Caloric restriction extends lifespan in a clonal plant.

When subjected to dietary caloric restriction (CR), individual animals often outlive well-fed conspecifics. Here, we address whether CR also extends lifespan in plants. Whereas caloric intake in animals comes from ingestion, in plants it derives from photosynthesis. Thus, factors that reduce photosynthesis, such as reduced light intensity, can induce CR. In two lab experiments investigating the aquatic macrophyte Lemna minor, we tracked hundreds of individuals longitudinally, with light intensity-and hence, CR-manipulated using neutral-density filters. In both experiments, CR dramatically increased lifespan through a process of temporal scaling. Moreover, the magnitude of lifespan extension accorded with the assumptions that (a) light intensity positively relates to photosynthesis following Michaelis-Menten kinetics, and (b) photosynthesis negatively relates to lifespan via a power law. Our results emphasize that CR-mediated lifespan extension applies to autotrophs as well as heterotrophs, and suggest that variation in light intensity has quantitatively predictable effects on plant aging trajectories.

Pace and shape of senescence in three species of duckweed.

Senescence is progressive bodily deterioration associated with declines in survival and fecundity in older age classes. There is great diversity in patterns of senescence across species, but these patterns can be difficult to compare formally due to variation in the absolute time scales in which species live and die: members of some species live for a matter of days, others for millennia. To address this issue, the "pace-shape" approach was developed to decouple absolute time from analyses and instead standardize life history traits in terms of average life expectancy, facilitating intra- and interspecific comparisons. Here, we use this approach to distinguish the generic form of demographic trajectories (shape) from the time scale on which the trajectories occurred (pace) in three species of tiny, free-floating aquatic plants known as duckweeds (Lemna gibba L., L. minor L., and L. turionifera Landolt), which have mean lifespans of less than a month under typical lab conditions, and exhibit age-related declines in survivorship and reproduction. Using a randomized block design in which we tracked a final total of 430 individuals, we report differences in pace and shape among the three species. Specifically, the largest, least-fecund, and typically longest-lived species, L. gibba, tended to exhibit more rapid decreases in time-standardized survivorship and fecundity compared with the other two species. This study emphasizes variation in aging patterns that can be found among plant species, including those in the same genus, and provides further validation for the utility of applying the pace and shape approach in interspecific comparisons.

Parental Age Effects and the Evolution of Senescence.

Most theory on the evolution of senescence implicitly assumes that all offspring are of equal quality. However, in addition to age-related declines in survival and fecundity (classically defined senescence), many organisms exhibit age-related declines in offspring quality, a phenomenon known as a parental age effect. Theoretical work suggests that parental age effects may alter age trajectories of selection and therefore shape the evolution of senescence; however, to date, these analyses have been limited to idealized life cycles and models of maternal care in human populations. To gain a broader understanding of how parental age effects may shape age trajectories of selection, we extend the classic age-structured population projection model to also account for parental age structure and apply this model to empirical data from an aquatic plant known to exhibit parental age effects (the duckweed Lemna minor), as well as a diverse set of simulated life cycles. Our results suggest that parental age effects alter predictions from classic theory on the evolution of senescence. Age-related declines in offspring quality reduce the relative value of late-life reproduction, leading to steeper age-related declines in the force of natural selection than would otherwise be expected and potentially favoring the evolution of more rapid rates of senescence.

Cross-tolerance to Desiccation and Cold in Khapra Beetle (Coleoptera: Dermestidae).

Khapra beetle, Trogoderma granarium Everts, is unusual in two key respects. First, they are among the most cold hardy of stored-product insect pests even though they originate in hot and dry regions of the Indian subcontinent. Second, their larvae can enter into diapause to survive harsh environmental conditions. In the present study, we examined whether these two phenomena are related, i.e., due to cross-tolerance. Cross-tolerance is the tolerance to one ecological stress when induced by a separate stress. To investigate this, khapra beetle larvae were reared at different relative humidities (3, 28, 49, and 79%) in either nondiapausing or diapausing conditions. Then the cold tolerance of larvae was estimated by measuring mortality after different durations at -10°C. For nondiapausing larvae, relative humidity had little effect on cold tolerance with the lethal time to 50% mortality (LT50) occurring between 2 and 4 d. For diapausing larvae, cold tolerance increased with greater desiccation stress with LT50's of 5, 7, 10, and 18 d at 79, 49, 28, and 3% RH, respectively. This suggests that the physiological mechanisms that protect diapausing larvae from desiccation may also increase cold tolerance, even though these insects may rarely be exposed to low temperatures.

