Hypoxia drives plastic divergence in cichlid body shape

Organisms experience multiple selective agents that can influence phenotypes through heritable and/or plastic changes, often reflecting complex interactions between phenotype and environment. Environmental factors can directly influence phenotypes, but also indirectly affect phenotypic variation when genetic/plastic change in one trait results in correlated genetic/plastic change in another trait. In fishes, body shape is a trait that might be particularly prone to influence from environmental pressures that act on other morphological features. Variation in dissolved oxygen among aquatic environments has a large impact on the size of the gills and brains of fishes. It is likely that dissolved oxygen interacts with other environmental factors to both directly and indirectly influence patterns of body shape variation. We examined effects of dissolved oxygen on body shape variation among populations of an African cichlid fish (Pseudocrenilabrus multicolor) from multiple high- and low-oxygen sites within a single drainage in Uganda. A split-brood laboratory experiment was used to estimate plasticity of gill and brain size, and we used morphometric analyses to identify variation in body shape in F₁ offspring. Several analyses enabled us to identify genetic effects among populations, and effects of oxygen acting either directly on body shape or indirectly through its effects on gill and brain size. A large part of the variation in body shape was due to plastic variation in gill size associated with dissolved oxygen. Fish raised under low oxygen had deeper heads and shorter bodies, and this variation was driven by both direct effects of oxygen and indirect effects of gill size variation. Body shape variation in fishes should reflect interacting effects of multiple environmental factors that act directly or indirectly on morphology. Body shape might be particularly difficult to predict when phenotypes are plastic, because changes among populations would occur rapidly and be unrelated to genetic variation.     

Ecological drivers of song evolution in birds: Disentangling the effects of habitat and morphology

Environmental differences influence the evolutionary divergence of mating signals through selection acting either directly on signal transmission (“sensory drive”) or because morphological adaptation to different foraging niches causes divergence in “magic traits” associated with signal production, thus indirectly driving signal evolution. Sensory drive and magic traits both contribute to variation in signal structure, yet we have limited understanding of the relative role of these direct and indirect processes during signal evolution. Using phylogenetic analyses across 276 species of ovenbirds (Aves: Furnariidae), we compared the extent to which song evolution was related to the direct influence of habitat characteristics and the indirect effect of body size and beak size, two potential magic traits in birds. We find that indirect ecological selection, via diversification in putative magic traits, explains variation in temporal, spectral, and performance features of song. Body size influences song frequency, whereas beak size limits temporal and performance components of song. In comparison, direct ecological selection has weaker and more limited effects on song structure. Our results illustrate the importance of considering multiple deterministic processes in the evolution of mating signals.     

Life-history evolution in Australian snakes: a path analysis

I recently attempted to investigate interspecific patterns in ecological traits of Australian snakes using univariate statistical techniques (Shine 1994), but high intercorrelations among variables (especially with mean adult body size) made it difficult to interpret the observed patterns. In the present paper, I attempt to tease apart causal factors using multivariate (path) analysis on the same data set (103 species, based on dissection of >22000 museum specimens). Two separate path analyses were conducted: one that treated each species as an independent unit (and thus, ignored phylogeny) and the other based on independent phylogenetic contrasts. Path coefficients from the two types of analyses were similar in magnitude, and highly correlated with each other, suggesting that most interspecific patterns among traits may reflect functional association rather than phylogenetic conservatism. Path analysis showed that indirect effects of one variable upon another (i.e., mediated via other traits) were often stronger than direct effects. Thus, even when two variables appeared to be uncorrelated in the univariate analysis, this apparent lack of relationship sometimes masked strong but conflicting indirect effects. For example, a tradeoff between clutch size and offspring size tends to mask the direct effect of mean adult body size on clutch size. Path analysis may also suggest original causal hypotheses. For example, interspecific allometry of sexual size dimorphism (as seen in Australian snakes, and many other animal groups) may result from a strong effect of another allometrically-tied trait (offspring size) on growth trajectories of females.     

