratory connectivity at the population level. Irrespective of origin, their isotopic niches were surprisingly similar within a particular period, although sites of residence were distant. However, niche characteristics differed markedly between breeding and non-breeding periods, indicating a consistent seasonal isotopic niche shift in the sampled populations. Although nightingales of distinct breeding populations migrated to different non-breeding areas, they chose similar foraging conditions within specific periods. However, nightingales clearly changed resource use between breeding and non-breeding periods, indicating adaptations to changes in food availability.

Finding food in a changing world: Small-scale foraging habitat preferences of an insectivorous passerine in the Alps.

Organisms living in high-elevation habitats are usually habitat specialists who occupy a narrow ecological niche. To envision the response of alpine species to a changing environment, it is fundamental to understand their habitat preferences on multiple spatial and temporal scales. However, information on small-scale habitat use is still widely lacking. We investigated the foraging habitat preferences of the migratory northern wheatear Oenanthe oenanthe during the entire presence at a breeding site in the central Alps. We repeatedly observed 121 adult and juvenile individuals. We applied Bayesian logistic regression models to investigate which habitat characteristics influenced foraging habitat selection on a fine spatial scale, and how habitat use varied temporally. Throughout their presence on the breeding grounds, northern wheatears showed a consistent preference for a mosaic of stones and bare ground patches with slow-growing, short vegetation. The proximity of marmot burrows was preferred, whereas dense and low woody vegetation was avoided. After arrival at the breeding site, short vegetation, preferably close to the snow, was favored. The preference for open habitat patches that provide access to prey underlines the critical role of small-scale habitat heterogeneity for northern wheatears. The strong and consistent preference for a habitat that is under pressure from land-use and climate change suggests that this alpine bird species may be sensitive to habitat loss, leading to a potential range contraction. We highlight the need to conserve habitat diversity on a small spatial scale to ensure the long-term availability of suitable habitat for northern wheatears in the Alps.

Multi-sensor geolocators unveil global and local movements in an Alpine-breeding long-distance migrant.

BACKGROUND: To understand the ecology of long-distance migrant bird species, it is necessary to study their full annual cycle, including migratory routes and stopovers. This is especially important for species in high-elevation habitats that are particularly vulnerable to environmental change. Here, we investigated both local and global movements during all parts of the annual cycle in a small trans-Saharan migratory bird breeding at high elevation. METHODS: Recently, multi-sensor geolocators have opened new research opportunities in small-sized migratory organisms. We tagged Northern Wheatears Oenanthe oenanthe from the central-European Alpine population with loggers recording atmospheric pressure and light intensity. We modelled migration routes and identified stopover and non-breeding sites by correlating the atmospheric pressure measured on the birds with global atmospheric pressure data. Furthermore, we compared barrier-crossing flights with other migratory flights and studied the movement behaviour throughout the annual cycle. RESULTS: All eight tracked individuals crossed the Mediterranean Sea, using islands for short stops, and made longer stopovers in the Atlas highlands. Single non-breeding sites were used during the entire boreal winter and were all located in the same region of the Sahel. Spring migration was recorded for four individuals with similar or slightly different routes compared to autumn. Migratory flights were typically nocturnal and characterized by fluctuating altitudes, frequently reaching 2000 to 4000 m a.s.l, with a maximum of up to 5150 m. Barrier-crossing flights, i.e., over the sea and the Sahara, were longer, higher, and faster compared to flights above favourable stopover habitat. In addition, we detected two types of altitudinal movements at the breeding site. Unexpected regular diel uphill movements were undertaken from the breeding territories towards nearby roosting sites at cliffs, while regional scale movements took place in response to local meteorological conditions during the pre-breeding period. CONCLUSION: Our data inform on both local and global scale movements, providing new insights into migratory behaviour and local movements in small songbirds. This calls for a wider use of multi-sensor loggers in songbird migration research, especially for investigating both local and global movements in the same individuals.

Grazer density and songbird counts in a restored conservation area.

