What to do in the face of multiple threats? Incorporating dependencies within a return on investment framework for conservation

Aim Our study aimed to determine priority areas for conservation investment with explicit consideration of the impacts of multiple threatening processes, and the dependencies that exist between actions required to abate these threats. Location Australia. Methods We analysed the return on investment for two different management actions aimed at reducing the impact of invasive species on the native fauna and flora of Australia. We focussed on the management of the European red fox (Vulpes vulpes) and European rabbit (Oryctolagus cuniculus) at two spatial scales: across 72 biogeographic regions of Australia and within one high‐priority biogeographic region. We considered each action independently and also explicitly accounted for the option of an integrated fox and rabbit management action. We accounted for the spatial distributions of the threatened species within our analysis and determined how this refined spatial information influenced both the priority areas and the timing of this investment. Results Integrated fox and rabbit management was identified as a higher priority than singular threat abatement in most bioregions, whereas rabbit control alone was the most frequent priority if dependencies between actions were ignored. At the regional scale, funding was entirely directed to integrated action when seven or more species within the priority region were impacted by more than one threat. The total allocation of funding and timing of initial investment remained relatively insensitive to differences in the spatial overlap of species distributions. Main conclusions Our findings indicate that prioritizing conservation actions without explicit consideration of the impacts of multiple threats can reduce the cost‐effectiveness of investments. The benefits expected from investment in abating one threat alone may be overestimated where other processes continue to threaten species persistence. We conclude that future attention should be directed to refining our understanding of the cost‐efficiencies delivered through integrated actions and institutional mechanisms to achieve their delivery.     

The changing fates of the world's mammals

A recent complete assessment of the conservation status of 5487 mammal species demonstrated that at least one-fifth are at risk of extinction in the wild. We retrospectively identified genuine changes in extinction risk for mammals between 1996 and 2008 to calculate changes in the International Union for Conservation of Nature (IUCN) Red List Index (RLI). Species-level trends in the conservation status of mammalian diversity reveal that extinction risk in large-bodied species is increasing, and that the rate of deterioration has been most accelerated in the Indomalayan and Australasian realms. Expanding agriculture and hunting have been the main drivers of increased extinction risk in mammals. Site-based protection and management, legislation, and captive-breeding and reintroduction programmes have led to improvements in 24 species. We contextualize these changes, and explain why both deteriorations and improvements may be under-reported. Although this study highlights where conservation actions are leading to improvements, it fails to account for instances where conservation has prevented further deteriorations in the status of the world's mammals. The continued utility of the RLI is dependent on sustained investment to ensure repeated assessments of mammals over time and to facilitate future calculations of the RLI and measurement against global targets.     

Synergistic effects of food and predators on annual reproductive success in song sparrows

The behaviour literature is full of studies showing that animals in every taxon balance the probability of acquiring food with the risk of being preyed upon. While interactions between food and predators clearly operate at an individual scale, population-scale studies have tended to focus on only one factor at a time. Consequently, interactive (or 'synergistic') effects of food and predators on whole populations have only twice before been experimentally demonstrated in mammals. We conducted a 2 x 2 experiment to examine the joint effects of food supply and predator pressure on the annual reproductive success of song sparrows (Melospiza melodia). Our results show that these two factors do not operate in an additive way, but instead have a synergistic effect on reproduction. Relative to controls, sparrows reared 1.1 more young when food was added and 1.3 more when predator pressure was low. When these treatments were combined 4.0 extra young were produced, almost twice as many as expected from an additive model. These results are a cause for optimism for avian conservation because they demonstrate that remedial actions, aimed at simultaneously augmenting food and reducing predators, can produce dramatic increases in reproductive success.     

