The generalized Price equation: Forces that change population statistics

The Price equation partitions the change in the expected value of a population measure. The first component describes the partial change caused by altered frequencies. The second component describes the partial change caused by altered measurements. In biology, frequency changes often associate with the direct effect of natural selection. Measure changes reflect processes during transmission that alter trait values. More broadly, the two components describe the direct forces that change population composition and the altered frame of reference that changes measured values. The classic Price equation is limited to population statistics that can be expressed as the expected value of a measure. Many statistics cannot be expressed as expected values, such as the harmonic mean and the family of rescaled diversity measures. We generalize the Price equation to any population statistic that can be expressed as a function of frequencies and measurements. We obtain the generalized partition between the direct forces that cause frequency change and the altered frame of reference that changes measurements

The generalized Price equation: forces that change population statistics

The Price equation partitions the change in the expected value of a population measure. The first component describes the partial change caused by altered frequencies. The second component describes the partial change caused by altered measurements. In biology, frequency changes often associate with the direct effect of natural selection. Measure changes reflect processes during transmission that alter trait values. More broadly, the two components describe the direct forces that change population composition and the altered frame of reference that changes measured values. The classic Price equation is limited to population statistics that can expressed as the expected value of a measure. Many statistics cannot be expressed as expected values, such as the harmonic mean and the family of rescaled diversity measures. We generalize the Price equation to any population statistic that can be expressed as a function of frequencies and measurements. We obtain the generalized partition between the direct forces that cause frequency change and the altered frame of reference that changes measurements

Species interactions and diversity: A unified framework using Hill numbers

Biodiversity describes the variety of organisms on planet earth. Ecologists have long hoped for a synthesis between analyses of biodiversity and analyses of biotic interactions among species, such as predation, competition, and mutualism. However, it is often unclear how to connect details of these interactions with complex modern analyses of biodiversity. To resolve this gap, we propose a unification of models of biotic interactions and measurements of diversity. We show that analyses of biodiversity obscure details about biotic interactions. For example, identical changes in biodiversity can arise from predation, competition or mutualism. Our approach indicates that traditional models of community assembly miss key facets of diversity change. Instead, we suggest that analyses of diversity change should focus on partitions, which measure mechanisms that directly shape changes in diversity, notably species level selection and immigration, rather than traditional analyses of biotic interactions

Species interactions and diversity: A unified framework using Hill numbers

Biodiversity describes the variety of organisms on planet earth. Ecologists have long hoped for a synthesis between analyses of biodiversity and analyses of biotic interactions among species, such as predation, competition and mutualism. However, it is often unclear how to connect details of these interactions with complex modern analyses of biodiversity. To resolve this gap, we propose a unification of models of biotic interactions and measurements of diversity. We show that analyses of biodiversity obscure details about biotic interactions. For example, identical changes in biodiversity can arise from predation, competition or mutualism. Our approach indicates that traditional models of community assembly miss key facets of diversity change. Instead, we suggest that analyses of diversity change should focus on partitions, which measure mechanisms that directly shape changes in diversity, notably species level selection and immigration, rather than traditional analyses of biotic interactions

Disentangling niche theory and beta diversity change

Beta diversity describes the differences in species composition among communities. Changes in beta diversity over time are thought to be due to selection based on species’ niche characteristics. For example, theory predicts that selection that favors habitat specialists will increase beta diversity. In practice, ecologists struggle to predict how beta diversity changes. To remedy this problem, we propose a novel solution that formally measures selection’s effects on beta diversity. Using the Price equation, we show how change in beta diversity over time can be partitioned into fundamental mechanisms including selection among species, variable selection among communities, drift, and immigration. A key finding of our approach is that a species’ short-term impact on beta diversity cannot be predicted using information on its long-term environmental requirements (i.e., its niche). We illustrate how our approach can be used to partition causes of diversity change in a montane tropical forest before and after an intense hurricane. Previous work in this system highlighted the resistance of habitat specialists and the recruitment of light-demanding species but was unable to quantify the importance of these effects on beta diversity. Using our approach, we show that changes in beta diversity were consistent with ecological drift. We use these results to highlight the opportunities presented by a synthesis of beta diversity and formal models of selection

Disentangling niche theory and beta diversity change

Beta diversity describes the differences in species composition among communities. Changes in beta diversity over time are thought to be due to selection based on species’ niche characteristics. For example, theory predicts that selection that favours habitat specialists will increase beta diversity. In practice, ecologists struggle to predict how beta diversity changes. To remedy this problem, we propose a novel solution that formally measures selection’s effects on beta diversity. Using the Price equation, we show how change in beta diversity over time can be partitioned into fundamental mechanisms including selection among species, variable selection among communities, drift, and immigration. A key finding of our approach is that a species’ short-term impact on beta diversity cannot be predicted using information on its long-term environmental requirements (i.e. its niche). We illustrate how our approach can be used to partition causes of diversity change in a montane tropical forest before and after an intense hurricane. Previous work in this system highlighted the resistance of habitat specialists and the recruitment of light-demanding species but was unable to quantify the importance of these effects on beta diversity. Using our approach, we show that changes in beta diversity were consistent with ecological drift. We use these results to highlight the opportunities presented by a synthesis of beta diversity and formal models of selection

Global assessment of three Rumex species reveals inconsistent climatic niche shifts across multiple introduced ranges