Direct and indirect effects of environmental temperature on the evolution of reproductive strategies: an information-theoretic approach

For ectotherms, environmental temperature affects the optimal size and number of offspring via multiple mechanisms. First, temperature influences the performance of offspring, which directly affects the optimal size of offspring. Second, temperature influences maternal body size, which indirectly affects the optimal size and/or number of offspring when larger females acquire more energetic resources or provide better parental care. Although traditional statistical approaches might distinguish the relative importance of these effects, an information-theoretic approach enables one to estimate effects more accurately by identifying the best evolutionary model in a set of candidate models. Here, we use the Akaike Information Criterion to calculate the likelihoods of seven path models, each derived from one or more optimality models of reproduction. Variation in reproductive traits among populations of lizards (Sceloporus undulatus) was used to quantify support for the models. Our results overwhelmingly supported a model based on an indirect effect of temperature that is mediated by maternal size. Path coefficients of this model were consistent with the hypotheses that, first, larger females can acquire more energy for reproduction and, second, the survival of offspring depends on both their size and their density. Our analyses exemplify how information theory can identify evolutionary hypotheses that merit experimental testing.     

Female mating decisions: maximizing fitness?

Sexual selection theory assumes that maximizing fitness is the ultimate goal in every mating decision. Fitness can be maximized directly by increasing the number of offspring (direct benefits) or indirectly by maximizing offspring's lifetime reproductive success (indirect benefits). Whereas there is considerable evidence in the literature for the influence of mating decisions on direct benefits, indirect benefits have been more elusive. Here, we review the variables that influence mating decisions made by females of freshwater fish and how these affect their fitness directly, as well as indirectly. Females enhance their fitness by matching their mating decisions to current environmental conditions, using a wide range of pre- and post-copulation mechanisms that enable them to maximize benefits from mating. Male sexual traits and courtship displays are signals used by females as a way of assessing male quality in terms of both direct and indirect benefits. Polyandry is very common among freshwater fish species, and indirect benefits have been hypothesized as drivers of its predominance. Despite intensive theoretical work, and multiple suggestions of the effects of indirect benefits, to date no study has been able to demonstrate experimentally the existence of indirect benefits in freshwater fish species. Additionally, most studies of direct benefits measure short-term benefits of mating decisions. In both cases, lifetime reproductive success is not assessed. Therefore, we are led to conclude that evidence as to whether female mating decisions result in direct and/or indirect benefits in freshwater fish species is still lacking. These results should be considered in light of the ongoing debate about the significance of indirect benefits in female mating decisions.     

Selection on fruit traits is mediated by the interplay between frugivorous birds,fruit flies,parasitoid wasps and seed‐dispersing ants

Every organism on Earth must cope with a multitude of species interactions both directly and indirectly throughout its life cycle. However, how selection from multiple species occupying different trophic levels affects diffuse mutualisms has received little attention. As a result, how a given species amalgamates the combined effects of selection from multiple mutualists and antagonists to enhance its own fitness remains little understood. We investigated how multispecies interactions (frugivorous birds, ants, fruit flies and parasitoid wasps) generate selection on fruit traits in a seed dispersal mutualism. We used structural equation models to assess whether seed dispersers (frugivorous birds and ants) exerted phenotypic selection on fruit and seed traits in the spiny hackberry (Celtis ehrenbergiana), a fleshy‐fruited tree, and how these selection regimes were influenced by fruit fly infestation and wasp parasitoidism levels. Birds exerted negative correlational selection on the combination of fruit crop size and mean seed weight, favouring either large crops with small seeds or small crops with large seeds. Parasitoids selected plants with higher fruit fly infestation levels, and fruit flies exerted positive directional selection on fruit size, which was positively correlated with seed weight. Therefore, higher parasitoidism indirectly correlated with higher plant fitness through increased bird fruit removal. In addition, ants exerted negative directional selection on mean seed weight. Our results show that strong selection on phenotypic traits may still arise in perceived diffuse species interactions. Overall, we emphasize the need to consider diverse direct and indirect partners to achieve a better understanding of the mechanisms driving phenotypic trait evolution in multispecies interactions.     

Natural selection for earlier male arrival to breeding grounds through direct and indirect effects in a migratory songbird

For migratory birds, the earlier arrival of males to breeding grounds is often expected to have fitness benefits. However, the selection differential on male arrival time has rarely been decomposed into the direct effect of male arrival and potential indirect effects through female traits. We measured the directional selection differential on male arrival time in the pied flycatcher (Ficedula hypoleuca) using data from 6 years and annual number of fledglings as the fitness proxy. Using structural equation modeling, we were able to take into account the temporal structure of the breeding cycle and the hierarchy between the examined traits. We found directional selection differentials for earlier male arrival date and earlier female laying date, as well as strong selection differential for larger clutch size. These selection differentials were due to direct selection only as indirect selection for these traits was nonsignificant. When decomposing the direct selection for earlier male arrival into direct and indirect effects, we discovered that it was almost exclusively due to the direct effect of male arrival date on fitness and not due to its indirect effects via female traits. In other words, we showed for the first time that there is a direct effect of male arrival date on fitness while accounting for those effects that are mediated by effects of the social partner. Our study thus indicates that natural selection directly favored earlier male arrival in this flycatcher population.     