Investing in biodiversity: an economic perspective on global priority setting

Biodiversity investment priorities are a major concern for funding agencies and parties to the Convention on Biodiversity. We present a cost-effectiveness index designed to rank global biodiversity investments addressing weaknesses identified in several existing procedures. First, we explicitly address the issue of cost. Biodiversity conservation can be expensive -- ensuring that money is efficiently spent is important if conserving maximum biodiversity is an objective. Second, a high degree of threat to biodiversity is commonly accepted as constituting the principal reason for intervention and a basis for prioritization. The possibility that a high degree of threat might constitute a reason for non-intervention is rarely considered. The index presented in this study seeks to address these shortcomings by incorporating biodiversity ‘cost’, as measured by investment, and biodiversity ‘benefit’, as measured by a representative biodiversity indicator, species, richness. These elements form the basis of the cost -- benefit ratio needed for cost-effectiveness analysis. Investment in biodiversity is affected by issues of vulnerability (threat) and viability (success). A successful investment intervention will, however, depend on the probability or likelihood of success and the degree of threat prevalent in a particular country. These are integrated into the index as probabilities which will influence the amount of biodiversity ‘saved’ by an intervention. We apply the index using data for the Asia – Pacific region, to provide a cost-effective priority investment index (CEPII) ranking by country. Acute data limitations at the global level particularly in applying complementarity, necessitate caution in the interpretation of the index which, like other methods, requires some subjective choice of success and threat surrogates. The index continues the task of combining scientific and socioeconomic criteria relevant to global priorities. This revised version was published online in November 2006 with corrections to the Cover Date.     

The evolution of intergenerational discounting in offspring quality

Intergenerational effects occur when an individual's actions affect not only its own survivorship and reproduction but also those of its offspring and possibly later descendants. In the presence of intergenerational effects, short-term and long-term measures of success (such as the expected numbers of surviving offspring and of farther descendants, respectively) may be in conflict. When such conflicts occur, life-history theory normally takes long-term measures to predict the outcome of selection. This ignores the fact that, because traits change in time--through mutation, sex, and recombination--long-term relations disintegrate. We study this issue with numerical simulations and analytical models combining intergenerational effects and evolutionary change. In the models, the parental investment per offspring, as well as the total reproductive effort, stand for investments in future generations. The models show that the rate of evolutionary change determines the level of those investments. Higher rates of mutation and of sexual as opposed to parthenogenetic reproduction favor lower parental investment per offspring and lower total reproductive effort. It follows that the level of investment of ancestors in descendants responds to the genetic relatedness between the generations of the lineage, in a manner unaccounted for by preexisting theory.     

A quantitative analysis on the effects of critical factors limiting the effectiveness of species conservation in future time

The effectiveness of conservation plans depends on environmental, ecological, and socioeconomic factors. Global change makes conservation decisions even more challenging. Among others, the components of most concern in modern‐day conservation assessments are as follows: the magnitude of climate and land‐use changes; species dispersal abilities; competition with harmful socioeconomic activities for land use; the number of threatened species to consider; and, relatedly, the available budget to act. Here, we provide a unified framework that quantifies the relative effects of those factors on conservation. We conducted an area‐scheduling work plan in order to identify sets of areas along time in which the persistence expectancies of species are optimized. The approach was illustrated using data of potential distribution of ten nonvolant mammal species in Iberia Peninsula from current time up to 2080. Analyses were conducted considering possible setups among the factors that are likely to critically impact conservation success: three climate/land‐use scenarios; four species’ dispersal kernel curves; six land‐use layer types; and two planning designs, in which assessments were made independently for each species, or joining all species in a single plan. We identified areas for an array of investments levels capable to circumvent the spatial conflicts with socioeconomic activities. The effect of each factor on the estimated species persistence scores was assessed using linear mixed models. Our results evidence that conservation success is highly reliant on the resources available to abate land‐use conflicts. Nonetheless, under the same investment levels, planning design and climate change were the factors that most shaped species persistence scores. The persistence of five species was especially affected by the sole effect of planning design and consequently, larger conservation investments may retard climatic debts. For three species, the negative effects of a changing climate and of multiple‐species planning designs added up, making these species especially at risk. Integrated assessments of the factors most likely to limit species persistence are pivotal to achieve effectiveness.     

Why Do Cuckolded Males Provide Paternal Care?

In most species, males do not abandon offspring or reduce paternal care when they are cuckolded by other males. This apparent lack of adjustment of paternal investment with the likelihood of paternity presents a potential challenge to our understanding of what drives selection for paternal care. In a comparative analysis across birds, fish, mammals, and insects we identify key factors that explain why cuckolded males in many species do not reduce paternal care. Specifically, we show that cuckolded males only reduce paternal investment if both the costs of caring are relatively high and there is a high risk of cuckoldry. Under these circumstances, selection is expected to favour males that reduce paternal effort in response to cuckoldry. In many species, however, these conditions are not satisfied and tolerant males have outcompeted males that abandon young.     

