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Figure 2

Schematic figure of the labeling process. Participants usually upload several images in a single report. The best photo is picked by the validator who first marks the harassing or non-appropriate photos as hidden. All the non-best photos are marked as not classified. In some rare events, two or three images are annotated from the same report. The mosquito images are classified into four different categories (Aedes albopictus, Aedes aegypti, other species or can not tell) and also the confidence of the label is marked as probable or confirmed. In this paper we excluded the not classified, the hidden and the can not tell images.

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Between 2014 and 2019, 7686 citizen-made mosquito photos were labeled through Mosquito Alert by entomology experts, with labels indicating whether Ae. albopictus appear in the photos. The photos were included in reports that Mosquito Alert participants uploaded, and each report could contain several photos, see Fig. 2. The entomology experts usually labeled the best photo of the report, but sometimes they labeled two (420 times) or three (49 times) for a single report, meaning that the dataset consisted of 7168 reports. For 6699 reports, only one image was labeled by the experts; for 420 reports two were labeled; for 49 reports three were labeled. Although these reports usually contain several photos, only the ones with expert labels were used in the analysis, as cannot be assumed that all of the photos in a report would have been given the same label.
The main goals of Mosquito Alert during this 6 year period were to monitor Ae. albopictus spreading and provide early detection of Ae. aegypti in Spain. Although people participate in Mosquito Alert all over the world, the majority of the participants and the majority of the photos are in Spain (see Fig. 1). As Ae. aegypti has not been reported in Spain in recent times, most Mosquito Alert participants lived in areas where Ae. aegypti is not present, so most of the photos are of Ae. albopictus. For the detailed yearly distribution of the photos, see Table 1.
Table 1 The collected and expert validated dataset for the period 2014–2019.
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A popular deep learning model, ResNet5026 was trained and evaluated on the collected dataset with yearly cross-validation. ResNet50 was used because of its wide popularity and its proven classification power in various datasets. As presenting infinitesimal increments of the classification power is not a goal of this paper, we do not report various ImageNet state-of-the-art model performances. Yearly cross-validation was used to rule out any possibility of information leakage (possibility of a user submitting multiple reports for the same mosquito).
The trained model is not only capable of generating highly accurate predictions, but it can also ease the human annotator workload by auto-marking the images where the neural network is confident and more accurate, leaving more uncertain cases for the entomology experts. Moreover, while visualizing the erroneous predictions a few re-occurring patterns were identified, which can serve as a proposal for how to make images that can be best processed by the model.
Several aspects of the dataset were explored as follows.
Classification
Since Mosquito Alert was centered around Ae. albopictus during the relevant time period (2014–2019), the collected dataset is biased towards this species (Table 1). We explored training classifiers on the Mosquito Alert dataset alone and also tied training on a balanced dataset, where 3896 negative samples were added from the IP10227 dataset of various non-mosquito insects as negative samples. From the IP102 dataset, images similar to mosquitoes, and images of striped insects were selected. Although the presented mosquito alert dataset is filtered to contain only mosquito images, in later use, non-mosquito images might be uploaded by the citizens. Training the CNN on a combination of mosquito and non-mosquito images can improve the model to make correct predictions, classifying non-tiger mosquitoes for those cases too. For testing, in each fold, only the Mosquito Alert dataset was used.
The trained classifiers achieved an extremely high area under the receiver operating characteristic curve (ROC AUC) score of 0.96 (see Fig. 3). The fact that the ROC AUC score for each fold was always over 0.95 proves the consistency of our classifier. Inspecting the confusion matrix shows us that the model tends to make more false positive predictions (assuming tiger mosquito is defined as the positive outcome) than false negatives, resulting in high sensitivity. The augmentation of the Mosquito Alert dataset with various insects from IP102 images to make it more balanced resulted in a slight performance boost and narrowed the gap between the number of false positive and false negative samples as expected, see Table 2.
Figure 3

Left: ROC curve calculated on the prediction of the 7686 images in the Mosquito Alert dataset with yearly cross-validation. The blue line shows the case when only the Mosquito Alert dataset was used for training, the orange when the training dataset was balanced out with the addition of non-tiger mosquito insect images from the IP102 dataset. Also a zoom into the part of the ROC curve, where the two methods differ the most is highlighted. Right: the confusion matrix was calculated on the same predictions when only the Mosquito Alert dataset was used for training. For both, a positive label means tiger mosquito is present.