RESTORE-Cognitive functional therapy with or without movement sensor biofeedback versus usual care for chronic, disabling low back pain: study protocol for a randomised controlled trial.

INTRODUCTION: Low back pain (LBP) is the leading cause of disability globally and its costs exceed those of cancer and diabetes combined. Recent evidence suggests that individualised cognitive and movement rehabilitation combined with lifestyle advice (cognitive functional therapy (CFT)) may produce larger and more sustained effects than traditional approaches, and movement sensor biofeedback may enhance outcomes. Therefore, this three-arm randomised controlled trial (RCT) aims to compare the clinical effectiveness and economic efficiency of individualised CFT delivered with or without movement sensor biofeedback, with usual care for patients with chronic, disabling LBP. METHODS AND ANALYSIS: Pragmatic, three-arm, randomised, parallel group, superiority RCT comparing usual care (n=164) with CFT (n=164) and CFT-plus-movement-sensor-biofeedback (n=164). Inclusion criteria include: adults with a current episode of LBP >3 months; sought primary care ≥6 weeks ago for this episode of LBP; average LBP intensity of ≥4 (0-10 scale); at least moderate pain-related interference with work or daily activities. The CFT-only and CFT-plus-movement-sensor-biofeedback participants will receive seven treatment sessions over 12 weeks plus a 'booster' session at 26 weeks. All participants will be assessed at baseline, 3, 6, 13, 26, 40 and 52 weeks. The primary outcome is pain-related physical activity limitation (Roland Morris Disability Questionnaire). Linear mixed models will be used to assess the effect of treatment on physical activity limitation across all time points, with the primary comparison being a formal test of adjusted mean differences between groups at 13 weeks. For the economic (cost-utility) analysis, the primary outcome of clinical effect will be quality-adjusted life years measured across the 12-month follow-up using the EuroQol EQ-5D-5L . ETHICS AND DISSEMINATION: Approved by Curtin University Human Research Ethics Committee (HRE2018-0062, 6 Feb 2018). Study findings will be disseminated through publication in peer-reviewed journals and conference presentations. TRIAL REGISTRATION NUMBER: Australian New Zealand Clinical Trials Registry (ACTRN12618001396213).

Does movement matter in people with back pain? Investigating 'atypical' lumbo-pelvic kinematics in people with and without back pain using wireless movement sensors.

BACKGROUND: Interventions for low back pain (LBP) commonly target 'dysfunctional' or atypical lumbo-pelvic kinematics in the belief that correcting aberrant movement improves patients' pain and activity outcomes. If atypical kinematic parameters and postures have a relationship to LBP, they could be expected to more prevalent in people with LBP compared to people without LBP (NoLBP). This exploratory study measured, defined and compared atypical kinematic parameters in people with and without LBP. METHODS: Wireless inertial motion and EMG sensors were used to measure lumbo-pelvic kinematics during standing trunk flexion (range of motion (ROM), timing, sequence coordination, and extensor muscle activation) and in sitting (relative sitting position, pelvic tilt range) in a sample of 126 of adults without LBP and 140 chronic LBP subjects. Atypical movement was defined using the 10th/90th centiles of the NoLBP group. Mean differences and prevalence rates for atypical movement were calculated. Dichotomised pain scores for 'high-pain-on-bending' and 'high-pain-on-sitting' were tested for their association with atypical kinematic variables. RESULTS: For standing flexion, significant mean differences, after adjusting for age and gender factors, were seen for the LBP group with (i) reduced ROM (trunk flexion (NoLBP 111o, LBP 93o, p < .0001), lumbar flexion (NoLBP 52o, LBP 46o, p < .0001), pelvic flexion (NoLBP 59o, LBP 48o, p < .0001), (ii) greater extensor muscle activation for the LBP group (NoLBP 0.012, LBP 0.25 p < .0001), (iii) a greater delay in pelvic motion at the onset of flexion (NoLBP - 0.21 s; LBP - 0.36 s, p = 0.023), (iv) and longer movement duration for the LBP group (NoLBP 2.28 s; LBP 3.18 s, p < .0001). Atypical movement was significantly more prevalent in the LBP group for small trunk (× 5.4), lumbar (× 3.0) and pelvic ROM (× 3.9), low FRR (× 4.9), delayed pelvic motion at 20o flexion (× 2.9), and longer movement duration (× 4.7). No differences between groups were seen for any sitting parameters. High pain intensity was significantly associated with small lumbar ROM and pelvic ROM. CONCLUSION: Significant movement differences during flexion were seen in people with LBP, with a higher prevalence of small ROM, slower movement, delayed pelvic movement and greater lumbar extensor muscle activation but without differences for any sitting parameter.