Male meadow voles respond differently to risk and intensity of sperm competition

There are 2 models of male adjustment of sperm investment inthe ejaculate in relation to sperm competition. The "risk model"predicts that as "risk" of sperm competition increases, sperminvestment also increases. This prediction has been supportedin many species, including mammals. The "intensity model" involvesthe number of competing males copulating with the same femaleand predicts that males will allocate the highest sperm investmentat low sperm competition intensity (SCI) and then decreasingsperm investments as SCI increases. Two alternative outcomesare that sperm investment is unaffected by SCI and that sperminvestment increases as SCI increases. There are studies supportingall 3 possible outcomes in relation to SCI but no data on mammals.The present paper presents the first study of SCI in a mammalspecies, the meadow vole, Microtus pennsylvanicus. We used odorsof conspecific males to simulate low and high intensities ofsperm competition. We found that males allocate the highestsperm investment at low SCI and decrease significantly theirsperm investment at high SCI. We also found that males allocatethe lowest sperm investment at low sperm competition risk (SCR)and the highest sperm investment at high SCR. All these resultsagree with current theoretical models of sperm competition.     

Immunological sex differences in socially promiscuous African ground squirrels

Differences in how males and females respond to foreign antigens are common across taxa. Such sexual differences in the immune system are predicted to be greater in species with high promiscuity and sociality as these factors increase the likelihood of disease transmission. Intense sperm competition is thought to further this sexual dichotomy as increased investment in spermatogenesis likely incurs additional immunological costs. Xerus inauris, a ground squirrel found throughout southern Africa, is extremely social and promiscuous with one of the highest male reproductive investments among rodents. These life-history attributes suggest males and females should demonstrate a large dichotomy in immunity. Contrary to our prediction, we found no difference in spleen mass between the sexes. However, we did find significant biases in leukocyte types and red blood cell counts, possibly reflecting responses to parasite types. Among males, we predicted greater investments in spermatogenesis would result in reduced immunological investments. We found a negative association between testes and spleen size and a positive relationship between testes and number of lice suggesting trade-offs in reproductive investment possibly due to the costs associated with spermatogenesis and immunity. We suggest when measuring sexual differences in immunity it is important to consider the effects of reproductive pressures, parasite types, and life history costs.     

A climatic stability approach to prioritizing global conservation investments

Climate change is impacting species and ecosystems globally. Many existing templates to identify the most important areas to conserve terrestrial biodiversity at the global scale neglect the future impacts of climate change. Unstable climatic conditions are predicted to undermine conservation investments in the future. This paper presents an approach to developing a resource allocation algorithm for conservation investment that incorporates the ecological stability of ecoregions under climate change. We discover that allocating funds in this way changes the optimal schedule of global investments both spatially and temporally. This allocation reduces the biodiversity loss of terrestrial endemic species from protected areas due to climate change by 22% for the period of 2002-2052, when compared to allocations that do not consider climate change. To maximize the resilience of global biodiversity to climate change we recommend that funding be increased in ecoregions located in the tropics and/or mid-elevation habitats, where climatic conditions are predicted to remain relatively stable. Accounting for the ecological stability of ecoregions provides a realistic approach to incorporating climate change into global conservation planning, with potential to save more species from extinction in the long term.     

A strategic road map for conserving the Endangered dhole Cuon alpinus in India

1. Large carnivores face high extinction risks, often exacerbated by the absence of adequate information on their ecological requirements, and the high economic and socio-political commitments that their conservation warrants. Country-scale conservation plans can serve as effective frameworks to prioritise areas, actions, and conservation investments.
2. We explore conservation tenets of retention, recovery, and restoration for the Endangered dhole Cuon alpinus in India – a global stronghold for the species. Specifically, we: 1) examine the current status of dholes in India’s states using a recent distribution assessment; 2) identify areas for directing management interventions – zones to be targeted for population recovery and for habitat recovery; 3) identify potential areas for range expansion; 4) use eco-socio-political criteria to determine state-wise conservation priority scores and likelihood of conservation action; and 5) conduct an exhaustive review of all published literature on dholes.
3. Dholes occupy ~49% of potential habitats in 685 of mainland India’s 2342 sub-districts. We identified 143 sub-districts with potential for dhole population recovery, 145 for habitat recovery, and 404 for range expansion. Of the 34 mainland states/union territories, 17 were identified as high priority for dhole conservation. Of these, nine are adequately equipped to implement management actions to conserve dholes, while eight need to improve capacity towards increasing likelihood of conservation success.
4. Literature on dholes (from 1874 to 2019; n=237) was dominated by natural history notes, followed by distribution records and studies of population ecology. A majority of the reviewed studies were from India (55% of 215 country-specific papers). The number of studies showed an exponential increase over time: 43% were published in the last decade.
5. Our review of published literature revealed significant knowledge gaps in terms of quantitative ecological assessments across all dhole range-countries. Given this context, our results provide a comprehensive, multi-dimensional, and administratively feasible road map for dhole conservation in India, with potential applicability in other dhole range-countries and also for other threatened species.