Leaf trait integration mediates species richness variation in a species-rich neotropical forest domain

Environmental gradients are known to drive changes in mean trait values, but changes in the trait integration strength across local communities are less well understood, particularly with regard to possible links with species richness variation. Here, we tested if climate, soil, and topography gradients drive species richness indirectly via constraints on trait integration in the Atlantic Forest of South America. We evaluated seven traits (from leaf, wood, seed, and plant size) of 1456 species occurring across 84 local communities. Generalized least square models and a path model were applied to test direct and indirect relationships. Correlations were higher between leaf traits (average r?=?0.28) and lower when other traits were included (average r?=?0.16). In line with this result, species richness was related to a multivariate index of interspecific trait integration (ITI) computed for leaf traits, but not to the ITI for all the seven traits. Abiotic gradients influenced species richness both directly and indirectly through the leaf trait integration. A total of 33% and 26% of the variation in species richness and ITI, respectively, were explained by the models, with climatic conditions showing higher contribution than topographic and edaphic factors. These results support a significant but reduced environmental selection role behind the trait-based community assembly and may suggest that other processes are involved in the constrain of trait integration at larger spatial scales. In addition, different directional trends in trait–trait relationships across local communities suggest that global trait relationships may not necessarily hold at local contexts.

     

Climatic effects on life-history traits of moose in Estonia

Weather variables can influence life-history traits of ungulates. In this study, we assessed the suitability of regional climate indices including the NAO and two measures of local climate—the maximal extent of ice on the Baltic Sea (MIE) and absolute values of its annual deviations from the multi-year mean (VMIE)—to examine how density-independent processes influence moose body size and fecundity. We predicted that both winter severity (large values of MIE) and variability (large values of VMIE) depress moose traits (e.g., severe winters increase energy expenditure because of large snow depth or low temperatures, while the warmer than average winters may impose greater energetic demands on thermoregulation due to wet and windy weather, or may have indirect negative effects on summer foraging conditions). We estimated direct, delayed (lag) and cumulative effects of each climate measure. Both MIE and VMIE negatively affected jawbone length, with the effect size varying between the respective climatic indices and among age classes. In contrast to results obtained using local climatic variables, the NAO index had no significant effect on jawbone length. The probability of multiple ovulation was negatively influenced by direct effects of VMIE and delayed effects of MIE and NAO. We conclude that MIE and VMIE capture different aspects of the local climate and that these indices can be used in parallel as determinants of growth and fecundity of northern ungulates in coastal regions of the Baltic Sea.     

Broad‐scale geographic patterns in body size and hind wing development of western Palaearctic carabid beetles(Coleoptera: Carabidae)

Research into large‐scale ecological rules has a long tradition but has received increasing attention over the last two decades. Whereas environmental, especially climatic, influences on the geographic distribution of species traits such as body size are well understood in mammals and birds, our knowledge of the determinants and mechanisms which shape spatial patterns in invertebrate traits is still limited. This study analyzes macroecological patterns in two traits of the highly diverse invertebrate taxon of carabid beetles: body size and hind wing development, the latter being directly linked to species’ dispersal abilities. We tested for potential impacts of environmental variables (spatial, areal, topographic and climate‐related) representing both contemporary conditions and historical processes on large‐scale patterns in the two traits. Regression models revealed hump‐shaped relationships with latitude for both traits in the categories 1) all species, 2) widespread and 3) endemic (restricted‐range) species: body size and the proportion of flightless species increased from northern towards southern Europe and then decreased towards North Africa. The shared and independent influence of environmental factors was analyzed by variation partitioning. While contemporary environmental productivity and stability (represented by measures of ambient energy and water energy balance) had strong positive relationships with carabid body size, patterns in hind wing development were most notably influenced by topography (elevation range). Regions with high elevation range and low historical climate variability (since the last ice age), which likely offer long‐term stable habitats (i.e. glacial refugia), coincide with regions with high proportions of flightless species. Thus geographic patterns in carabid traits tend to be formed not only by recent climate but also by dispersal and historical climate and processes (i.e. glaciations and postglacial colonization).     