Subgroups of lumbo-pelvic flexion kinematics are present in people with and without persistent low back pain.

BACKGROUND: Movement dysfunctions have been associated with persistent low back pain (LBP) but optimal treatment remains unclear. One possibility is that subgroups of persistent LBP patients have differing movement characteristics and therefore different responses to interventions. This study examined if there were patterns of flexion-related lumbo-pelvic kinematic and EMG parameters that might define subgroups of movement. METHODS: This was a cross-sectional, observational study of 126 people without any history of significant LBP and 140 people with persistent LBP (n = 266). Wireless motion and surface EMG sensors collected lumbo-pelvic data on flexion parameters (range of motion (ROM) of trunk, lumbar, and pelvis), speed, sequence coordination and timing, and EMG extensor muscle activity in forward bending (flexion relaxation)), and sitting parameters (relative position, pelvic tilt range and tilt ratio). Latent class analysis was used to identify patterns in these parameters. RESULTS: Four subgroups with high probabilities of membership were found (mean 94.9%, SD10.1%). Subgroup 1 (n = 133 people, 26% LBP) had the greatest range of trunk flexion, fastest movement, full flexion relaxation, and synchronous lumbar versus pelvic movement. Subgroup 2 (n = 73, 71% LBP) had the greatest lumbar ROM, less flexion relaxation, and a 0.9 s lag of pelvic movement. Subgroup 3 (n = 41, 83% LBP) had the smallest lumbar ROM, a 0.6 s delay of lumbar movement (compared to pelvic movement), and less flexion relaxation than subgroup 2. Subgroup 4 (n = 19 people, 100% LBP) had the least flexion relaxation, slowest movement, greatest delay of pelvic movement and the smallest pelvic ROM. These patterns could be described as standard (subgroup 1), lumbar dominant (subgroup 2), pelvic dominant (subgroup 3) and guarded (subgroup 4). Significant post-hoc differences were seen between subgroups for most lumbo-pelvic kinematic and EMG parameters. There was greater direction-specific pain and activity limitation scores for subgroup 4 compared to other groups, and a greater percentage of people with leg pain in subgroups 2 and 4. CONCLUSION: Four subgroups of lumbo-pelvic flexion kinematics were revealed with an unequal distribution among people with and without a history of persistent LBP. Such subgroups may have implications for which patients are likely to respond to movement-based interventions.

Sequential interactions-in which one player plays first and another responds-promote cooperation in evolutionary-dynamical simulations of single-shot Prisoner's Dilemma and Snowdrift games.

Cooperation is a central topic in evolutionary biology because (a) it is difficult to reconcile why individuals would act in a way that benefits others if such action is costly to themselves, and (b) it underpins many of the 'major transitions of evolution', making it essential for explaining the origins of successively higher levels of biological organization. Within evolutionary game theory, the Prisoner's Dilemma and Snowdrift games are the main theoretical constructs used to study the evolution of cooperation in dyadic interactions. In single-shot versions of these games, wherein individuals play each other only once, players typically act simultaneously rather than sequentially. Allowing one player to respond to the actions of its co-player-in the absence of any possibility of the responder being rewarded for cooperation or punished for defection, as in simultaneous or sequential iterated games-may seem to invite more incentive for exploitation and retaliation in single-shot games, compared to when interactions occur simultaneously, thereby reducing the likelihood that cooperative strategies can thrive. To the contrary, I use lattice-based, evolutionary-dynamical simulation models of single-shot games to demonstrate that under many conditions, sequential interactions have the potential to enhance unilaterally or mutually cooperative outcomes and increase the average payoff of populations, relative to simultaneous interactions-benefits that are especially prevalent in a spatially explicit context. This surprising result is attributable to the presence of conditional strategies that emerge in sequential games that can't occur in the corresponding simultaneous versions.

