Macroecology studies patterns across many species, populations or places: how abundance, body size, geographic range and species richness vary, and which processes could produce those patterns. Its practical value is learning what can be generalised beyond one field site while recognising when a change in scale, sampling or environment makes a generalisation fail.
The gold standard is a pattern with clearly defined measurements, a credible explanation, an honest account of uncertainty and a test in a genuinely different setting. A straight line on a logarithmic graph is a starting point. This guide develops that standard through original numerical examples, from counting occupied grid cells to checking an abundance–body-size model. All numerical cases are teaching examples with stated assumptions, not measurements of named species or places.
This subject connects the Gold Standard collection with Education: learning that transfers into life. For explanations of neighbouring fields, use the How X Works hub and the Biogeography specialist guide.
Choose your macroecology route
Connect cross-species patterns to measurements, mechanisms and tests at a new scale.
Route 1 · Chapters 1–3: Define the question, quantities and scale
Route 2 · Chapters 4–6: Compare richness, abundance and occupancy
Route 3 · Chapters 7–9: Understand scaling, logarithms and ranges
Route 4 · Chapters 10–11: Check observation and prediction
Route 5 · Chapters 12–14: Transfer, repair and continue
Chapter index
Define the question, quantities and scale · Chapters 1–3
Compare richness, abundance and occupancy · Chapters 4–6
Understand scaling, logarithms and ranges · Chapters 7–9
Check observation and prediction · Chapters 10–11
Transfer, repair and continue · Chapters 12–14
Imagine three investigations of birds. One follows survival in a single population. Another tests whether two species compete at a feeding site. A third compares local density, body mass and range size across hundreds of species. The third asks how attributes vary across a broad set of organisms, rather than treating each species as a separate story.
That comparison does not automatically require a continental map. A carefully defined collection of local communities can support a macroecological question. Conversely, a large map of one species is not automatically an analysis of general ecological patterns. The organising question matters more than the size of the picture.
Brown and Maurer’s 1989 paper developed a macroecological approach around statistical distributions of body mass, population density and geographic range among species. Its enduring methodological lesson is to examine variation across a whole assemblage while asking how processes at different scales could be connected. Its historical estimates and proposed mechanisms should not be mistaken for current settled facts.
Give every comparison a defined population
“Animals become less abundant as they become larger” leaves too much unspecified. Does abundance mean individuals per hectare in occupied habitat, total individuals across a continent, or the number of records submitted by observers? Are marine fish being compared with forest mammals? Is body mass measured in adults or mixed life stages?
A testable version is narrower: among a specified set of resident species, does mean adult mass predict independently estimated density in comparable occupied habitat during a defined season? That sentence identifies the rows, measurements and intended comparison before any graph is drawn.
Use Population Ecology when the central question concerns demographic change within populations, and Community Ecology when it concerns assemblage composition and interactions. Macroecology connects such explanations across species and places; it does not replace them.
A spreadsheet can contain one row per observation, one row per species, or one row per survey. These are different statistical objects. Before combining files, write down what a row represents and which rows can refer to the same organism, event or location.
Abundance is a number of organisms within a defined boundary. Density divides that number by a relevant area or volume. Occupancy is the fraction of defined sampling units containing the species. Richness is the number of species recognised within the stated boundary and period. A record is evidence produced by observation; its relationship to those quantities depends on the method.
One landscape, three valid answers
Suppose ten equal one-hectare plots contain counts of 8, 4, 0, 0, 0, 0, 0, 0, 0 and 0 individuals of a plant. Assume complete counting and a clear rule for distinguishing individuals. Total abundance is 12. Density over the entire sampled area is 12/10 = 1.2 individuals per hectare. Mean density conditional on occupancy is 12/2 = 6 individuals per hectare. Occupancy is 2/10 = 0.2.
None of these answers is wrong. Trouble begins when one species receives the conditional density and another receives the landscape density. Their numerical comparison then mixes population concentration with geographic spread.