Direct and indirect facilitation affect community productivity through changes in functional diversity in an alpine system

Background and AimsFacilitation is an important ecological process for plant community structure and functional composition. Although direct facilitation has accrued most of the evidence so far, indirect facilitation is ubiquitous in nature and it has an enormous potential to explain community structuring. In this study, we assess the effect of direct and indirect facilitation on community productivity via taxonomic and functional diversity.MethodsIn an alpine community on the Tibetan Plateau, we manipulated the presence of the shrub Dasiphora fruticosa and graminoids in a fenced meadow and a grazed meadow to quantify the effects of direct and indirect facilitation. We measured four plant traits: height, lateral spread, specific leaf area (SLA) and leaf dry matter content (LDMC) of forbs; calculated two metrics of functional diversity [range of trait and community-weighted mean (CWM) of trait]; and assessed the responses of functional diversity to shrub facilitation. We used structural equation modelling to explore how shrubs directly and indirectly drove community productivity via taxonomic diversity and functional diversity.Key ResultsWe found stronger effects from herbivore-mediated indirect facilitation than direct facilitation on productivity and taxonomic diversity, regardless of the presence of graminoids. For functional diversity, the range and CWM of height and SLA, rather than lateral spread and LDMC, generally increased due to direct and indirect facilitation. Moreover, we found that the range of traits played a primary role over taxonomic diversity and CWM of traits in terms of shrub effects on community productivity.ConclusionsOur study reveals that the mechanism of shrub direct and indirect facilitation of community productivity in this alpine community is expanding the realized niche (i.e. expanding range of traits). Our findings indicate that facilitators might increase trait dispersion in the local community, which could alleviate the effect of environmental filters on trait values in harsh environments, thereby contributing to ecosystem functioning.     

Rates of molecular evolution in tree ferns are associated with body size,environmental temperature,and biological productivity

Variation in rates of molecular evolution (heterotachy) is a common phenomenon among plants. Although multiple theoretical models have been proposed, fundamental questions remain regarding the combined effects of ecological and morphological traits on rate heterogeneity. Here, we used tree ferns to explore the correlation between rates of molecular evolution in chloroplast DNA sequences and several morphological and environmental factors within a Bayesian framework. We revealed direct and indirect effects of body size, biological productivity, and temperature on substitution rates, where smaller tree ferns living in warmer and less productive environments tend to have faster rates of molecular evolution. In addition, we found that variation in the ratio of nonsynonymous to synonymous substitution rates (dN/dS) in the chloroplast rbcL gene was significantly correlated with ecological and morphological variables. Heterotachy in tree ferns may be influenced by effective population size associated with variation in body size and productivity. Macroevolutionary hypotheses should go beyond explaining heterotachy in terms of mutation rates and instead, should integrate population‐level factors to better understand the processes affecting the tempo of evolution at the molecular level.     

Warming and top predator loss drive ecosystem multifunctionality

Global change affects ecosystem functioning both directly by modifications in physicochemical processes, and indirectly, via changes in biotic metabolism and interactions. Unclear, however, is how multiple anthropogenic drivers affect different components of community structure and the performance of multiple ecosystem functions (ecosystem multifunctionality). We manipulated small natural freshwater ecosystems to investigate how warming and top predator loss affect seven ecosystem functions representing two major dimensions of ecosystem functioning, productivity and metabolism. We investigated their direct and indirect effects on community diversity and standing stock of multitrophic macro and microorganisms. Warming directly increased multifunctional ecosystem productivity and metabolism. In contrast, top predator loss indirectly affected multifunctional ecosystem productivity via changes in the diversity of detritivorous macroinvertebrates, but did not affect ecosystem metabolism. In addition to demonstrating how multiple anthropogenic drivers have different impacts, via different pathways, on ecosystem multifunctionality components, our work should further spur advances in predicting responses of ecosystems to multiple simultaneous environmental changes.     

Reproductive plasticity, ovarian dynamics and maternal effects in response to temperature and flight in Pararge aegeria

In nature, ovipositing females may be subjected to multiple extrinsic and intrinsic environmental factors simultaneously. To adequately assess a species response to environmental conditions during oviposition it may therefore be necessary to consider the interaction between multiple intrinsic and extrinsic factors simultaneously. Using the butterfly, Pararge aegeria, this study examined the combined effects of extrinsic (temperature and flight) and intrinsic (body mass and age) factors on ovarian dynamics, egg provisioning and reproductive output, and explored how these effects subsequently influenced offspring fitness when egg-stage development occurred in a low humidity environment. Both temperature- and flight-mediated plasticity in female reproductive output was observed, and there were strong temperature by flight interaction effects for the traits oocyte size and egg mass. As females aged, mean daily fecundity differed across temperature treatments, but not across flight treatments. Overall, temperature had more pronounced effects on ovarian dynamics than flight. Flight mainly influenced egg mass via changes in relative water content. A mismatch between the physiological response of females to high temperature and the requirements of their offspring had a negative impact on offspring fitness via effects on egg hatching success.     