Calculating Competitive Intransitivity: Computational Challenges.

Intransitive (or "rock-paper-scissors") competition is compelling because it promotes species coexistence and because recent work suggests that it may be common in natural systems. One class of intransitivity indices works by considering s, the minimum number of competitive reversals to convert a given competitive community (i.e., a "tournament") to a hierarchy. The most straightforward example of such "reversal-based" indices is Petraitis's index, [Formula: see text], where M is the maximum s across all possible n-species tournaments. Using exhaustive searches, we prove that Petraitis's formula for M (and, therefore, t) does not hold for [Formula: see text]. Furthermore, determination of s for even moderate values of n may prove difficult, as the equivalent graph theoretical problem is NP (nondeterministic polynomial time) hard; there is no known computationally feasible way to compute an exact answer for anything but small values of n, let alone a closed-form solution. Petraitis's t is a valuable index of intransitivity; however, at present its use is limited to relatively species-poor systems. More broadly, reversal-based indices, while intuitive, may be problematic because of this computability issue.

Offspring of older parents are smaller-but no less bilaterally symmetrical-than offspring of younger parents in the aquatic plant Lemna turionifera.

Offspring quality decreases with parental age in many taxa, with offspring of older parents exhibiting reduced life span, reproductive capacity, and fitness, compared to offspring of younger parents. These "parental age effects," whose consequences arise in the next generation, can be considered as manifestations of parental senescence, in addition to the more familiar age-related declines in parent-generation survival and reproduction. Parental age effects are important because they may have feedback effects on the evolution of demographic trajectories and longevity. In addition to altering the timing of offspring life-history milestones, parental age effects can also have a negative impact on offspring size, with offspring of older parents being smaller than offspring of younger parents. Here, we consider the effects of advancing parental age on a different aspect of offspring morphology, body symmetry. In this study, we followed all 403 offspring of 30 parents of a bilaterally symmetrical, clonally reproducing aquatic plant species, Lemna turionifera, to test the hypothesis that successive offspring become less symmetrical as their parent ages, using the "Continuous Symmetry Measure" as an index. Although successive offspring of aging parents older than one week became smaller and smaller, we found scant evidence for any reduction in bilateral symmetry.

How consistent are lordosis, range of movement and lumbo-pelvic rhythm in people with and without back pain?

BACKGROUND: Comparing movements/postures in people with and without lower back pain (LBP) may assist identifying LBP-specific dysfunction and its relationship to pain or activity limitation. This study compared the consistency in lumbo-pelvic posture and movement (range and pattern) in people with and without chronic LBP (>12 week's duration). METHODS: Wireless, wearable, inertial measurement units measured lumbar lordosis angle, range of movement (ROM) and lumbo-pelvic rhythm in adults (n = 63). Measurements were taken on three separate occasions: two tests on the same day with different raters and a third (intra-rater) test one to two weeks later. Participants performed five repetitions of tested postures or movements. Test data were captured automatically. Minimal detectable change scores (MDC90) provided estimates of between-test consistency. RESULTS: There was no significant difference between participants with and without LBP for lordosis angle. There were significant differences for pelvic flexion ROM (LBP 60.8°, NoLBP 54.8°, F(1,63) = 4.31, p = 0.04), lumbar right lateral flexion ROM (LBP 22.2°, NoLBP 24.6° F(1,63) = 4.48, p = .04), trunk right lateral flexion ROM (LBP 28.4°, NoLBP 31.7°, F(1,63) = 5.9, p = .02) and lumbar contribution to lumbo-pelvic rhythm in the LBP group (LBP 45.8 %, F(1,63) = 4.20, NoLBP 51.3 % p = .044). MDC90 estimates for intra and inter-rater comparisons were 10°-15° for lumbar lordosis, and 5°-15° for most ROM. For lumbo-pelvic rhythm, we found 8-15 % variation in lumbar contribution to flexion and lateral flexion and 36-56 % variation in extension. Good to excellent agreement (reliability) was seen between raters (mean r = .88, ICC (2,2)). CONCLUSION: Comparisons of ROM between people with and without LBP showed few differences between groups, with reduced relative lumbar contribution to trunk flexion. There was no difference between groups for lordosis. Wide, within-group differences were seen for both groups for ROM and lordosis. Due to variability between test occasions, changes would need to exceed 10°-15° for lumbar lordosis, 5°-15° for ROM components, and 8-15 % of lumbar contribution to lumbo-pelvic rhythm, to have 90 % confidence that movements had actually changed. Lordosis, range of movement and lumbo-pelvic rhythm typically demonstrate variability between same-day and different-day tests. This variability needs to be considered when interpreting posture and movement changes.