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Table 2 Yearly cross-validation results with using the Mosquito Alert dataset alone and its IP102 augmented version.
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How to take a good picture?
Inspection of the weaknesses of a machine learning model is a fruitful way to gain a deeper understanding of the underlying problems and mechanisms. In our case, a careful review of the mispredicted images led us to useful insights into what makes a photo hard to classify for the deep learning model. On Fig. 8, a few selected examples are presented. Unlike humans, deep learning models rely more on textures than on shapes28. As a consequence, grid-like background patterns or striped objects may easily confuse the machine classifier. A larger rich training set can help to avoid these pitfalls, but we also have the option to advise the participants. If participants avoid confusing setups when taking photos, this can improve the accuracy of the automated classification. These guidelines can be added to the Mosquito Alert application to help participants make good images of mosquitoes.

Do not use striped structure (e.g. mosquito net or fly-flap) as a background.

Avoid complex backgrounds when possible. A few examples: patterned carpet, different nets, reflecting/shiny background, bumpy wallpaper.

Use clear, white background (e.g. a sheet of plain paper is perfect if possible) or hold the mosquito with finger pads.

Make sure that as much as possible the mosquito is in focus and covers a large area of the photo.

In general, it is desirable to have a clean white background with the mosquito centered, and with the image containing as little background as possible.
Dataset size impact on model performance
Modern deep CNNs tend to generate better predictions when trained on larger datasets. In this experiment, we trained a ResNet50 model on 10–20–(cdots )–90–100% of 6686 images and evaluated the model on the remaining 1000 images. The 1000 images were selected from the same year (2019) and all of them came from reports with only one photo. There were 709 tiger mosquitoes out of the 1000 test images. ROC AUC and accuracy were calculated with a 500 round bootstrapping of the 1000 test images.
Figure 4

Training a ResNet50 model on a subsampled training dataset. The model was tested against the same 1000 test images for all the steps and statistics of the test metric was calculated with a 500 round bootstrapping. The curve proves the diversity of the Mosquito Alert dataset and also suggests that in the future when the dataset will be even larger, the classification performance will increase.

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The mean and the standard deviation of the 500 rounds are shown in Fig. 4 for each training data size. From the figure, we can conclude that the predictive power of the model increases as more data are used. The shape of the curves also suggests that the dataset did not reach its plateau. In the upcoming years, as the dataset size increases, ROC AUC and accuracy enhancement is expected.
On measuring image quality
Through the examined period, Mosquito Alert outreach was promoting a mosquito-targeted data collection strategy. Participants were expected to report two mosquito species (Ae. aegypti and Ae. albopictus). By defining these species as positive samples and all the other potential species of mosquito as negative, the submission decision by participants becomes a binary classification problem. In the majority of cases, when participants submit an image we should expect them to think of having a positive sample. Later, based on entomological expert validation, the true label for the image was obtained.
The main goal of such a surveillance system is to keep the sensitivity of the users as high as possible while keeping their specificity at an acceptable level. Therefore, measuring the sensitivity and specificity of the users would be a plausible quality measure. Unfortunately, there is no available information regarding the non-submitted mosquitoes (the true negative and false negative ones), meaning it is impossible to measure sensitivity. The specificity can be measured only in a special case, when there are no false positive images submitted by the user, resulting in a specificity of 1. Based on the latter argument, focusing on metrics derived from the ratio of the submitted tiger mosquito images vs. all submitted images is not meaningful. Instead, the quality can be measured by the usefulness of the photos from the viewpoint of the expert validator or a CNN, as presented in the next chapter.
Quality evolution of the images through time and space
The Mosquito Alert dataset is a unique collection of mosquito images, because, among other things, it is built from 5 consecutive years (not counting 2014, where less than 100 reports were submitted) and it also provides geolocation tags. This uniqueness of the dataset provides potential identification of time and spatial evolution and dependence of the citizen-based mosquito image quality. To explore such an evolution, we performed two different experiments. Geolocation tags were converted to country, region, and city-level information via the geopy Python package. It was found, that the vast majority (95% of all) of the reports were coming from Spain so we performed the analysis only for the Spanish data.
Figure 5

Number of submitted reports and the fraction of their ratio where the entomology expert annotator could tell if tiger mosquito was presented on the photo or not. The charts are shown for the four cities, where Mosquito Alert was the most popular.