The same problem appears when a database contains 100 photographs of one conspicuous bird and ten photographs of a secretive bird. Photograph totals do not establish a tenfold abundance difference. Observation effort, repeated sightings and detectability can all affect the ratio.
GBIF’s sampling-event guidance distinguishes records accompanied by survey methods and effort from opportunistic occurrences. For a regional comparison, preserve event identifiers, surveyed area, dates and effort alongside detections. A well-documented small survey can answer an abundance question that a much larger collection of unstandardised sightings cannot.
Spatial grain is the size of the observational unit; extent is the overall region covered. Increasing grain combines neighbouring units. Increasing extent adds territory. Both can change measured patterns, but they change different parts of the question.
Consider a square landscape divided into sixteen one-hectare cells. A species occurs in four cells. Fine-grain occupancy is 4/16 = 25%. Now merge the cells into four non-overlapping four-hectare blocks. If the four occupied cells all lie in one block, coarse occupancy is 1/4 = 25%. If each lies in a different block, coarse occupancy is 4/4 = 100%.
No colonisation occurred. The organisms did not move. Aggregation changed the measurement, and their spatial arrangement determined the answer. An occupancy value without its grid size and geometry is therefore incomplete information.
Time can be aggregated too
A breeding-season range and a whole-year range need not describe the same habitat use. Combining records across decades can create a map of places occupied at some time, not places occupied simultaneously. A site visited in different seasons can also accumulate species that never coexist there on a single date.
Define the temporal window before interpreting such a compilation. If the aim is current occupancy, old records may provide historical context without establishing present presence. If the aim is long-term use, a short survey may miss the very variation being studied.
The practical repair is to keep three labels attached to every result: unit size, overall boundary and time window. Repeat the analysis at a second reasonable grain when possible. If the conclusion changes, report that sensitivity rather than selecting the most attractive graph. Landscape Ecology develops the consequences of spatial configuration; macroecology asks how those consequences alter comparisons across many species.
A common descriptive model writes species richness as S = cA^z, where A is area, c is a scale coefficient and z controls how quickly predicted richness rises with area. Its usefulness depends on the domain, sampling design and range of areas for which it is fitted. It is not an instruction that every ecosystem must follow one exponent.
Suppose a teaching model uses c = 10 and z = 0.25, with A measured in hectares. At 16 hectares, S = 10 × 16^0.25 = 20. At 256 hectares, S = 10 × 256^0.25 = 40. Area increased sixteenfold while predicted richness doubled. The model expresses a diminishing proportional gain per additional hectare over this range.
Units change the coefficient
Sixteen hectares is 0.16 square kilometres. Keeping c = 10 while substituting 0.16 gives a different answer because the coefficient belongs to the original area units. Since A in hectares equals 100 times A in square kilometres, the new coefficient is 10 × 100^0.25, approximately 31.62. Then 31.62 × 0.16^0.25 gives the same 20 species.
This unit check is an inexpensive way to catch a seemingly sophisticated but invalid calculation. The exponent remains unchanged by this unit conversion; the intercept does not.
A nested sampling curve, comparisons among separate islands, and comparisons among habitat fragments need not estimate the same relationship. Larger samples can include more individuals; larger regions can include more habitat types; isolated areas can differ in immigration and extinction. Those explanations require different evidence.
Do not simply reverse the teaching equation to announce an immediate number of extinctions after habitat removal. Which habitat is removed, where species live, population persistence and the time since disturbance all matter. Island Biogeography supplies the island-specific context. The equation here demonstrates conditional prediction and dimensional consistency, not a universal conservation forecast.
Two communities can each contain four species but distribute individuals very differently. Suppose one has counts 25, 25, 25 and 25; the other has 70, 10, 10 and 10. Both contain 100 individuals and four species. The second is dominated by one species, while the first has equal representation.