Competitive intransitivity, population interaction structure, and strategy coexistence.

Intransitive competition occurs when competing strategies cannot be listed in a hierarchy, but rather form loops-as in the game rock-paper-scissors. Due to its cyclic competitive replacement, competitive intransitivity promotes strategy coexistence, both in rock-paper-scissors and in higher-richness communities. Previous work has shown that this intransitivity-mediated coexistence is strongly influenced by spatially explicit interactions, compared to when populations are well mixed. Here, we extend and broaden this line of research and examine the impact on coexistence of intransitive competition taking place on a continuum of small-world networks linking spatial lattices and regular random graphs. We use simulations to show that the positive effect of competitive intransitivity on strategy coexistence holds when competition occurs on networks toward the spatial end of the continuum. However, in networks that are sufficiently disordered, increasingly violent fluctuations in strategy frequencies can lead to extinctions and the prevalence of monocultures. We further show that the degree of disorder that leads to the transition between these two regimes is positively dependent on population size; indeed for very large populations, intransitivity-mediated strategy coexistence may even be possible in regular graphs with completely random connections. Our results emphasize the importance of interaction structure in determining strategy dynamics and diversity.

Comparing lumbo-pelvic kinematics in people with and without back pain: a systematic review and meta-analysis.

BACKGROUND: Clinicians commonly examine posture and movement in people with the belief that correcting dysfunctional movement may reduce pain. If dysfunctional movement is to be accurately identified, clinicians should know what constitutes normal movement and how this differs in people with low back pain (LBP). This systematic review examined studies that compared biomechanical aspects of lumbo-pelvic movement in people with and without LBP. METHODS: MEDLINE, Cochrane Central, EMBASE, AMI, CINAHL, Scopus, AMED, ISI Web of Science were searched from inception until January 2014 for relevant studies. Studies had to compare adults with and without LBP using skin surface measurement techniques to measure lumbo-pelvic posture or movement. Two reviewers independently applied inclusion and exclusion criteria, and identified and extracted data. Standardised mean differences and 95% confidence intervals were estimated for group differences between people with and without LBP, and where possible, meta-analyses were performed. Within-group variability in all measurements was also compared. RESULTS: The search identified 43 eligible studies. Compared to people without LBP, on average, people with LBP display: (i) no difference in lordosis angle (8 studies), (ii) reduced lumbar ROM (19 studies), (iii) no difference in lumbar relative to hip contribution to end-range flexion (4 studies), (iv) no difference in standing pelvic tilt angle (3 studies), (v) slower movement (8 studies), and (vi) reduced proprioception (17 studies). Movement variability appeared greater for people with LBP for flexion, lateral flexion and rotation ROM, and movement speed, but not for other movement characteristics. Considerable heterogeneity exists between studies, including a lack of detail or standardization between studies on the criteria used to define participants as people with LBP (cases) or without LBP (controls). CONCLUSIONS: On average, people with LBP have reduced lumbar ROM and proprioception, and move more slowly compared to people without LBP. Whether these deficits exist prior to LBP onset is unknown.

Static cooperator-defector patterns in models of the snowdrift game played on cycle graphs.