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First, we explored the fraction of the photos, where the entomology expert marked “can not tell”, because the photo was not descriptive enough to decide which species were presented. Figure 5 shows the ratio of the useful mosquito reports, when mosquito decision was possible, compared to all the mosquito reports. The chart shows the above-mentioned ratio for four Spanish cities, which have the most reports submitted (the same information is showed on Supplementary Fig. S1 as a heatmap over Spain). The Mann–Kendall test on the fraction of useful reports shows p-values of 0.09, 0.09, 0.81, 0.22 for Barcelona, Valencia, Málaga, and Girona, which does not justify the presence of a significant trend in image quality, although any conclusions drawn from five data points must be handled with a pinch of salt. It does not mean anything about the individual participants’ quality progression, because Mosquito Alert is highly open and dynamic, and active participants can constantly change. Of note, through these years, the tiger mosquitoes have widely spread from the east coast to the southern and western regions of Spain29. New (and naive) citizen scientists living in the newly colonized regions have been systematically called to action and participation, thus, limiting the overall learning rate of the Mosquito Alert participants’ population. Our results suggest, that either a dynamic balance exists between naive and experienced participants over the period of data recollection, or mosquito photographing skills are independent of the user experience level. The expectation would be that as the population in Spain became more aware of the presence of tiger mosquitoes and their associated public health risks, the system should experience an increase in the useful report ratio, at least for tiger mosquitoes, and most tiger mosquito photos maybe classified automatically.
Figure 6

1000 random samples were selected for each years data. Separated ResNet50 models were trained on each of the years and each model was tested on the rest of the years data. Metrics were calculated with a 500 round random sampling with replacement from the test data. Left: mean of the 500 round bootstrapped accuracy calculations. Right: mean of the 500 round bootstrapped ROC AUC calculations.

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Second, we subsampled randomly 1000 images from all years between 2015 and 2019. Then we trained a different ResNet50 on data from the different years and generated predictions for the rest of the data, for each year separately. This way we can explore if data from any year is a “better training material” than the others. The results see Fig. 6, shows that 2015 is the worst training material, providing 0.83–0.84 ROC AUC score for the test period, while the rest (period 2016–2019) is similar, ROC AUC varies between 0.90 and 0.93. The reason why the 2015 data found to be the least favourable for training is its class imbalance, meaning that data from 2015 is extremely biased towards tiger mosquitoes (94%), so when training on 2015 data, the model does not see enough non-tiger mosquito samples, while for the other years lower class imbalance was found (70–80%), see Table 1. In general, machine learning models for classification require a substantial amount of examples for each possible class, in our case tiger and non-tiger mosquitoes, therefore worse performance is expected when training on the 2015 data.
Other than the varying class imbalance, we can conclude that the Mosquito Alert dataset quality is consistent, we did not find any concerning difference between training and testing our model for any of the 2016–2017–2018–2019 data pairs.
Pre-filtering the images before expert validation
Generating human annotations for an image classification task is a labour-intensive and expensive part of any project especially if the annotation requires expert knowledge. Therefore, having a model that generates accurate predictions for a well-defined subset of the data saves a lot of time and cost. We assume that the trained classifier is more accurate when the prediction probability is whether high or low and more inaccurate when it is close to 0.5. With this assumption in mind one can tune the (p_{low}) and (p_{high}) probabilities, in a way that images with a prediction probability (p_{low}< p < p_{high}) are discarded and sent to human validation. Figure 7 Randomly selecting 100,000 (p_{low}) and (p_{high}) thresholds on the predictions which were created via yearly cross-validation. Each time only samples were kept where the predicted probability were out of the ([p_{low};p_{high}]) interval. Each point shows the kept data fraction and the prediction accuracy. Varying the lower and upper predicted probability almost 98% of the images are correctly predicted while keeping 80% of all the images. Full size image Varying (p_{low}) and (p_{high}) provides a trade-off between prediction accuracy and the portion of images sent to human validation. Based on Fig. 7 sending 20% of the images to human validation while having an almost 98% accurate prediction for 80% of the dataset is a fruitful way to combine human labour-power and machine learning together. More