Grazing by large herbivores is increasingly used as a management tool in European nature reserves. The aim is usually to support an open but heterogeneous habitat and its corresponding plant and animal communities. Previous studies showed that birds may profit from grazing but that the effect varies among bird species. Such studies often compared bird counts among grazed areas with different stocking rates of herbivores. Here, we investigated how space use of Konik horses and Highland cattle is related to bird counts in a recently restored conservation area with a year-round natural grazing management. We equipped five horses and five cattle with GPS collars and correlated the density of their GPS positions on the grazed area with the density of bird observations from winter through the breeding season. We found that in the songbirds of our study site, both the overall density of bird individuals and the number of species increased with increasing density of GPS positions of grazers. Correlations of bird density with horse density were similar to correlations with cattle density. Of the eight most common songbird species observed in our study area, the Eurasian Skylark and the Common Starling had the clearest positive correlations with grazer density, while the Blackbird showed a negative correlation. Skylarks and Starlings in our study area thus seem to profit from year-round natural grazing by a mixed group of horses and cattle.

Differential effects of moving versus stationary territorial intruders on territory defence in a songbird.

1. In territorial contests, not only acoustic or other signals, but also the movements of a territorial intruder are likely to influence the response of a resident. 2. We tested this movement hypothesis by simulating moving vs. stationary intruders into the territories of winter wrens Troglodytes troglodytes, using the same non-interactive song playbacks in both treatments. 3. Male winter wrens showed a different long-term singing reaction in response to a moving than to a stationary intruder. 4. One day after experiencing an intruder that was switching between three locations, residents started to sing earlier before sunrise, and they sang more and longer songs at dawn than before the intrusion. 5. Residents receiving the same playback from one location only reacted by starting to sing later relative to sunrise, and by singing fewer and shorter songs than before the intrusion. 6. We could not discriminate between the treatments when examining the short-term singing reactions during and immediately after the playbacks. However, our results clearly demonstrate an effect of the spatial behaviour of territorial intruders on the long-term territory defence of residents at dawn, about 24 h after an intrusion. 7. We argue that spatial behaviour of territorial intruders should be an integral part of the study of animal territory defence behaviour. Investigating long-term changes in territory defence at dawn is a sensitive tool for discriminating between different types of intruders.

Sex-specific timing of mate searching and territory prospecting in the nightingale: nocturnal life of females.

Formal models have shown that diel variation in female mate searching is likely to have profound influence on daily signalling routines of males. In studies on acoustic communication, the temporal patterns of the receivers' signal evaluation should thus be taken into account when investigating the functions of signalling. In bird species in which diel patterns of signalling differ between males singing to defend a territory or to attract a mate, the diel patterns of mate and territory prospecting are suggested to depend on the sex of the prospector. We simulated newly arriving female nightingales (Luscinia megarhynchos) by translocating radio-tagged females to our study site. The mate-searching females prospected the area mostly at night, visiting several singing males. The timing of female prospecting corresponded to the period of the night when the singing activity of unpaired males was higher than that of paired males. In contrast to females, territory searching males have been shown to prospect territories almost exclusively during the dawn chorus. At dawn, both paired and unpaired males sang at high rates, suggesting that in contrast to nocturnal singing, dawn singing is important to announce territory occupancy to prospecting males. In the nightingale, the sex-specific timing of prospecting corresponded to the differential signalling routines of paired and unpaired males. The temporal patterns in the behaviour of signallers and receivers thus appear to be mutually adapted.

Species turnover reveals hidden effects of decreasing nitrogen deposition in mountain hay meadows.