     

Coral reef fish populations can persist without immigration

Determining the conditions under which populations may persist requires accurate estimates of demographic parameters, including immigration, local reproductive success, and mortality rates. In marine populations, empirical estimates of these parameters are rare, due at least in part to the pelagic dispersal stage common to most marine organisms. Here, we evaluate population persistence and turnover for a population of orange clownfish, Amphiprion percula, at Kimbe Island in Papua New Guinea. All fish in the population were sampled and genotyped on five occasions at 2-year intervals spanning eight years. The genetic data enabled estimates of reproductive success retained in the same population (reproductive success to self-recruitment), reproductive success exported to other subpopulations (reproductive success to local connectivity), and immigration and mortality rates of sub-adults and adults. Approximately 50% of the recruits were assigned to parents from the Kimbe Island population and this was stable through the sampling period. Stability in the proportion of local and immigrant settlers is likely due to: low annual mortality rates and stable egg production rates, and the short larval stages and sensory capacities of reef fish larvae. Biannual mortality rates ranged from 0.09 to 0.55 and varied significantly spatially. We used these data to parametrize a model that estimated the probability of the Kimbe Island population persisting in the absence of immigration. The Kimbe Island population was found to persist without significant immigration. Model results suggest the island population persists because the largest of the subpopulations are maintained due to having low mortality and high self-recruitment rates. Our results enable managers to appropriately target and scale actions to maximize persistence likelihood as disturbance frequencies increase.     

Across islands and continents,mammals are more successful invaders than birds

Many invasive species cause ecological or economic damage, and the fraction of introduced species that become invasive is an important determinant of the overall costs caused by invaders. According to the widely quoted tens rule, about 10% of all introduced species establish themselves and about 10% of these established species become invasive. Global taxonomic differences in the fraction of species becoming invasive have not been described. In a global analysis of mammal and bird introductions, I show that both mammals and birds have a much higher invasion success than predicted by the tens rule, and that mammals have a significantly higher success than birds. Averaged across islands and continents, 79% of mammals and 50% of birds introduced have established themselves and 63% of mammals and 34% of birds established have become invasive. My analysis also does not support the hypothesis that islands are more susceptible to invaders than continents, as I did not find a significant relationship between invasion success and the size of the island or continent to which the species were introduced. The data set used in this study has a number of limitations, e.g. information on propagule pressure was not available at this global scale, so understanding the mechanisms behind the observed patterns has to be postponed to future studies.     

Integrating Economic Costs and Biological Traits into Global Conservation Priorities for Carnivores

Background

Prioritization schemes usually highlight species-rich areas, where many species are at imminent risk of extinction. To be ecologically relevant these schemes should also include species biological traits into area-setting methods. Furthermore, in a world of limited funds for conservation, conservation action is constrained by land acquisition costs. Hence, including economic costs into conservation priorities can substantially improve their conservation cost-effectiveness.

Methodology/Principal Findings

We examined four global conservation scenarios for carnivores based on the joint mapping of economic costs and species biological traits. These scenarios identify the most cost-effective priority sets of ecoregions, indicating best investment opportunities for safeguarding every carnivore species, and also establish priority sets that can maximize species representation in areas harboring highly vulnerable species. We compared these results with a scenario that minimizes the total number of ecoregions required for conserving all species, irrespective of other factors. We found that cost-effective conservation investments should focus on 41 ecoregions highlighted in the scenario that consider simultaneously both ecoregion vulnerability and economic costs of land acquisition. Ecoregions included in priority sets under these criteria should yield best returns of investments since they harbor species with high extinction risk and have lower mean land cost.