A rank–abundance plot orders species from most to least numerous and displays their abundances or proportions. This reveals dominance and the tail of uncommon species. However, rank removes identity: a species ranked first at one site might be absent from the other. Keep the original species-by-site matrix alongside the graph.
A simple concentration calculation
For a completely known community, sum the squared species proportions. In the equal case, the result is 4 × 0.25² = 0.25. In the dominated case it is 0.70² + 3 × 0.10² = 0.52. These are probabilities that two independent draws with replacement identify the same species. Their reciprocals are 4 and approximately 1.92, expressing diversity as an effective number of equally common species under this particular weighting.
The result does not mean that the second community contains only 1.92 actual species. It means its concentration matches that of a hypothetical equally abundant community with that effective diversity. A different weighting of rare species answers a different question.
Real samples introduce another layer. Unobserved species are absent from the table, not necessarily from the habitat. A short sample can miss a long tail of rare species. Chao and Jost’s 2012 study develops comparisons standardised by sample completeness, rather than merely equal sample size. Use the appropriate estimation method and uncertainty, rather than treating an incomplete list as a census.
For learning, calculate richness and concentration side by side, then state what each ignores. For field interpretation, also document the sampling process that produced the counts.
CHAPTER 6 OF 14
6. Abundance and occupancy: disentangle an identity from a mechanism
Across equal-sized units, mean abundance including zeros equals the occupied fraction multiplied by mean abundance in occupied units. This is an arithmetic identity when all three quantities use the same units and data. It is not, by itself, evidence that occupying more places causes populations to become denser.
Suppose species A occupies eight of ten equal plots, with five individuals in each occupied plot. Its total is 40 and its overall mean is four per plot. Species B occupies two plots, with twenty individuals in each. Its total is also 40 and its overall mean is also four. Occupancy differs fourfold, yet total abundance is identical.
Now compare conditional density. Species B is four times denser where present. A graph using overall mean abundance could conceal that contrast; a graph using conditional density could show the opposite ranking. State which quantity is being plotted before searching for an ecological explanation.
Mechanisms need discriminating observations
A positive abundance–occupancy association could involve broad habitat tolerance, access to widespread resources, dispersal or other processes. Sampling can contribute too: a species with more individuals may be easier to detect in more places. Gaston and colleagues’ work on aggregation and abundance–occupancy is relevant because spatial clustering affects the relationship between counts and occupied units.
To distinguish explanations, ask what additional measurement would differ between them. Habitat breadth calls for independent habitat-use information. A dispersal hypothesis calls for evidence about movement and establishment. A detection explanation calls for repeat surveys or another design that estimates observation performance.
One more diagnostic is to separate between-species and within-species questions. A cross-species association between abundance and occupancy does not guarantee that a single declining species will move along the same line through time. Its habitat distribution, observation process and demographic constraints may differ from the cross-species average.
An allometric model relates biological quantities through a power function. For a deliberately simplified density model, write D = kM^-0.75, with D in individuals per square kilometre and M in kilograms. Here k fixes the predicted density at a mass of one kilogram. The exponent specifies a proportional relationship, not a fixed numerical decrease per kilogram.
Assume k = 80. A one-kilogram species has predicted density 80. A sixteen-kilogram species has predicted density 80 × 16^-0.75 = 10. A sixteenfold increase in mass corresponds to an eightfold decrease in predicted density. The calculation is exact for this stipulated model; actual observations need not follow it.
Damuth’s 1981 study analysed body size and density among mammalian primary consumers. It is a foundational empirical reference for this kind of comparison, not permission to assign the same exponent to every taxon, habitat, life stage or definition of abundance.
Biomass and energy are different quantities
Under the teaching model, population biomass density is D × M. It is 80 kilograms per square kilometre for the one-kilogram species and 160 for the sixteen-kilogram species. Fewer individuals does not mean lower biomass.