Variation in wood density
The values of Chinese fir’s wood physical properties varied considerably among different geographic sources and Tukey-HSD testing showed that some of these differences were statistically significant (Fig. 1). The maximum value (HNYX-T) of wood all-dry density (WDD) was 62.70% higher than the minimum (FJYK-P). The WDD of each source was consistent with the classification and performance indexes of conifer trees in the timber strength grade for structural use, a standard in China’s forestry industry39: FJYK-P was at level S10 ( HNZJJ-P  > FJYK-P, for which the maximum 58.0% higher than the minimum value. According to the wood grading standards in the grain compression index, HNZJJ-P and FJYK-P were at level II (29.1–44.0 MPa) and the rest of geographic sources were at level III (44.1–59.0 MPa) (Table 3).
The compression strength perpendicular to the grain of total tensile (CPG.TT) among geographic sources was ranked as follows: HNYX-T  > JXCS-R  > HNYX-P  > HNZJJ-P  > FJYK-P (Table 4). Its maximum value (HNYX-T) was 29.3% higher than the minimum (FJYK-P). The ranking for compression strength perpendicular to the grain of total radial (CPG.TR) was slightly different: HNYX-T  > JXCS-R  > HNYX-P  > HNZJJ-P  > FJYK-P, for which the maximum was 42.1% higher than the minimum value. Compression strength perpendicular to the grain of part radial (CPG.PR) had the same rank order as CPG.TT, with a maximum value (HNYX-T) 35.0% higher than the minimum (FJYK-P). Finally, compression strength perpendicular to the grain of part tensile (CPG.PT) was ranked as HNYX-T  > JXCS-R  > HNZJJ-P  > HNYX-P  > FJYK-P for the five geographic sources of Chinese fir.
Table 4 The statistical analysis of wood mechanical properties of Chinese fir.
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Factors influencing wood physical properties
Climate factors effect on wood physical properties
The influence of precipitation on the three kinds of density was consistent. Pre in January, October, November, and December was positively related to wood density, while it was negatively correlated with density in others months, especially in May (r = − 0.39), June (r = − 0.59), and August (r = − 0.64). On a seasonal scale, Pre in summer was negatively correlated with density (r = − 0.77), but it was positively correlated with autumn (r = 0.22). MaxT was positively correlated with density during the whole year, except in May (r = − 0.34), and likewise with wood density but most strongly in summer (r = 0.75). MinT was positively correlated with density, especially in Jan (r  > 0.7), though it was not significantly so in February and October (r  0.45). Pre showed no significant correlation with TSR.LD, RSR.LD, DDS.LD, and DDS.RD, whose correlation coefficients were 0.1–0.3. But Pre was negatively correlated with VSR.LD most of the year (except July, October). AveT was negatively correlation with TSR.RD, RSR.RD, and VSR.RD in January, February, March, and winter; however, AveT showed no significant correlation with DDS.RD. AveT was negatively correlated with TSR.LD, RSR.LD, DDS.LD, and VSR.LD during the whole year. In general, MinT had a significant positive relationship to TSR.RD (r = 0.47), RSR.RD (r = 0.48), and VSR.RD (r = 0.52), except in October, and it was negatively correlated with DDS.RD. MinT was positively related to RSR.LD, VSR.LD, yet negative related to DDS.LD. MaxT was negatively correlated with TSR.RD, RSR.RD, VSR.RD in January, February, May, and December, and winter. MaxT showed no significant correlation with DDS.RD, RSR.LD, DDS.LD or VSR.LD (Fig. 2c).
Pre had significant negative correlations with all of the mechanical properties in May, June, August, and summer, as evince by Fig. 2b, which also showed positive correlations in October. As we can seen, the effects of Pre on wood density and mechanical properties have the same tendency. Pre in all other months was not significantly correlated with mechanical properties (r  0.75), while it was showed no significant correlation in Feb and Oct (r  1000. Through stepwise regression modeling, 14 variables without multicollinearity were retained (i.e., MOE, MOR, TSG, CSG, CPG.TT, CPG.TR, CPG.PT, CPG.PR, DDS.RD, WDD, DDS.LD, TSR.RD, RSR.RD, VSR.LD).
PCA was applied to the above 14 selected physical variables. These results showed that the physical properties of wood loaded strongly on the first axis of the PCA, explaining 51.8% of variation in the 14 tested properties, while the second axis explained 11.0% of it. MOE, MOR, TSR.RD, RSR.RD, and VSR.LD loaded on the positive axis of PC1 and PC2. Both DDS.LD and DDS.RD loaded on the negative axis of PC1 and PC2, while TSG, CSG, CPG.TT, CPG.TR, CPG.PT, CPG.PR, and WDD loaded on the positive axis of PC1 and the negative axis of PC2 (Fig. 3). For a comprehensive evaluation of Chinese fir’s wood physical properties, we calculated the comprehensive scores of five geographic sources via the PCA. In this respect, significant differences were detected among the five geographic sources. Among them, the comprehensive score of HNYX-T was the highest whereas that of FJYK-P was the lowest (Fig. 4).
Figure 3