Florivory indirectly decreases the plant reproductive output through changes in pollinator attraction

Species often interact indirectly with each other via their traits. There is increasing appreciation of trait‐mediated indirect effects linking multiple interactions. Flowers interact with both pollinators and floral herbivores, and the flower‐pollinator interaction may be modified by indirect effects of floral herbivores (i.e., florivores) on flower traits such as flower size attracting pollinators. To explore whether flower size affects the flower‐pollinator interaction, we used Eurya japonica flowers. We examined whether artificial florivory decreased fruit and seed production, and also whether flower size affected florivory and the number of floral visitors. The petal removal treatment (i.e., artificial florivory) showed approximately 50% reduction in both fruit and seed set in natural pollination but not in artificial pollination. Furthermore, flower size increased the number of floral visitors, although it did not affect the frequency of florivory. Our results demonstrate that petal removal indirectly decreased 75% of female reproductive output via decreased flower visits by pollinators and that flower size mediated indirect interactions between florivory and floral visitors.     

Scaling up the diversity–resilience relationship with trait databases and remote sensing data: the recovery of productivity after wildfire

Understanding the mechanisms underlying ecosystem resilience – why some systems have an irreversible response to disturbances while others recover – is critical for conserving biodiversity and ecosystem function in the face of global change. Despite the widespread acceptance of a positive relationship between biodiversity and resilience, empirical evidence for this relationship remains fairly limited in scope and localized in scale. Assessing resilience at the large landscape and regional scales most relevant to land management and conservation practices has been limited by the ability to measure both diversity and resilience over large spatial scales. Here, we combined tools used in large‐scale studies of biodiversity (remote sensing and trait databases) with theoretical advances developed from small‐scale experiments to ask whether the functional diversity within a range of woodland and forest ecosystems influences the recovery of productivity after wildfires across the four‐corner region of the United States. We additionally asked how environmental variation (topography, macroclimate) across this geographic region influences such resilience, either directly or indirectly via changes in functional diversity. Using path analysis, we found that functional diversity in regeneration traits (fire tolerance, fire resistance, resprout ability) was a stronger predictor of the recovery of productivity after wildfire than the functional diversity of seed mass or species richness. Moreover, slope, elevation, and aspect either directly or indirectly influenced the recovery of productivity, likely via their effect on microclimate, while macroclimate had no direct or indirect effects. Our study provides some of the first direct empirical evidence for functional diversity increasing resilience at large spatial scales. Our approach highlights the power of combining theory based on local‐scale studies with tools used in studies at large spatial scales and trait databases to understand pressing environmental issues.     

Predator cue and prey density interactively influence indirect effects on Basal resources in intertidal oyster reefs

Predators can influence prey abundance and traits by direct consumption, as well as by non-consumptive effects of visual, olfactory, or tactile cues. The strength of these non-consumptive effects (NCEs) can be influenced by a variety of factors, including predator foraging mode, temporal variation in predator cues, and the density of competing prey. Testing the relative importance of these factors for determining NCEs is critical to our understanding of predator-prey interactions in a variety of settings. We addressed this knowledge gap by conducting two mesocosm experiments in a tri-trophic intertidal oyster reef food web. More specifically, we tested how a predatory fish (hardhead catfish, Ariopsis felis) directly influenced their prey (mud crabs, Panopeus spp.) and indirectly affected basal resources (juvenile oysters, Crassostrea virginica), as well as whether these direct and indirect effects changed across a density gradient of competing prey. Per capita crab foraging rates were inversely influenced by crab density, but they were not affected by water-borne predator cues. As a result, direct consumptive effects on prey foraging rates were stronger than non-consumptive effects. In contrast, predator cue and crab density interactively influenced indirect predator effects on oyster mortality in two experiments, with trait-mediated and density-mediated effects of similar magnitude operating to enhance oyster abundance. Consistent differences between a variable predator cue environment and other predator cue treatments (no cue and constant cue) suggests that an understanding of the natural risk environment experienced by prey is critical to testing and interpreting trait-mediated indirect interactions. Further, the prey response to the risk environment may be highly dependent on prey density, particularly in prey populations with strong intra-specific interactions.     