Now add a separate assumption: individual energy use scales as M^0.75 with the same proportional coefficient across the comparison. Multiplying by D makes the mass exponents cancel. Predicted population energy use per area would then be independent of body mass. That conclusion depends on both assumptions and compatible measurements. It does not follow from a density slope alone.
Record whether mass is an adult mean, a population mean or a seasonal estimate. Juvenile-rich populations and mixed sexes can have different mean masses. Similarly, a density measured in favourable habitat cannot automatically represent the whole range. The useful skill is to unpack the model into measurements and assumptions before interpreting its elegant algebra.
Taking logarithms of D = kM^b gives log(D) = log(k) + b log(M). The slope describes proportional scaling. A tenfold increase in M multiplies predicted D by 10^b. This can make values spanning several orders of magnitude easier to compare, provided positive quantities and consistent units are used.
Changing logarithm base on both axes does not change the fitted power-law interpretation. Changing only one axis does. Zero counts create a different problem: log(0) is undefined. Adding one is sometimes a deliberate modelling choice, but its effect depends on units and small values. It cannot be treated as a neutral universal repair.
An average on one scale is not an average on another
Take three hypothetical densities: 1, 10 and 100. Their arithmetic mean is 37. Their base-ten logarithms are 0, 1 and 2; the mean logarithm is 1, which transforms back to 10. That is the geometric mean. Both summaries are legitimate, but they answer different questions.
Consequently, exponentiating a fitted log-scale prediction does not automatically give the arithmetic mean on the original scale. The intended prediction and the model’s error distribution must be specified; a suitable correction may be needed. State whether a prediction represents a median-like central value, a geometric summary or an expected count.
Inspect the residuals as well as the line. If errors consistently increase with body mass, or one habitat type falls above the line, the model may be missing structure. A strong visual fit can also depend heavily on a few extreme observations. Repeat the calculation without each influential point and explain material changes.
The practical question is not “does the graph look linear?” It is “which process and error model make this relationship a defensible predictor for the cases we care about?”
A range boundary describes a geographic envelope. Occupancy describes presence within specified units. A species may occur across a broad envelope but occupy only scattered suitable patches inside it. Connecting distant records with a polygon can include substantial unsuitable or unsurveyed territory.
Consider two hypothetical species whose outer records fit within the same 100-square-kilometre boundary. One occupies 80 of a fixed set of 100 one-square-kilometre cells; the other occupies ten. Their envelopes are similar, but their occupied-cell counts differ eightfold. Neither measurement tells us how many individuals occupy those cells.
Boundaries can truncate a comparison
Suppose a study region includes the central part of species A’s global distribution and only the edge of species B’s. Comparing the fractions of this study region occupied by A and B is a regional analysis. Calling it a comparison of their global range sizes would be incorrect.
The same issue affects political boundaries. A species that is locally restricted may be widespread elsewhere. A species common within one protected area can still have a small total distribution. Define whether “rare” means locally sparse, geographically restricted, infrequently detected, or some combination.
Biogeography explains distributional histories and geographic constraints. Macroecological range comparisons need that context because a numerical summary can erase barriers, disjunctions and habitat differences that matter biologically.
Before comparing range sizes, align mapping resolution, taxonomic treatment, seasonal status and time period. Check whether a species split has divided one former range into two named units. That change in the database can alter a range-size distribution even if no organism has moved. Keep a dated taxonomy and explicit reconciliation decisions so a later analyst can distinguish biological change from changed classification.
Imagine ten plots that are all truly occupied. At the first survey, detection probability at an occupied plot is 0.4. At the second, improved equipment raises it to 0.8. Expected detections rise from four plots to eight even though true occupancy remains ten out of ten.
That example does not say every observed increase is an artefact. It shows why observation performance belongs inside the explanation. Counting more detections is insufficient to distinguish improved survey success from ecological expansion.
With independent repeat visits and constant per-visit detection probability 0.4, the probability of at least one detection in three visits is 1 − (1 − 0.4)^3 = 0.784. Repetition helps, but still does not guarantee detection. Dependence among visits, changing weather or temporary absence can invalidate the simple calculation.