Nitrogen (N) deposition is a major threat to biodiversity in many habitats. The recent introduction of cleaner technologies in Switzerland has led to a reduction in the emissions of nitrogen oxides, with a consequent decrease in N deposition. We examined different drivers of plant community change, that is, N deposition, climate warming, and land-use change, in Swiss mountain hay meadows, using data from the Swiss biodiversity monitoring program. We compared indicator values of species that disappeared from or colonized a site (species turnover) with the indicator values of randomly chosen species from the same site. While oligotrophic plant species were more likely to colonize, compared to random expectation, we found only weak shifts in plant community composition. In particular, the average nutrient value of plant communities remained stable over time (2003-2017). We found the largest deviations from random expectation in the nutrient values of colonizing species, suggesting that N deposition or other factors that change the nutrient content of soils were important drivers of the species composition change over the last 15 years in Swiss mountain hay meadows. In addition, we observed an overall replacement of species with lower indicator values for temperature with species with higher values. Apparently, the community effects of the replacement of eutrophic species with oligotrophic species was outweighed by climate warming. Our results add to the increasing evidence that plant communities in changing environments may be relatively stable regarding average species richness or average indicator values, but that this apparent stability is often accompanied by a marked turnover of species.

Manipulating the Alpha Level Cannot Cure Significance Testing.

We argue that making accept/reject decisions on scientific hypotheses, including a recent call for changing the canonical alpha level from p = 0.05 to p = 0.005, is deleterious for the finding of new discoveries and the progress of science. Given that blanket and variable alpha levels both are problematic, it is sensible to dispense with significance testing altogether. There are alternatives that address study design and sample size much more directly than significance testing does; but none of the statistical tools should be taken as the new magic method giving clear-cut mechanical answers. Inference should not be based on single studies at all, but on cumulative evidence from multiple independent studies. When evaluating the strength of the evidence, we should consider, for example, auxiliary assumptions, the strength of the experimental design, and implications for applications. To boil all this down to a binary decision based on a p-value threshold of 0.05, 0.01, 0.005, or anything else, is not acceptable.

The earth is flat (p > 0.05): significance thresholds and the crisis of unreplicable research.

The widespread use of 'statistical significance' as a license for making a claim of a scientific finding leads to considerable distortion of the scientific process (according to the American Statistical Association). We review why degrading p-values into 'significant' and 'nonsignificant' contributes to making studies irreproducible, or to making them seem irreproducible. A major problem is that we tend to take small p-values at face value, but mistrust results with larger p-values. In either case, p-values tell little about reliability of research, because they are hardly replicable even if an alternative hypothesis is true. Also significance (p ≤ 0.05) is hardly replicable: at a good statistical power of 80%, two studies will be 'conflicting', meaning that one is significant and the other is not, in one third of the cases if there is a true effect. A replication can therefore not be interpreted as having failed only because it is nonsignificant. Many apparent replication failures may thus reflect faulty judgment based on significance thresholds rather than a crisis of unreplicable research. Reliable conclusions on replicability and practical importance of a finding can only be drawn using cumulative evidence from multiple independent studies. However, applying significance thresholds makes cumulative knowledge unreliable. One reason is that with anything but ideal statistical power, significant effect sizes will be biased upwards. Interpreting inflated significant results while ignoring nonsignificant results will thus lead to wrong conclusions. But current incentives to hunt for significance lead to selective reporting and to publication bias against nonsignificant findings. Data dredging, p-hacking, and publication bias should be addressed by removing fixed significance thresholds. Consistent with the recommendations of the late Ronald Fisher, p-values should be interpreted as graded measures of the strength of evidence against the null hypothesis. Also larger p-values offer some evidence against the null hypothesis, and they cannot be interpreted as supporting the null hypothesis, falsely concluding that 'there is no effect'. Information on possible true effect sizes that are compatible with the data must be obtained from the point estimate, e.g., from a sample average, and from the interval estimate, such as a confidence interval. We review how confusion about interpretation of larger p-values can be traced back to historical disputes among the founders of modern statistics. We further discuss potential arguments against removing significance thresholds, for example that decision rules should rather be more stringent, that sample sizes could decrease, or that p-values should better be completely abandoned. We conclude that whatever method of statistical inference we use, dichotomous threshold thinking must give way to non-automated informed judgment.