Conclusions/Significance

Our study highlights ecoregions of particular importance for the conservation of the world''s carnivores defining global conservation priorities in analyses that encompass socioeconomic and life-history factors. We consider the identification of a comprehensive priority-set of areas as a first step towards an in-situ biodiversity maintenance strategy.     

Mapping Bushmeat Hunting Pressure in Central Africa

Hunting and trade of wild animals for their meat (bushmeat), especially mammals, is commonplace in tropical forests worldwide. In West and Central Africa, bushmeat extraction has increased substantially during recent decades. Currently, such levels of hunting pose a major threat to native wildlife. In this paper, we compiled published data on hunting offtake of mammals, from a number of studies conducted between 1990 and 2007 in Cameroon, Central African Republic, Democratic Republic of Congo, Equatorial Guinea, Gabon, and Republic of Congo. From these data sources, we estimated annual extraction rates of all hunted species and analyzed the relationship between environmental and anthropogenic variables surrounding each hunting rate and levels of bushmeat extraction. We defined hunting pressure as a function of bushmeat offtake and number of hunted species and confirm that hunting pressure is significantly correlated with road density, distance to protected areas and population density. These correlations are then used to map hunting pressure across the Congo Basin. We show that predicted risk areas show a patchy distribution throughout the study region and that many protected areas are located in high‐risk areas. We suggest that such a map can be used to identify areas of greatest impact of hunting to guide large‐scale conservation planning initiatives for central Africa.     

The importance of roads, nutrients, and climate for invasive plant establishment in riparian areas in the northwestern United States

Natural and anthropogenic site characteristics play a role in determining the current distribution of invasive plant species. An understanding of these characteristics can be used to prioritize areas for monitoring and control efforts and to determine appropriate management actions to lower site invasion risk. We used species distribution models to look for attributes associated with invasion and to determine the extent to which these attributes varied across a suite of species. We modeled the presence-absence of 11 invasive plant species along riparian areas in the northwestern United States using the model Random Forests. We found that climate variables were most important for predicting species distributions across the large study area and factors related to nutrients, land cover, and disturbance had moderate importance. We also found that there was a general pattern related to invasion for almost all species. Invasion was more likely to occur at hotter, drier sites near roads in unforested areas. In addition, high nutrient levels and proximity to streams with lower baseflow values also generally increased the likelihood that at least one invasive species would be present. Examining patterns across a broad range of regions can help suggest general mechanisms of invasion as well as provide region-specific management recommendations.     

Spatiotemporal patterns of duck nest density and predation risk: a multi‐scale analysis of 18 years and more than 10 000 nests

Many avian species are behaviorally‐plastic in selecting nest sites, and may shift to new locations or habitats following an unsuccessful breeding attempt. If there is predictable spatial variation in predation risk, the process of many individuals using prior experience to adaptively change nest sites may scale up to create shifting patterns of nest density at a population level. We used 18 years of waterfowl nesting data to assess whether there were areas of consistently high or low predation risk, and whether low‐risk areas increased, and high‐risk areas decreased in nest density the following year. We created kernel density maps of successful and unsuccessful nests in consecutive years and found no correlation in predation risk and no evidence for adaptive shifts, although nest density was correlated between years. We also examined between‐year correlations in nest density and nest success at three smaller spatial scales: individual nesting fields (10–28 ha), 16‐ha grid cells and 4‐ha grid cells. Here, results were similar across all scales: we found no evidence for year‐to‐year correlation in nest success but found strong evidence that nest density was correlated between years, and areas of high nest success increased in nest density the following year. Prior research in this system has demonstrated that areas of high nest density have higher nest success, and taken together, our results suggest that ducks may adaptively select nest sites based on the local density of conspecifics, rather than the physical location of last year's nest. In unpredictable environments, current cues, such as the presence of active conspecific nests, may be especially useful in selecting nest sites. The cues birds use to select breeding locations and successfully avoid predators deserve continued attention, especially in systems of conservation concern.     