Design the evidence before correcting it
For an occupancy study, record repeat visits, conditions and effort. For an abundance study, choose a method appropriate to the organism and explicitly address repeat counting and missed individuals. The Dynamic Occupancy Models specialist article develops the separation of ecological state from detection over time.
Convenient access can also bias the sampled landscape. If observers favour roads or parks, an occurrence map describes both organism distributions and observer behaviour. Removing duplicate points does not necessarily remove that preference. Nor can a complex algorithm recover information about unsampled environments without assumptions.
A useful field form has separate entries for “surveyed and not detected” and “not surveyed”. A blank cell must not silently become absence. Keep rejected records with rejection reasons, preserve uncertainty in coordinates and dates, and document filters. These habits make it possible to audit a surprising pattern before treating it as a biological discovery.
Neighbouring sites may share climate, soils, history and survey teams. Closely related species may share inherited traits. Repeated years at one location are not equivalent to independent regions. Ignoring such structure can make a model appear more transferable than it is.
Roberts and colleagues’ 2017 study examines cross-validation for spatial, temporal, hierarchical and phylogenetic structure. Its relevant lesson is that validation design must match the prediction task. Randomly withholding nearby observations can test interpolation among familiar conditions without establishing performance in a new region.
A prediction audit with numbers
Suppose a model predicts richness of 20, 30 and 40 species at three withheld sites. Observed richness is 18, 35 and 37. Absolute errors are 2, 5 and 3, so mean absolute error is 10/3, approximately 3.33 species. The signed errors, prediction minus observation, are 2, −5 and 3, averaging zero.
Zero average signed error does not mean accurate predictions: positive and negative errors cancelled. Report an error magnitude as well as bias. Then ask whether the withheld sites resemble the eventual application. Three nearby sites provide little evidence about performance on another continent.
Correlation also leaves causal alternatives open. Richness and temperature might covary with rainfall, habitat structure or historical processes. A model useful for prediction does not automatically identify the effect of experimentally changing temperature.
Write down competing explanations and one observation that would challenge each. Compare models using data withheld at the relevant level, and inspect failures by habitat or taxonomic group. When a model fails in a new setting, first check measurement compatibility; then examine whether the ecological relationships themselves have changed. Both are legitimate discoveries, but they require different repairs.
A monitoring team reports that a species occupied 25% of grid cells last year and 100% this year. It concludes that the species expanded fourfold. Last year used sixteen one-hectare cells; this year used four four-hectare blocks covering exactly the same landscape. The species was present in four fine cells, one inside each coarse block, in both years. Assume perfect detection.
Answer and reasoning
There is no evidence of expansion in this example. At the original grain, occupancy remains 4/16 = 25%. At the new grain, occupancy is 4/4 = 100% in both years. The fourfold numerical ratio compares different denominators and spatial units. It cannot measure biological change.
The repair is to recompute both years on a common grid, using the same boundary, season and presence rule. If only coarse observations survive from the second year, the fine pattern cannot generally be reconstructed. Report that information loss instead of inventing detailed locations.
Now change one condition: at the common fine grain, detections rise from four cells to eight, but the second year uses twice the survey effort. Expansion is now possible, but improved detection is another explanation. Repeat-survey information or an appropriate observation model is needed to separate them.
Finally, suppose standardised surveys establish a genuine increase from four occupied fine cells to eight. Has abundance doubled? Not necessarily. Four cells with twenty individuals each and eight cells with ten each both contain 80 individuals. Spatial spread and numerical population growth remain separate quantities.
This exercise links three habits: preserve the unit of comparison, separate detection from state, and distinguish occupancy from abundance. A strong answer explains which additional data would settle the next question. It does not simply replace one confident headline with another.
If a richness gradient disappears after equalising survey completeness, investigate the original sampling imbalance. The repair is to narrow the claim to what comparable evidence supports. Do not present the unadjusted gradient as a biological result and hide the sensitivity analysis elsewhere.