Sequence diagram plot of PCA analysis showing the relationship among physical properties of wood.

Full size image

Figure 4

Mean comprehensive score of PCA plot with 95% CI. Different letters (a, b, c, d, e) mean significant difference at 0.05 level.

Full size image More

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We have introduced and investigated a spatially explicit evolutionary food web model that allows us to explore the distribution of species in space and time, as well as the waxing and waning of species ranges with time. This is the first model that makes it possible to explore these features in the context of trophic networks, showing how they are influenced by competition as well as by predators and prey. Indeed, our model produces empirically well-known patterns in space and time, such as lifetime distributions, species-area relationships, distance decay of similarity, and temporal change of geographic range. On top, we obtain a variety of additional result and gain insights into the mechanisms that generate these patterns. While one might argue that some patterns must emerge trivially in a model like ours, the multitude of patterns emerging together is remarkable.
We find that most species only appear for short times and have small ranges. For species that conquer larger portions of the web we analysed the shape of the range evolution and found that basal species show the empirically observed “hat” pattern more often than species in higher trophic levels. This indicates that the trophic position of a species plays a major role for its range expansion success as well as the shape of its range expansion trajectory over time. To our knowledge, this has not been discussed in the literature so far.
Recently Zliobaite et al.11 analyzed which factors are more correlated to the rise and fall of the range expansion trajectory in fossil data sets of basal mammals. The range expansion follows the so called “hat pattern” that consists of five phases in a species lifetime: origination, expansion, peak, decline and extinction. They found that the temporal location of the peak of the hat pattern is more impacted by competition while the brims are more influenced by abiotic environmental factors. They also compared the range curves of different random walk models with the shape of empirical data and found that a random walk model with competition and environmental factor provides the most realistic looking curves.
Our results for basal species provide an illustration of the mechanism that might lead to these findings. There is one major difference in assumptions: the “environment” in our case is the trophic environment (network structure and abundance distribution). We do not model an abiotic surrounding, yet basal range curves look strikingly hat shaped. A species needs to fit into this trophic environment (network) to first establish a viable population (origination). To successfully increase its range it needs to disperse to neighbouring habitats and be a viable competitor there as well. This leads to the extinction of another species as the dispersing competitor takes its place. As neighbouring basal communities are similar in our systems, the chances are high that the species can spread on a large portion on the grid replacing other species (expansion). This continues until the species has reached the maximum range (peak). It is only a matter of time then until this process is repeated with the species having become the inferior competitor. The species is then successively replaced by a better adapted species (decline). The species thus ages as the network structure changes. At some point the species has vanished on all habitats (extinction). This means that we observe the same dynamics as suggested by Zliobaite et al., but with the trophic and not the abiotic environment as the main driver of the initial increase and later decrease of the range. The truth is probably that both the trophic and abiotic environment are important, as both play an important role in real ecosystems.
Regarding higher trophic species in our system the range expansion curves look more diverse and often do not resemble the hat shape. These species depend on the composition on the layer below. As this layer changes the fate of the higher species changes as well. The emergence of a new prey species that spreads over the network can save a consumer species from extinction. This cannot happen for basal species as these are more or less completely controlled by competition. The studies that we know often deal with basal species, so we are not convinced that the hat pattern is ubiquitous for all species. Future empirical work could focus on predator range expansion and try to find a case where a predator species could regain its range after the emergence of a new prey.