Climatic niche shifts occur when species occupy different climates in the introduced range than in their native range. Climatic niche shifts are known to occur across a range of taxa, however we do not currently understand whether climatic niche shifts can consistently be predicted across multiple introduced ranges. Using three congeneric weed species, we investigate whether climatic niche shifts in one introduced range are consistent in other ranges where the species has been introduced. We compared the climatic conditions occupied by Rumex conglomeratus, R. crispus, and R. obtusifolius between their native range (Eurasia) and three different introduced ranges (North America, Australia, New Zealand). We considered metrics of niche overlap, expansion, unfilling, pioneering, and similarity to determine whether climatic niche shifts were consistent across ranges and congeners. We found that the presence and direction of climatic niche shifts was inconsistent between introduced ranges for each species. Within an introduced range, however, niche shifts were qualitatively similar among species. North America and New Zealand experienced diverging niche expansion into drier and wetter climates respectively, whilst the niche was conserved in Australia. This work highlights how unique characteristics of an introduced range and local introduction history can drive different niche shifts, and that comparisons between only the native and one introduced range may misrepresent a species’ capacity for niche shifts. However, predictions of climatic niche shifts could be improved by comparing related species in the introduced range rather than relying on the occupied environments of the native range

Comparing the above and below-ground chemical defences of three Rumex species between their native and introduced provenances

Compared to their native range, non-native plants often experience reduced levels of herbivory in the introduced range. This may result in reduced pressure to produce chemical defences that act against herbivores. We measured the most abundant secondary metabolites found in Rumex spp., namely oxalates, phenols and tannins. To test this hypothesis, we compared native (UK) and introduced (NZ) provenances of three different Rumex species (R. obtusifolius, R. crispus and R. conglomeratus, Polygonaceae) to assess whether any significant differences existed in their levels of chemical defences in either leaves and roots. All three species have previously been shown to support a lower diversity of insect herbivores and experience less herbivory in the introduced range. We further examined leaf herbivory on plants from both provenances when grown together in a common garden experiment in New Zealand to test whether any differences in damage might be consistent with variation in the quantity of chemical defences. We found that two Rumex species (R. obtusifolius and R. crispus) showed no evidence for a reduction in chemical defences, while a third (R. conglomeratus) showed only limited evidence. The common garden experiment revealed that the leaves analysed had low levels of herbivory (∼0.5%) with no differences in damage between provenances for any of the three study species. Roots tended to have a higher concentration of tannins than shoots, but again showed no difference between the provenances. As such, the findings of this study provide no evidence for lower plant investments in chemical defences, suggesting that other factors explain the success of Rumex spp. in New Zealand

Effects of different dispersal patterns on the presence-absence of multiple species

Predicting which species will be present (or absent) across a geographical region remains one of the key problems in ecology. Numerous studies have suggested several ecological factors that can determine species presence-absence: environmental factors (i.e. abiotic environments), interactions among species (i.e. biotic interactions) and dispersal process. While various ecological factors have been considered, less attention has been given to the problem of understanding how different dispersal patterns, in interaction with other factors, shape community assembly in the presence of priority effects (i.e. where relative initial abundances determine the long-term presence-absence of each species). By employing both local and non-local dispersal models, we investigate the consequences of different dispersal patterns on the occurrence of priority effects and coexistence in multi-species communities. In the case of non-local, but short-range dispersal, we observe agreement with the predictions of local models for weak and medium dispersal strength, but disagreement for relatively strong dispersal levels. Our analysis shows the existence of a threshold value in dispersal strength (i.e. saddle-node bifurcation) above which priority effects disappear. These results also reveal a co-dimension 2 point, corresponding to a degenerate transcritical bifurcation: at this point, the transcritical bifurcation changes from subcritical to supercritical with corresponding creation of a saddle-node bifurcation curve. We observe further contrasting effects of non-local dispersal as dispersal distance changes: while very long-range dispersal can lead to species extinctions, intermediate-range dispersal can permit more outcomes with multi-species coexistence than short-range dispersal (or purely local dispersal). Overall, our results show that priority effects are more pronounced in the non-local dispersal models than in the local dispersal models. Taken together, our findings highlight the profound delicacy in the mediation of priority effects by dispersal processes: “big steps” can have more influence than many “small steps”

Can the enemy release hypothesis explain the success of Rumex (Polygonaceae) species in an introduced range?

The enemy release hypothesis states that introduced plants have a competitive advantage due to their release from co-evolved natural enemies (i.e., herbivores and pathogens), which allows them to spread rapidly in new environments. This hypothesis has received mixed support to date, but previous studies have rarely examined the herbivore community, plant damage, and performance simultaneously and largely ignored below-ground herbivores. We tested for enemy release by conducting large scale field surveys of insect diversity and abundance in both the native (United Kingdom) and introduced (New Zealand) ranges of three dock (Rumex, Polygonaceae) species: R. conglomeratus Murray (clustered dock), R. crispus L. (curly dock) and R. obtusifolius L. (broad-leaved dock). We captured both above- and below-ground insect herbivores, measured herbivore damage, and plant biomass as an indicator for performance. In the introduced range, Rumex plants had a lower diversity of insect herbivores, all insect specialists present in the native range were absent and plants had lower levels of herbivore damage on both roots and leaves. Despite this, only R. crispus had greater fresh weight in the introduced range compared to the native range. This suggests that enemy release, particularly from below-ground herbivores, could be a driver for the success of R. crispus plants in New Zealand, but not for R. conglomeratus and R. obtusifolius