Evolutionary graph theory is an extension of evolutionary game theory in which each individual agent, represented by a node, interacts only with a subset of the entire population to which it belongs (i.e., those to which it is connected by edges). In the context of the evolution of cooperation, in which individuals playing the cooperator strategy interact with individuals playing the defector strategy and game payoffs are equated with fitness, evolutionary games on graphs lead to global standoffs (i.e., static patterns) when all cooperators in a population have the same payoff as any defectors with which they share an edge. I consider the simplest type of regular-connected graph, the cycle graph, in which every node has exactly two edges (k = 2), for the prisoner's dilemma game and the snowdrift game, the two most important pairwise games in cooperation theory. I show that for simplified payoff structures associated with these games, standoffs are only possible for two valid cost-benefit ratios in the snowdrift game. I further show that only the greater of these two cost-benefit ratios is likely to be attracting in most situations (i.e., likely to spontaneously result in a global standoff when starting from nonstandoff conditions). Numerical simulations confirm this prediction. This work contributes to our understanding of the evolution of pattern formation in games played in finite, sparsely connected populations.

Modifying patterns of movement in people with low back pain -does it help? A systematic review.

BACKGROUND: Physiotherapy for people with low back pain frequently includes assessment and modification of lumbo-pelvic movement. Interventions commonly aim to restore normal movement and thereby reduce pain and improve activity limitation. The objective of this systematic review was to investigate: (i) the effect of movement-based interventions on movement patterns (muscle activation, lumbo-pelvic kinematics or postural patterns) of people with low back pain (LBP), and (ii) the relationship between changes in movement patterns and subsequent changes in pain and activity limitation. METHODS: MEDLINE, Cochrane Central, EMBASE, AMI, CINAHL, Scopus, AMED, ISI Web of Science were searched from inception until January 2012. Randomised controlled trials or controlled clinical trials of people with LBP were eligible for inclusion. The intervention must have been designed to influence (i) muscle activity patterns, (ii) lumbo-pelvic kinematic patterns or (iii) postural patterns, and included measurement of such deficits before and after treatment, to allow determination of the success of the intervention on the lumbo-pelvic movement. Twelve trials (25% of retrieved studies) met the inclusion criteria. Two reviewers independently identified, assessed and extracted data. The PEDro scale was used to assess method quality. Intervention effects were described using standardised differences between group means and 95% confidence intervals. RESULTS: The included trials showed inconsistent, mostly small to moderate intervention effects on targeted movement patterns. There was considerable heterogeneity in trial design, intervention type and outcome measures. A relationship between changes to movement patterns and improvements in pain or activity limitation was observed in one of six studies on muscle activation patterns, one of four studies that examined the flexion relaxation response pattern and in two of three studies that assessed lumbo-pelvic kinematics or postural characteristics. CONCLUSIONS: Movement-based interventions were infrequently effective for changing observable movement patterns. A relationship between changes in movement patterns and improvement in pain or activity limitation was also infrequently observed. No independent studies confirm any observed relationships. Challenges for future research include defining best methods for measuring (i) movement aberrations, (ii) improvements in movements, and (iii) the relationship between changes in how people move and associated changes in other health indicators such as activity limitation.

Green-beard effect predicts the evolution of traitorousness in the two-tag Prisoner's dilemma.

Cooperation, a costly interaction in which individuals benefit one another, plays a crucial role in many of the major transitions of evolution. Yet, as illustrated by the Prisoner's dilemma, cooperative systems are fragile because cooperators can be exploited by defectors who reap the benefits of cooperation but do not reciprocate. This barrier to cooperation may be overcome if cooperators have a recognisable phenotypic tag that allows them to adopt the conditional strategy of cooperating with fellow tag-mates while defecting against others, a mechanism known as the 'green-beard effect'. The resulting intra-tag cooperator strategy is particularly effective in structured populations where local clumps of cooperative tag-mates can find refuge. While intra-tag cooperation is robust against unconditional defectors in the spatial Prisoner's dilemma (at least when the cost of cooperation is low), the role of extra-tag cooperators - individuals who cooperate only with those bearing a different tag - has received little attention, despite the fact that these traitors form mixed-tag aggregations whose heterogeneous makeup potentially allows the exploitation of multiple other strategies. Using a spatial model of the two-tag Prisoner's dilemma, I show that extra-tag cooperation readily evolves under low to intermediate cost-benefit ratios of mutual cooperation (r). Specifically, at low r, mixed-tag aggregations of extra-tag cooperators take over the population, while at intermediate r, such aggregations coexist with intra-tag cooperators and unconditional defectors with whom they engage in non-transitive spatial invasibility. In systems with more than two tags, however, the dilution of extra-tag cooperators within mixed-tag aggregations prevents the strategy from being effective. Thus, the same beard chromodynamics that promotes within-group cooperation also predicts the evolution of traitorous between-group cooperation, but only when the number of beard colours is low.