A qualitative difference between the basic trophic layer and higher layers occurred in our data also with respect to the similarity of networks in nearby habitats. The similarity index decays particularly slowly for the basal layer. Theory on distance decay suggests that spatial heterogeneity is a main driver in community turnover in two ways: (1) competitive species sorting along environmental gradients and (2) topological influences that let species with different dispersal abilities experience different landscapes6. As we use a homogeneous landscape we expect the first driver to be non-existent for the basal layer, as all habitats hold the same type and amount of resource. As species do not fundamentally differ in their dispersal abilities and we do not have a heterogeneous spatial topology, the second point is only weakly relevant for the basal species. They have slightly different chances of being chosen for dispersal as we choose the next disperser depending on the biomass density. As we have seen, biomass densities are quite similar for basal species. What remains is a temporal aspect: species that are older can reside on more habitats and have thus a higher chance of being chosen to disperse. To put the cart before the horse, this confirms the theory on distance decay: we expect a much faster decay in a heterogeneous environment, and this is exactly what we observe for higher trophic layers, which experience heterogeneity due to the spatial turnover in basal species composition. A trend to faster decay rates in higher trophic levels was also found in a meta-study7.
A model is always a simplification of reality. Some of the assumptions underlying our model are worth discussing. Species in nature are not restricted to the one-dimensional niche space that we assume. In fact, the original Webworld model characterised species by a large vector of traits31. We, in contrast, characterized species by three traits, all of which are based on body mass. We think that this is the reason why we do not observe super abundant species, but species densities are all of a similar order of magnitude. With a higher-dimensional trait space there must exist more diverse species types and probably also super abundant species, which have a globally optimal trait vector. Nevertheless, our simplification leads to an overall shape of the rank abundance curves that is realistic, as one would expect from a niche apportionment model40. Harpole and Tilman showed that diversity and evenness of grassland communities decreased when niche dimensionality was reduced by adding limiting nutrients to plot experiments41. In turn this indicates that rank abundance curves for less dimensional communities will be flatter. This is in line with the shape of our rank abundance curves.
The probably most interesting trait to add to each species would be its dispersal rate, and to let the dispersal rate evolve. We would expect that this would lead to higher-level species dispersing faster than lower-level species, thus making the differences in range between the different trophic levels smaller. In fact, a previous predator-prey model showed that the predator’s dispersal ability evolved in accordance to spatio-temporal fluctuations of the prey; with higher dispersal rates evolving for larger fluctuations in prey42. However, in the context of food webs the evolution of dispersal is poorly understood and a model like ours would be a good starting point.
Our choice of parameters is guided by the aim to make the model feasible. To be able to perform computer simulations on a large number of habitats we chose a relatively small value for the amount of resource R, so that the number of species of a local food web remained below 25. As we wanted to simulate food webs and not only basal communities we needed to choose a value of the efficiency (lambda ) that allows for the emergence of several trophic layers. In the original Webworld Model, (lambda ) was identified with the proportion of biomass that is passed from one trophic layer to the next. The value of 0.65 that we use here is much larger than the empirically established value of 0.143. However, in the original Webworld model no distinction was made between resident biomass and biomass fluxes. Therefore the variable B was identified with biomass, while its occurrence in Eq. (4) in fact suggests that it represents biomass flux. A further reason for the difference between the model value and the empirical value of (lambda ) is that the model does not take into account energy input due to the below-ground ecological processes. Due to all these simplifications of the model, we do not consider it important to provide an empirical justification of the precise value of the parameter (lambda ), but base its value on the condition that the model yields food webs with several trophic levels.
In contrast to other models, the model used here does not rely on an extrinsic extinction rate that randomly extirpates species that might be well adapted to the network. All extinction events are driven by the trophic dynamics, yet we observe an ongoing species turn over. We thus study the pure food web dynamics without a heterogeneous or fluctuating environment and still observe ecological reasonable species distributions. This indicates that incorporating abiotic environments and their fluctuations is not necessarily needed to study food web dynamics.