If an abundance–mass slope changes when zeros are excluded, distinguish density in occupied habitat from density over the whole landscape. Those are different response variables. Select the one that matches the question and report the other when it explains the contrast.
If an apparent range expansion coincides with a new recording platform, compare consistent survey subsets and inspect changes in observer coverage. More submitted records may be useful new evidence without being evidence of more organisms.
When an average reverses the story
Suppose low-productivity habitat contains species groups with mean densities 2 and 4, while high-productivity habitat contains corresponding groups with means 20 and 40. Within either habitat, the second group is twice as dense. But if the first group is sampled mostly in productive habitat and the second mostly in unproductive habitat, pooled means can reverse their ranking.
For a concrete weighting, let the first group have nine high-productivity observations and one low-productivity observation. Its pooled mean is (9 × 20 + 2)/10 = 18.2. Let the second have one high-productivity observation and nine low-productivity observations. Its mean is (40 + 9 × 4)/10 = 7.6. The pooled ranking reverses despite the consistent within-habitat relationship.
The repair is to inspect subgroup composition, define the target population and use an analysis that respects the design. Merely increasing sample size under the same imbalance can make the misleading pooled pattern more precise.
For every diagnostic, keep a short record: observed symptom, plausible measurement explanation, plausible ecological explanation, discriminating check and revised claim. This turns model criticism into a reproducible part of learning rather than an embarrassing afterthought.
Is macroecology just large-scale biogeography?
The fields overlap, but the emphasis differs. Biogeography asks how distributions arise across space and history. Macroecology emphasises statistical patterns across organisms and places, including abundance and body-size distributions that may not begin with a geographic boundary question. A useful project often needs both perspectives.
Does a scaling law predict an individual species accurately?
Not necessarily. A relationship across species can summarise central tendency while individual species vary greatly. Use its prediction interval and relevant biological information. Do not replace a local census with an allometric estimate when decisions depend on the actual population.
Is a larger dataset always more convincing?
Only if it improves the relevant evidence. A million duplicated or preferentially collected records cannot automatically answer a question requiring standardised absences or density. Sample size, representativeness, measurement quality and independence are separate properties.
Can these ideas be learned without advanced software?
Yes. Begin with a species-by-plot table, clearly labelled zeros and survey areas. Calculate totals, occupancy and conditional density. Aggregate neighbouring plots and explain what changes. Then plot body mass against density on ordinary and logarithmic axes, using a small synthetic dataset so every calculation can be checked manually.
A practical study route
For a classroom project, use the worked examples here to write a one-page measurement contract before calculating anything: organisms included, spatial grain, extent, dates, units and missing-data rules. For an outdoor investigation, choose an ethical, non-destructive survey of organisms that can be identified reliably, record effort and acknowledge identification uncertainty. Avoid disturbing wildlife to improve a count.
For a research route, choose one pattern and two competing explanations. Design a validation set that represents the intended transfer, then preserve the raw data, cleaning decisions, fitted model and failed predictions. For a conservation route, connect broad patterns to local habitat and population evidence through Conservation Biology. A broad model can guide questions and sampling without determining a site decision on its own.
Energy-based explanations also benefit from Ecosystem Ecology: population counts, biomass stocks and energy flows have different units and cannot be substituted for one another.
Read the evidence in a productive order
Start with Brown and Maurer for the comparative question, Damuth for an influential body-size analysis, Chao and Jost for sample completeness, and Roberts and colleagues for validation design. Use GBIF’s documentation when assembling observation data. These sources serve different purposes: a conceptual approach, an empirical relationship, an estimation method, a testing framework and data guidance. Their publication dates and linked titles are provided where each enters the argument.
The final transfer test is to explain what would remain valid if the species, region, grid size or survey method changed. Carry forward the definitions and reasoning; retest the numerical relationship.