Changes in seasonal climate outpace compensatory density‐dependence in eastern brook trout

Understanding how multiple extrinsic (density‐independent) factors and intrinsic (density‐dependent) mechanisms influence population dynamics has become increasingly urgent in the face of rapidly changing climates. It is particularly unclear how multiple extrinsic factors with contrasting effects among seasons are related to declines in population numbers and changes in mean body size and whether there is a strong role for density‐dependence. The primary goal of this study was to identify the roles of seasonal variation in climate driven environmental direct effects (mean stream flow and temperature) vs. density‐dependence on population size and mean body size in eastern brook trout (Salvelinus fontinalis). We use data from a 10‐year capture‐mark‐recapture study of eastern brook trout in four streams in Western Massachusetts, USA to parameterize a discrete‐time population projection model. The model integrates matrix modeling techniques used to characterize discrete population structures (age, habitat type, and season) with integral projection models (IPMs) that characterize demographic rates as continuous functions of organismal traits (in this case body size). Using both stochastic and deterministic analyses we show that decreases in population size are due to changes in stream flow and temperature and that these changes are larger than what can be compensated for through density‐dependent responses. We also show that the declines are due mostly to increasing mean stream temperatures decreasing the survival of the youngest age class. In contrast, increases in mean body size over the same period are the result of indirect changes in density with a lesser direct role of climate‐driven environmental change.     

Intraspecific variation in gill morphology of juvenile Nile perch, Lates niloticus, in Lake Nabugabo, Uganda

Several studies have demonstrated intraspecific variation in fish gill size that relates to variation in dissolved oxygen (DO) availability across habitats. In Lake Nabugabo, East Africa, ecological change over the past 12 years has coincided with a shift in the distribution of introduced Nile perch such that a larger proportion of the population now inhabits waters in or near wetland ecotones where DO is lower than in open waters of the lake. In this study, we compared gill size of juvenile Nile perch between wetland and exposed (open-water) habitats of Lake Nabugabo in 2007, as well as between Nile perch collected in 1996 and 2007. For Nile perch of Lake Nabugabo [<20 cm total length (TL)], there was a significant habitat effect on some gill traits. In general, fish from wetland habitats were characterized by a longer total gill filament length and average gill filament length than conspecifics from exposed habitats. Nile perch collected from wetland areas in 2007 had significantly larger gills (total gill filament length) than Nile perch collected in 1996, but there was no difference detected between Nile perch collected from exposed sites in 2007 and conspecifics collected in 1996.     

Uncovering a Nuisance Influence of a Phenological Trait of Plants Using a Nonlinear Structural Equation: Application to Days to Heading and Culm Length in Asian Cultivated Rice (Oryza Sativa L.)

Phenological traits of plants, such as flowering time, are linked to growth phase transition. Thus, phenological traits often influence other traits through the modification of the duration of growth period. This influence is a nuisance in plant breeding because it hampers genetic evaluation of the influenced traits. Genetic effects on the influenced traits have two components, one that directly affects the traits and one that indirectly affects the traits via the phenological trait. These cannot be distinguished by phenotypic evaluation and ordinary linear regression models. Consequently, if a phenological trait is modified by introgression or editing of the responsible genes, the phenotypes of the influenced traits can change unexpectedly. To uncover the influence of the phenological trait and evaluate the direct genetic effects on the influenced traits, we developed a nonlinear structural equation (NSE) incorporating a nonlinear influence of the phenological trait. We applied the NSE to real data for cultivated rice (Oryza sativa L.): days to heading (DH) as a phenological trait and culm length (CL) as the influenced trait. This showed that CL of the cultivars that showed extremely early heading was shortened by the strong influence of DH. In a simulation study, it was shown that the NSE was able to infer the nonlinear influence and direct genetic effects with reasonable accuracy. However, the NSE failed to infer the linear influence in this study. When no influence was simulated, an ordinary bi-trait linear model (OLM) tended to infer the genetic effects more accurately. In such cases, however, by comparing the NSE and OLM using an information criterion, we could assess whether the nonlinear assumption of the NSE was appropriate for the data analyzed. This study demonstrates the usefulness of the NSE in revealing the phenotypic influence of phenological traits.