Ecological niche modelling of montane mammals in the Great Basin, North America: examining past and present connectivity of species across basins and ranges

Aim The goal of this study was to determine the extent of suitable habitats across the basins and ranges of the Great Basin for 13 montane mammals in the present and during the Last Glacial Maximum (LGM). For all these mammal species, we test whether: (1) more suitable habitat was available in basin areas during the LGM; (2) suitable habitat shifted upwards in elevation between the LGM and the present; (3) more ranges have suitable habitat than are currently occupied; and (4) these species are currently restricted to suitable habitats at higher‐elevation range areas. We also examine whether and how much distributional response varies among these montane mammal species. Location The Great Basin of western North America. Methods We re‐examine the past and present distributions of 13 Great Basin montane mammals using ecological niche modelling techniques that utilize now widely available species occurrence data and new, fine‐scale past climatological GIS layers in the present and at the LGM. These methods provide an objective, repeatable means for visual comparison of past and present modelled distributions for species examined in previous biogeographical studies. Results Our results indicate greater areal and lower elevational suitable habitat in the LGM than at present for nearly all montane mammals, and that there is more suitable habitat at present than is currently occupied. Our results also show that lowland areas provide suitable dispersal routes between ranges for most of the montane mammals both at the LGM and at present. However, three of the 13 species have little to no predicted suitable habitat in the LGM near currently occupied ranges, in contrast to the pattern for the other 10. For these species, the model results support more recent long‐distance colonization. Main conclusions Our finding of suitable lowland dispersal routes in the present for most species supports and greatly extends similar findings from single‐species studies. Our results also provide a visually striking confirmation that changes in species distribution and colonization histories of Great Basin montane mammals vary in a fashion related to the tolerances and requirements of each of these species; this has previously been hypothesized but not rigorously tested for multiple montane mammals in the region.     

From Affective Experience to Motivated Action: Tracking Reward-Seeking and Punishment-Avoidant Behaviour in Real-Life

Many of the decisions and actions in everyday life result from implicit learning processes. Important to psychopathology are, for example, implicit reward-seeking and punishment-avoidant learning processes. It is known that when specific actions get associated with a rewarding experience, such as positive emotions, that this will increase the likelihood that an organism will engage in similar actions in the future. Similarly, when actions get associated with punishing experiences, such as negative emotions, this may reduce the likelihood that the organism will engage in similar actions in the future. This study examines whether we can observe these implicit processes prospectively in the flow of daily life. If such processes take place then we expect that current behaviour can be predicted by how similar behaviour was experienced (in terms of positive and negative affect) at previous measurement moments. This was examined in a sample of 621 female individuals that had participated in an Experience Sampling data collection. Measures of affect and behaviour were collected at 10 semi-random moments of the day for 5 consecutive days. It was examined whether affective experience that was paired with certain behaviours (physical activity and social context) at previous measurements modified the likelihood to show similar behaviours at next measurement moments. Analyses were performed both at the level of observations (a time scale with units of ± 90 min) and at day level (a time scale with units of 24 h). As expected, we found that affect indeed moderated the extent to which previous behaviour predicted similar behaviour later in time, at both beep- and day-level. This study showed that it is feasible to track reward-seeking and punishment-avoidant behaviour prospectively in humans in the flow of daily life. This opens up a new toolbox to examine processes determining goal-oriented behaviour in relation to psychopathology in humans.     

Effect of Heterogeneous Investments on the Evolution of Cooperation in Spatial Public Goods Game

Understanding the emergence of cooperation in spatial public goods game remains a grand challenge across disciplines. In most previous studies, it is assumed that the investments of all the cooperators are identical, and often equal to 1. However, it is worth mentioning that players are diverse and heterogeneous when choosing actions in the rapidly developing modern society and researchers have shown more interest to the heterogeneity of players recently. For modeling the heterogeneous players without loss of generality, it is assumed in this work that the investment of a cooperator is a random variable with uniform distribution, the mean value of which is equal to 1. The results of extensive numerical simulations convincingly indicate that heterogeneous investments can promote cooperation. Specifically, a large value of the variance of the random variable can decrease the two critical values for the result of behavioral evolution effectively. Moreover, the larger the variance is, the better the promotion effect will be. In addition, this article has discussed the impact of heterogeneous investments when the coevolution of both strategy and investment is taken into account. Comparing the promotion effect of coevolution of strategy and investment with that of strategy imitation only, we can conclude that the coevolution of strategy and investment decreases the asymptotic fraction of cooperators by weakening the heterogeneity of investments, which further demonstrates that heterogeneous investments can promote cooperation in spatial public goods game.