Rogge et al. analysed lifetime distributions and SAR curves in a model that is simpler than ours as it does not include population sizes22. The lifetime distributions that we find are considerably steeper (slope (-2.4)) compared to their value around (-1.7). It is also larger than the values reported for empirical findings, which lie between 1 and 2; Newman and Palmer pin them down to (1.7pm 0.3)10. Data for contemporary lifetime distributions show a power-law like shape23,44 with exponents that are in agreement with the exponent of paleological data10. It is noteworthy that there is no consensus whether lifetime distributions follow a power-law or an exponential law, as data often allow for both types of fit, due to (large) uncertainties in fossil data10,45. Exponentials, of course, have a changing slope in a double-logarithmic plot and can thus also be compatible with the exponent observed by us.
Curiously, our model shows steep lifetime distributions even though there is no external random extinction implemented as in other models22. One implication of our value (alpha > 2) is that our distribution has a well-defined mean. This features is shared with exponential distributions.
McPeek argues that lifetime distributions depend on the number and survival time of “transient” species, i.e. species that are on their way to extinction25. He reasons that the time to extinction is elongated for species that are similar, because the inferior competitor holds out longer when it competes with more similar species. If this applies to our type of model, this indicates that species in our system are, despite the one-dimensional niche axis, not as similar as species in the model of Rogge et al.22 that uses the same niche axis, as we observe shorter lifetimes. The difference is that interaction links in22 are binary (presence versus absence), whilst we use Gaussian feeding kernels. The fact that this difference affects the lifetime distributions emphasises the importance of considering details of the trophic interactions. The SAR curves on the contrary are flatter in our model than in the model by Rogge et al.  and in better agreement with empirical data.
O’Sullivan et al.18 found in a competitive metacommunity assembly models a similar collection of macroecological patterns (SAD, range size distribution RSD and SAR) as we did, when regional diversity was near equilibrium. They refer to the work of McGill16 who analysed the assumptions underlying models of macroecological patterns and found that three key ingredients seem to be sufficient for such patterns to emerge. Those are a left skewed SAD, clumping of populations in space, and species distributions in space that are uncorrelated from other species spatial distributions. O’Sullivan et al.18 report that all three ingredients occur in their model and are shaped by regional diversity equilibrium. The closer the system to regional equilibrium the stronger are the observed key patterns (SAD, RSD, Spatial non-correlation). They relate their finding with the theory of ecological structural stability, which revolves around the dynamics on a regional scale. Our communities, in contrast, are trophic communities, operate always near local and regional species equilibrium, i.e. in the regime where O’Sullivan and coauthors18 find the most prominent form of the basic patterns. Comparing the patterns we observe, we also see SADs that are left skewed, and a local clumping of species. We did not analyse the spatial correlation between species. As we have trophic layers of species there will be some correlation between predators and their prey as they can only persist in a habitat if prey is present. In addition to the results obtained by O’Sullivan et al.18, we also derive liefetime distributions, i.e., a paleoecological pattern that also seem to be connected to the metacommunity dynamics. This might indicate that spatial non-correlation is not the most important factor in the mechanisms producing macroecological patterns.
To conclude, our evolutionary food web model produces empirically well studied ecological and paleological patterns. We thus are armed with a valuable tool to broaden our understanding of the mechanisms behind those patterns. Our findings that trophic position influences geographic range and lifetime of a species might motivate further work regarding the interplay of abiotic and trophic factors on range expansion on evolutionary time scales.
More generally, evolutionary models can assist us in forming a deeper knowledge of the processes that lead to what is remnant in fossils. As recently pointed out by Marshall46 in his fifth law of paleobiology, extinction erases information. It is a strength of evolutionary food web models that they allow us to study processes whose extent eludes direct observations. More

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