The evolution of senescence in multi-component systems.

Actuarial senescence is characterized by an increase in mortality rate with increasing chronological age. The reliability theory of senescence proposes that organisms' vital functions can be modelled as a suite of damageable, irreplaceable elements (typically genes or their products) that protect their bearer from condition-dependent death so long as at least one of the elements remains intact. Current incarnations of the reliability theory of senescence are continuous-time models with no explicit evolutionary component. Here, we use elementary probability theory and evolutionary dynamics analysis to derive a discrete-time version of the reliability theory of senescence. We include three variations on this theme: the 'Series' model in which damage to any of n elements results in death, the 'Parallel' model, in which damage accumulates in random order and damage to all n elements results in death, and the 'Cascade' (multi-stage) model, which is like the Parallel model, except the irreparable damage necessarily follows a strict sequence. For simplicity, we refer to the state of having multiple elements as 'redundancy', but this does not imply that the elements are necessarily identical. We show that redundancy leads to actuarial senescence in the Parallel and Cascade models but not in the Series model. We further demonstrate that in the Parallel and Cascade models, lifetime reproductive output (a potential proxy for fitness in populations with discrete generations) is a positive but decelerating function of redundancy. The positive nature of the fitness function leads to the prediction that redundancy and senescence should evolve from non-redundant, non-senescing ancestral populations; however, the deceleration of the fitness function leads to the prediction that this evolution towards increased redundancy will eventually be limited by mutation-selection balance. Using evolutionary dynamics analysis involving the discrete-generation quasispecies equation, we confirm these two predictions. Finally, we show that a population's equilibrium redundancy is sensitive to the environmental conditions that prevailed during its evolution, such as the rate of extrinsic mortality.

Species coexistence, intransitivity, and topological variation in competitive tournaments.

Competitive intransitivity occurs when species' competitive abilities cannot be listed in a strict hierarchy, but rather form competitive loops, as in the game 'Rock-Paper-Scissors'. Indices are useful for summarizing intransitivity in communities; however, as with most indices, a great deal of information is compressed into single number. So while recent ecological theory, experiments, and natural history observations demonstrate that competitive intransitivity can promote species coexistence, the consequence of variation in the 'topology' of competitive interactions that is not accounted for by intransitivity indices is much less well understood. We use a continuous analytical model and two complementary discrete lattice models (one spatially explicit, the other aspatial) to demonstrate that such variation does indeed greatly affect species coexistence. Specifically, we show that although intransitivity indices are good at capturing broad patterns of coexistence, communities with different levels of intransitivity can have equal coexistence, and communities with equal intransitivity can have different coexistence, due to underlying variation in competitive network topology.

Neutral indirect effects of mycorrhizal fungi on a specialist insect herbivore.

Arbuscular mycorrhizal (AM) fungi can indirectly affect insect herbivore performance by altering traits in their host plant. Typically, generalist herbivores are negatively affected by AM fungi, whereas specialists are positively affected. This is thought to be caused by differential abilities of specialists and generalists to tolerate and/or exploit plant secondary compounds, the prevalence of which may be related to mycorrhizal colonization. We performed a feeding experiment in which specialist sunflower beetle larvae (Zygogramma exclamationis Fabricius, Chrysomelidae) were fed on mycorrhizal or nonmycorrhizal common annual sunflower plants (Helianthus annuus L., Asteraceae). To determine the indirect effects of AM fungi on the sunflower beetle larvae, we measured insect survival and relative growth rate. We also measured leaf area eaten, which allowed relative growth rate to be broken down into two components: relative consumption rate and efficiency of conversion of ingested food. Contrary to several previous studies, we detected no indirect effects of mycorrhizal fungi on larval survival or on relative growth rate or its components. Small effect sizes suggest that this is nonsignificant biologically, as well as statistically, rather than merely an issue of statistical power. Our results support an emerging view that indirect effects of mycorrhizal fungi on insect herbivores may be complex and idiosyncratic. We suggest that future research should emphasize the effects of mycorrhizal fungi on individual plant traits and how these interact to affect insect performance.